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]]>For access to the argument that I mention in the video, and all the other possible arguments, click here to download the PDF from mba.com.

Check out this week’s board!

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]]>The post GMAT Data Sufficiency Geometry Practice Questions appeared first on Magoosh GMAT Blog.

]]>1) In quadrilateral ABCD, is angle D ≤ 100 degrees?

__Statement #1__: AB = BC

__Statement #2__: angle A = angle B = angle C

2) Point P is a point inside triangle ABC. Is triangle ABC equilateral?

Statement #1: Point P is equidistant from the three vertices A, B, and C.

__Statement #2__: Triangle ABC has two different lines of symmetry that pass through point P.

3) ABC is an equilateral triangle, and point D is the midpoint of side BC. A is also a point on circle with radius r = 3. What is the area of the triangle?

__Statement #1__: The line that passes through A and D also passes through the center of the circle.

__Statement #2__: Including point A, the triangle intersects the circle at exactly four points.

4) ABCD is a square, and EFGH is a square, each vertex of which is on a side of ABCD. What is the ratio of the area of square EFGH to the area of square ABCD?

__Statement #1__: AE:AB = 4:7

__Statement #2__: The ratio of the area of triangle AHE to the area of square EFGH is 0.24

5) In the diagram above, the four triangles ABE, CBE, ADE, and CDE are all equal, and CD = 5. What is the area between the two circles?

__Statement #1__: AE = 3

__Statement #2__: angle BEC = 90 degrees

6) In trapezoid JKLM, KL//JM, and JK = LM = 5. What is the area of this trapezoid?

__Statement #1__: KL = 10 and JM = 15

__Statement #2__: angle J = 60 degrees

7) In the diagram above, ADF is a right triangle. BCED is a square with an area of 12. What is the area of triangle ADF?

__Statement #1__: angle DCF = 75 degrees

__Statement #2__: AB:EF = 3

8) FGHJ is a rectangle, such that FJ = 40 and FJ > FG. Point M is the midpoint of FJ, and a Circle C is constructed such that M is the center and FJ is the diameter. Circle C intersects the top side of the rectangle, GH, at two separate points. Point P is located on side GH. What is the area of triangle FJP?

__Statement #1__: One of the two intersections of Circle C with side GH is point P, one vertex of the triangle FJP.

__Statement #2__: One of the two intersections of Circle C with side GH is point R, such that RH = 7

9) Points A, B, and C are points on a circle with a radius of 6. Point D is the midpoint of side AC. What is the area of triangle ABC?

__Statement #1__: Segment BD passes through the center of the circle.

__Statement #2__: Arc AB has a length of 4(pi)

10) In the figure, ABCD is a trapezoid with BC//AD, AB = CE, BE//CG, and angle AEB = 90°. Point M is the midpoint of side BD. Point F, not shown, is a vertex on triangle EFG such that EF = FG. Is point F inside the trapezoid?

__Statement #1__: BE = EG

__Statement #2__: FG//CD

Full solutions will come at the end of this article.

Here are two previous blogs on GMAT DS questions about Geometry.

GMAT Data Sufficiency: Congruence Rules

GMAT Geometry: Is It a Square?

One big difference between Geometry on the PS questions and Geometry on the DS questions is that for all the PS questions, unless otherwise noted, you know that all diagrams are drawn as accurately as possible. That is the written guarantee of the test writers. By contrast, no guarantee at all accompanies the diagrams on the DS questions. Consider the following diagram.

This triangle appears equilateral. There is no guarantee that it is exactly equilateral, with three exactly equal sides and angles exactly equal to 60 degrees. If this were diagram given on a PS questions, we would know that the triangle is at least *close* to equilateral: all the side lengths are close to one another, and the angles are close to 60 degrees. We would know that much on a PS question. If this diagram were given on a DS question, then triangle ABC could be *absolutely any triangle on the face of the Earth*. It could be a right triangle, or a triangle with a big obtuse angle, or a tall & thin triangle, or a short & wide triangle, or etc. It could be any triangle at all. Aside from the bare fact that ABC is some kind of triangle, we can deduce nothing from the diagram on a DS question. Other than the bare facts of what’s connected to what, you can deduce nothing about lengths, angles, and shapes of figures given on DS questions. They may be 100% accurate or they may look nothing like the the shape described by the two statements.

Because of this, some DS questions are a real test of your capacity for spatial reasoning and geometric imagination. Many DS Geometry questions, including ones here, test your capacity to imagine how different the spatial scenario might be.

If this is not a natural gift for you, I strong recommend drawing out shapes on paper. Even get a ruler, compass, and protractor, and practice constructing specific shapes. Use straws or some other straight items to construct triangles in which you can adjust the sides and the angles. Strive to visualize and picture physically every rule of geometry you learn. By working with shapes you can see, and working with your hands, you will be engaging multiple parts of your brain that will give you a much deeper understanding of geometry.

If the above discussion gave you some insights, you may want to look back at those practice problems before jumping into the explanations below. If you don’t understand something said in an explanation here, draw it yourself, and explore the different possibilities within the constraints. The point of geometry is to see.

1) The figure is drawn as a square, but on GMAT DS, there’s no reason to assume the figure is drawn anywhere to scale.

If both statements are true, then the figure could be a square, in which the answer to the prompt question would be “yes,” or it could be this figure:

For this figure, all the conditions are met, and angle D is considerably larger than 100°; thus, the answer to the prompt question is “no.”

We could get either a “yes” or a “no” to the prompt consistent with these conditions, even with both statements put together.

Answer = **(E)**

2) __Statement #1__: As it turns out, for any triangle of any shape, there is *some* point that is equidistant from all three vertices: this is center of the circle that passes through all three vertices.

If all three angles of the triangle are acute, then the point is inside the triangle. If the triangle is a right triangle, then this center is always the midpoint of the hypotenuse. If the triangle has an obtuse angle, then the center is outside the triangle. All Statement #1 tells us is that triangle ABD has three acute angles. Beyond that, we know nothing. Statement #1, alone and by itself, is **not sufficient**.

__Statement #2__: A triangle that has a line of symmetry is isosceles. Let’s say that one line of symmetry goes through vertex A and point P. This would mean that AB = AC and that angle B = angle C. Now, let’s say that another line of symmetry goes through vertex B and point B. This would mean that AB = BC and angle A = angle C. Putting those together, we get three equal angles and three equal sides: an equilateral triangle. If a triangle has two separate lines of symmetry, it must be an equilateral triangle. We can give a definitive “yes” to the prompt question on the basis of this statement. Statement #2, alone and by itself, is **sufficient**.

Answer = **(B)**

3) Statement #1 tells us that the center of the circle is on the line of symmetry of the triangle through point A, but the triangle could be any size. In the diagram below, this line of symmetry is blue, and triangles of four different sizes are shown.

There actually would be an infinite number of possible triangle sizes on the basis of this statement alone. This statement is wildly **insufficient**.

Forget about Statement #1. With Statement #2 alone, a variety of off-center triangles with four intersection points are possible:

Notice AB is a chord of the circle as well as a side of the triangle. This chord could be a medium length chord or anything up to the full diameter, and different sides of the triangle would result in different areas. We still cannot give a definitive answer to the prompt question. This statement, alone and by itself, is **insufficient**.

Combined statements. If the center of the circle is on the line of symmetry of the triangle, then this places significant constraints on the number of intersections. For tiny triangles, they would simply intersect at point A and not reach the circle on the other side: one point of intersection, so this doesn’t work.

Larger triangles would touch the circle in three places, at the three vertices: this also doesn’t work.

Slightly larger, and those two vertices at B and C would “poke out” of the triangle, producing five points of intersection: Point A plus four other points.

The only way we will get exactly four points is when the sides get long enough and the side BC drops low enough that it is tangent to the circle.

The altitude of this triangle, AD is exactly equal to the diameter. We could use the ratios of the 30-60-90 triangle to figure out the sides, and thus figure out the area. If the sides get any longer, then side BC would break contact with the circle, and there would be only three points of intersection. This triangle, with the point of tangency at D, is the only triangle on this line of symmetry that has exactly four intersection points, and we can compute its area.

The combined statements allow us to give a numerical answer to the prompt question, so together, the statements are sufficient.

Answer = **(C)**

4) Statement #1: since we care only about ratios, we can set any lengths that are convenient. Let AE = 3 and AB = 7: then BE = 3. The figure is symmetrical on all four sides, so, for example, AH = 3. This means AEH is a right triangle with legs of 3 and 4—that is, a 3-4-5 triangle! The hypotenuse HE = 5. That’s the side of the smaller square, and 7 is the side of the larger square. The ratio of areas is 25/49. This statement leads directly to a numerical answer to the prompt question. This statement, alone and by itself, is **sufficient**.

Now, forget all about statement #1.

Statement #2: triangle to small square = 0.24 = 24/100 = 6/25. Let’s say that the central square has an area of 25 and one triangle has an area of 6. This means that four triangles together would have an area of 24. The big square equals the central square plus four triangles: 24 + 25 = 49. The ratio of the two squares = 25/49. This statement also leads directly to a numerical answer to the prompt question. This statement, alone and by itself, is **sufficient**.

Each statement sufficient on its own. Answer =** (D)**

5) __Statement #1__: If AE = 3, then it must be true that EC = 3, because the triangles are all equal. Also, AB = BC = CD = AD = 5. Because the four angles meeting at point E are all equal, it must be true that each one equals 90 degrees. Thus, we have four right triangles, and each one has a leg of 3 and an hypotenuse of 5. Thus, each must be a 3-4-5 triangle. This allows us to see that the radius of the smaller circle is EC = 3 and the radius of the larger circle is BE = 4. From these, we could figure out the areas and then subtract these areas to find the area between them. This statement allows us to arrive at a numerical answer to the prompt question. Statement #1, alone and by itself, is **sufficient**.

__Statement #2__: This statement tells us something we already could figure out from the prompt information. Technically, this statement is tautological. A tautological statement is one that contains no new information, nothing new that we couldn’t figure out on our own; examples of tautologies are “My favorite flavor of ice cream is the flavor I like most” or “Today is the day after yesterday.” Like those statements, Statement #2 adds nothing to our understanding. Statement #2, alone and by itself, is **not sufficient**.

Answer = **(A)**

6) This is question that demands visual insight.

__Statement #1__: Think about these lengths. The top, KL is twice the length of the slanted sides, and the bottom, JM, is three times the length. This means that we could build this trapezoid from five equilateral triangles.

With other combinations of four lengths, we would be able to get different quadrilaterals resulting (e.g. changing the tilt of a rhombus). With these lengths (5, 10, 5, 15), there is no other quadrilateral possible. (Try this with physical items with lengths in the ratio 1:2:1:3 to see for yourself.) Thus, we know all the angles. We know that each equilateral has side of 5, so we could figure out the area of each equilateral, then multiply by five. Thus, we can find the area on the bases of this statement alone. Statement #1, alone and by itself, is **sufficient**.

__Statement #2__: If we know just this, then the shape could have any width. It could be relative narrow or a mile-wide. We cannot determine a unique area on the basis of this statement alone. Statement #2, alone and by itself, is **not sufficient**.

Answer = **(A)**

7) We know the area of the square, so the side of the square is

Thus, we know the length of the vertical leg, CE, in right triangle CEF, and we know the horizontal leg, BC, in right triangle ABC. Furthermore, these two triangles must be similar to teach other and similar to the larger triangle, ADF, because all the angles are the same.

__Statement #1__: We know triangle CDE is a half a square, so it’s a 45-45-90 triangle. Angle DCE = 45 degrees. Well,

(Angle ECF) = (Angle DCF) – (Angle DCE) = 75 – 45 = 30 degrees

This means that CEF is a 30-60-90 triangles, and so is triangle ABC because they are similar. In each, we know the length of one side, so we could find the other sides and solve for the areas. Thus, we could find the area of the entire triangle ADF. This statement leads directly to a numerical answer to the prompt question. Statement #1, alone and by itself, is **sufficient**.

__Statement #1__: This is interesting. We know that triangles ABC and CEF are similar, so they are proportional. Let AB:BC = r. Then CE:EF = r as well.

Now, notice that both BC and CE are sides of the square. Let BC = CE = s.

Now, multiply those two fractions together, and the s terms will cancel.

This the ratio of the longer leg to the shorter leg in the 30:60:90 triangle. We know the sides of the square, so we can find all the lengths in triangles ABC and CEF, which would allow us to find all the areas. Thus, we could find the area of the entire triangle ADF. This statement leads directly to a numerical answer to the prompt question. Statement #2, alone and by itself, is **sufficient**.

Each statement is sufficient on its own. Answer = **(D)**

8) We know the diameter of the circle is FJ = 40, so its radius is r = 20. FJ = 40 is also the base of the triangle in question. We need the height of the triangle in order to find its area.

__Statement #1__: We know point P is one of the two points where the circle intersects side GH, the top of the rectangle. We still don’t know how tall the rectangle is. We know the height must be less than 20, so that the circle can intersect it, but we certainly don’t know the exact height.

Without an exact height, we cannot compute an exact area. Statement #1, alone and by itself, is **not sufficient**.

__Statement #2__: Construct Point Q, the midpoint of GH, and draw in segments MQ and MR. MQ joins midpoints of opposite sides of a rectangle, so this would be perpendicular to both FJ and GH.

We know that MR is a radius, so it has a length of 20. We know that QH is half the length of GH, so QH = 20. We know that RH = 7. Notice

QR + RH = QH

QR = QH – RH = 20 – 7 = 13

Now, look at right triangle MQR. We know the hypotenuse MR = 20. We know the horizontal leg QR = 13. We could use that most extraordinary mathematical theorem, the Pythagorean Theorem, to find the length of QM. On GMAT Data Sufficiency, we don’t have to carry out the actual calculation: it results in an ugly radical expression anyway. It’s enough to know that we could find the numerical value of QM, the height of the rectangle.

We don’t know the exact position of point P, but it’s somewhere on GH, and every point on GH has the same height above FJ, so this height would be equal to the height of the triangle. Thus, we could find the height of the triangle, and therefore the area. On the basis of this statement, we could give a numerical response to the prompt question. Statement #2, alone and by itself, is **sufficient**.

Answer = **(B)**

9) __Statement #1__: This one guarantees that BD is a line of symmetry in the diagram, so triangle ABC would have to be isosceles, but it could be any one of a number of a different sizes & shapes.

In all these examples, AB = BC and (angle A) = (angle C). The triangle could be equilateral, but it doesn’t have to be. These three examples have different areas, so this statement, by itself does not guarantee that we could calculate an exact area. Statement #1, alone and by itself, is **not sufficient**.

Now, forget all about statement #1.

__Statement #2__: We know that the radius is r = 6, so

Thus, we know that arc AB is 1/3 of the entire circumference. Therefore, it must occupy an angle of 1/3 of 360 degrees: arc AB must occupy 120 degrees.

In an equilateral triangle, all three angles would be 60 degrees and all three arcs would be 120 degrees. Here, all we know is that one arc, AB, is 120 degrees, and other two arcs could be other values. Thus, angle C must be 60 degrees, but other other angles can be other values.

In all three of those diagrams, AB is a 120 degree arc and angle C is 60 degrees. The triangle could be equilateral, but it doesn’t have to be. Statement #2, alone and by itself, is **not sufficient**.

Now combine the statements. From the first statement, we know that AB = BC and (angle A) = (angle C). From the second statement, we know that (angle C) = 60 degrees. Well, that would mean that (angle A) = 60 degrees as well, and that leaves exactly 60 degrees for angle B. If we have three 60 degree angles, we know that ABC is equilateral. If we know the radius of a circle, then we can calculate the area of an equilateral triangle with its three vertices on the circle (this would involve subdividing the equilateral into six 30-60-90 triangles).

With the combined information of both statements, we can find a definitive answer for the prompt question. Together, the statements are **sufficient**.

Answer = **(C) **

10) Start with what we know from the prompt. We know BCGE is a rectangle with two parallel vertical sides that are perpendicular to two parallel horizontal sides.

We know that ABE and CGD are right triangles with the same length vertical legs and the same length hypotenuses, so by the Pythagorean theorem, the third sides must be equal, AE = DG, and the two triangles are equal in every respect.

We know that entirely figure is symmetrical around a vertical line down the middle. The trapezoid is entirely symmetrical, and isosceles triangle EFG is also symmetrical. Suppose we constructed the midpoint of EG and called it Q. Then, line MQ would be the symmetry line of both the trapezoid and the isosceles triangle. This line MQ would be parallel to BE and CG, and it would be perpendicular to BC and EG. If we extended MQ above and below the trapezoid, we would be guaranteed that point F would lie somewhere on this line.

For this problem, I am going to jump ahead to the combined statements. Statement #1 tells us that BCGE is a square. Statement #2 tells that the sides of the trapezoid are parallel to the sides of the isosceles triangle (by symmetry, the parallelism must be true on both the right and the left side). Even with all this information, we cannot give a definitive answer to the prompt question.

You see, the missing piece are the lengths of AE and DG. By the symmetry of the diagram, we know AE = DG, but we don’t know how this size compares to BM = MC. In the diagram, it appears that DG < MC, but because this is a GMAT DS diagram, we can’t believe sizes on the diagram.

If DG < MC, then point F will be above M, outside of the trapezoid, as seen in the diagram on the left. If DG = MC, then point P will coincide with point M. If DG > MC, then point F will be below point M, inside the trapezoid.

Because we don’t know how the AE = DG length compares to the BM = MC length, we don’t know where point F falls, and we can’t give a definitive answer to the prompt question. Even combined, the statements are **insufficient**.

Answer = **(E)**

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]]>The post A Guide to the Harvard Business School Essay 2016 appeared first on Magoosh GMAT Blog.

]]>Like the other Harvard essay questions in recent years, this is astonishingly open-ended: as Bob Dylan said, “*but for the sky there are no fences facin’*.” The caveat of using clear and simple language is particularly striking: the Sermon on the Mount, Sojourner Truth’s spontaneous address at an 1851 Woman’s Convention, and Dr. King’s I Have a Dream speech all are examples, in straightforward language that anyone could appreciate, of works that communicate something profound about what it is to be human. The Gettysburg Address, a profound political statement, is also a masterpiece of earnest simplicity. What those four have in common is the gift of capturing, in specific memorable phrases, words that touch us to the core. That is the standard for which to strive.

Think about it. The folks on the HBS adcom already will know your GPA, your GMAT score, your work experience—all the cut-and-dry aspects of your qualifications. Keep in mind that, across the spectrum of HBS applicants, a great deal of the cut-and-dry stuff will look similar: impressive GPAs at impressive undergraduate institutions, impressive GMAT scores, impressive recommendations, impressive work experience, etc. Think about the intelligent folks who work on adcom: they see this slate of impressive data for candidate after candidate. These folks need something to give them a glimpse into the person behind the data. If your papers look like those of dozens of other applicants, and there is nothing to make you stand out as special, then they are unlikely to get excited about you in particular.

So don’t use the essay to repeat any of the cut-and-dry information: that would be simply redundant and annoying. Don’t craft an argument about why you would be particularly impressive, because this could very easily come off as weak and needy.

Think about about ordinary everyday human relationships. If I approach potential friends with the energy of “*Gee, I really want you to like me*,” that is likely to be perceived as needy and off-putting. By contrast, if I am confident in who I am and present myself unapologetically as who I am, that may put off some but it ultimately will garner more allegiance and enthusiasm. If you can balance unapologetic confidence with heartfelt compassion and sincere vulnerability, that is a combination that will open a great many doors.

If you have faced particular challenges in your life, these might already be present in other parts of your application (perhaps in your recommendations). If not, you might mention in passing the challenges unique to your situation, simply touch on them, but the whole focus of this essay should be where you are going, not where you have been.

Here are a few thoughts about how one might approach this essay. This advice is likely to applicable to many other essays on many other applications.

1) **Write from the heart, not from the head**: of course, once you have a message, it’s fine to use your head to make sure the grammar is good, etc. The core message, though, should come straight from your heart. This is your life: what inspires you? What gets you excited and passionate? Speak about what inspires you at the deepest level. Don’t make a head-centered argument. Think in terms of your heart, and make it your goal to speak to the hearts of your readers.

2) **Focus more on “why” than “what”**: a laundry list of what you want to do is not particularly engaging, no matter how impressive the items are. People connect with why. Simon Sinek argues that we should “start with why.” Why do you want to do what you want to do? Why does it matter to you? Why should it matter to anyone else? Say more about your vision and your dream than about your plans.

3) **Be completely honest and authentic**: the folks on HBS adcom want to know who you are. If you speak in your in full sincerity, they can feel who you are. If you try to make yourself appear as something other than what you are, in all likelihood this will not come off well. Make the essay an honest statement of who you are and what you are about. Nothing is more impressive than the utter sincerity of someone who has absolutely no intention of impressing anyone.

4) **Be poetic**: it can be hard to communicate one’s feelings, one’s dreams, the language of one’s heart, into words. Often a well-chosen metaphor is perfect for conveying what one has to say. In the fourth and fifth paragraphs of the “I Have a Dream” speech, Dr. King uses the metaphor of a bank check to discuss issues of racial justice, and this very plain metaphor became the occasion for powerful statements. A metaphor can powerfully convey your vision, but you must be careful: anything that sounds cliché will fall flat. It’s tricky, because sometimes the most brilliant metaphors are just a shade different from cliché. Please get extensive feedback on any metaphorical statement you choose.

Admittedly, this final recommendation would be more challenging if you don’t already have the habit of reading poetry for enjoyment. Of course, Bob Dylan, mentioned above, is justifiably called “the poet” of rock music. One poet I would recommend is David Whyte, who has work extensively with corporations and business people; his work *The Heart Aroused: Poetry and the Preservation of Soul in Corporate America* may be a particularly germane introduction to poetry for anyone contemplating an MBA, and studying that book may give you access to some of the metaphors that mean the most to you. If you want to be more daring in your exploration of business and poetry, you might examine the poems of the banker T.S. Eliot or the insurance executive Wallace Stevens.

In giving you such a wide open prompt, HBS is giving you a blank canvas. Some people, given a blank canvas, can barely produce stick figures. Given a blank canvas, Leonardo produced the Lady with an Ermine. Given a blank canvas, Botticelli produced Primavera. Given a blank canvas, Van Gogh painted wheat fields. *Every masterpiece began with a blank canvas*. That is precisely your situation in facing this essay. What masterpiece will you create?

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]]>The post Logical Splits on GMAT Sentence Correction appeared first on Magoosh GMAT Blog.

]]>

1) Napoleon entered Russia in June, 1812, with an army half a million strong, but __leaving in December, 1812, with just less__ than 30,000 troops.

(A) leaving in December, 1812, with just less

(B) just left in December, 1812, with fewer

(C) left in December, 1812, with just less

(D) left just in December, 1812, with less

(E) left in December, 1812, with just fewer

2) In the early 1800s, seven planets were known, but perturbations in the orbit of Uranus, the seventh planet, __suggesting the existence of a hypothetically__ eighth planet.

(A) suggesting the existence of a hypothetically

(B) suggesting the existence of a hypothetical

(C) to suggest the existence of a hypothetical

(D) suggested the existence of a hypothetical

(E) suggested the existence of a hypothetically

3) __Potassium, whose outer electron is easily lost, is a highly reactive metal__.

(A) Potassium, whose outer electron is easily lost, is a highly reactive metal

(B) Potassium is a highly reactive metal, it has an outer electron that is easily lost

(C) A highly reactive metal, potassium, with an outer electron that is easily lost

(D) The outer election of potassium, a highly reactive metal, is easily lost.

(E) A highly reactive metal that easily loses its outer electron is named “potassium.”

4) Although __Bryant was better at gaining the support of rural voters than was McKinley__, people who believed a silver-based economy would bring prosperity, McKinley won the 1896 election on a strong industry-based vote.

(A) Bryant was better at gaining the support of rural voters than was McKinley

(B) Bryant was better gaining the support of rural voters than McKinley

(C) Bryant was better than McKinley at gaining the support of rural voters

(D) compared to McKinley, Bryant had gained the support of rural voters more effectively

(E) unlike McKinley, Bryant was better at gaining the support of rural voters

5) __Since the discovery of the Tufted Badger and other species in the ecosystems outside Vancouver, the number of riparian mammals__ in the Pacific Northwest has increased considerably.

(A) Since the discovery of the Tufted Badger and other species in the ecosystems outside Vancouver, the number of riparian mammals

(B) Since the Tufted Badger and other species in the ecosystems outside Vancouver have been discovered, the number of riparian mammals

(C) Because the Tufted Badger and other species in the ecosystems outside Vancouver have been discovered, the total riparian mammal number

(D) With the discovery of the Tufted Badger and other species in the ecosystems outside Vancouver, the number of known riparian mammals

(E) With the discovery of the Tufted Badger, as well as other species, in the ecosystems outside Vancouver, the number of riparian mammals

6) __Developing East Asian information technology sectors, especially the ones in Vietnam, have been found by a consulting firm to be potential consumers for Cystar’s Hyperfast Server systems__.

(A) Developing East Asian information technology sectors, especially the ones in Vietnam, have been found by a consulting firm to be potential consumers to Cystar’s Hyperfast Server systems

(B) According to a consulting firm, developing East Asian information technology sectors, particularly Vietnam, would be potential consumers for Cystar’s Hyperfast Server systems

(C) The potential consumers of Cystar’s Hyperfast Server systems are, according to a consulting firm, are the developing East Asian information technology sectors, particularly those in Vietnam.

(D) Cystar’s Hyperfast Server systems has potential customers in the the developing East Asian information technology sectors, particularly those in Vietnam according to a consulting firm

(E) A consulting firm has found that developing East Asian information technology sectors, particularly in Vietnam, would be potential consumers of Cystar’s Hyperfast Server systems

7) __In the recent incidents of gang violence, it is the fact that innocent people were injured that has especially troubled the city leaders__.

(A) In the recent incidents of gang violence, it is the fact that innocent people were injured that has especially troubled the city leaders

(B) The city leaders were especially troubled by the innocent people who were injured in the recent incidents of gang violence

(C) The innocent people, injured in the recent incidents of gang violence, especially troubled the city leaders

(D) In the recent incidents of gang violence, it is a fact that innocent people were injured and that the city leaders were especially troubled

(E) In the recent incidents of gang violence, innocent people were in fact injured, and this has especially troubled the city leaders

8) __The Treaty of Utrecht, a series of documents signed in 1713, brought a peace that put an end to the plan of Louis XIV of France to upset the balance of power in Europe by gaining significant influence over the Spanish Empire__.

(A) The Treaty of Utrecht, a series of documents signed in 1713, brought a peace that put an end to the plan of Louis XIV of France to upset the balance of power in Europe by gaining significant influence over the Spanish Empire

(B) The Treaty of Utrecht, a series of documents signed in 1713, bringing peace by putting an end to the plan of Louis XIV of France, who wanted to upset the balance of power in Europe when he gained significant influence in the Spanish Empire

(C) A series of documents signed in 1713, known as the Treaty of Utrecht, restored peace to Europe by putting an end to the plan of Louis XIV of France, who, in gaining significant influence over the Spanish Empire, wanted to upset the balance of power in Europe

(D) The balance of power in Europe was threatened when Louis XIV of France tried to gain significant influence in the Spanish Empire; therefore the Treaty of Utrecht, a series of documents signed in 1713, restored the peace by ending this plan

(E) Louis XIV of France planned to upset the balance of power in Europe by gaining significant influence with the Spanish Empire, but in 1713, a series of documents known as the Treaty of Utrecht was signed, and this put a peaceful end to the plan

Explanations for these questions will come at the end of this article.

Some students naïvely believe that the GMAT Sentence Correction tests only grammar, and these students believe that by mastering grammar, they can master the SC questions. This view is mistaken. In fact, grammar, logic, and rhetoric all play a role. Here are a few previous blogs that address logical issues on the GMAT Sentence Correction.

a) Logical Predication on the GMAT Sentence Correction

b) GMAT Sentence Correction: Indefinite Pronouns and Logic

c) Logical Splits in GMAT Sentence Correction

It’s very important that the precise logical meaning of the sentence reflect what the sentence is trying to say. Many times in colloquial English, people say something that conveys meaning informally even though, rigorously, it is not logical. Many of the logic mistakes on the GMAT reflect this: we can tell what the sentence means, despite what it is saying. For the GMAT, a good sentence is one in which grammar and logic and rhetoric are all working together to convey a single meaning.

Since many GMAT takers overemphasize grammar and neglect logic, at least one or two answer choices on many SC questions are 100% grammatically correct but logically flawed. Some of the answer choices above follow this pattern. Once again, mastery of GMAT Sentence Correction requires understanding how grammar, logic, and rhetoric all work together and support each other.

If anything said here, or anything in those linked blogs, gave you any insights, then you may want to look over some of the questions again before studying the explanations below. Think about logic in the writing you observe. Advertisements are wonderful places to see blatant logical errors. Also, observe how high-quality, sophisticated writers use logical precision to make their points.

1) __Split #1__: countable vs. uncountable. Troops are countable, so we need to use “fewer,” not “less.” We can eliminate (A), (C), and (D) on the basis of this error.

__Split #2__: One of the more subtle logical splits on GMAT Sentence Correction involves the placement of adverb modifiers. In this sentence, where should the “just” fall? What do we want to denote as significantly limited? Choice (B) has “just left,” as if we expected Napoleon to do something else, something more complicated or exalted, than the act of leaving; that interpretation is not the meaning, because the sentence is not contrasting the intensity of that action with any other.

By contrast, “just fewer than 30,000” retains the meaning of the prompt and emphasizes the shocking reduction in Napoleon’s army, which is the point of the sentence.

The best answer is **(E)**.

2) A question about the events that led to the discovery of Neptune in 1846.

__Split #1__: the famous missing-verb mistake. In the overall organization of the sentence, we have a first independent clause, “seven planets were known,” then the conjunction “but,” which signals another independent clause coming. For this second independent clause, we get a noun for the subject, “perturbations in the orbit of Uranus,” and we need a full bonafide verb. Choices (A) & (B) give us a participle, and choice (C) gives us an infinitive, but these won’t do. We need the full verb “suggested,” which appears in (D) & (E). We can eliminate (A) & (B) & (C).

__Split #2:__ One kind of logic split involves the choice between an adjective and its corresponding adverb. Here, we have to choose between “hypothetical” and “hypothetically.”

As an adjective, it would have to modify the noun. If we say “a hypothetical eighth planet,” then we are saying that we don’t know whether the planet exists, but if it did exist after the first seven, of course it would be the eighth.

As an adverb, it would have to modify the adjective. If we say “a hypothetically eighth planet,” then we are saying that we are not sure where the planet would fall in the numbering system: it could be the eighth or could be some other number; in this phrasing, it sounds as if the numbering is in doubt, but not the existence of the planet itself.

What was actually in doubt at that moment in history was the planet itself. Of course, if it came after the first seven planets, it would be the eighth: that much was not in doubt. The existence of the planet was in doubt. The adjective “hypothetical” reflects this meaning. We can reject the choices with “hypothetically,” choices (A) and (E).

The only possible answer is **(D)**.

3) A question about potassium, the 19^{th} element on the Periodic Table. The five answers are all different, so we must treat each separately.

(A) Use of the possessive “whose” is perfectly fine either for a person or for an inanimate object. This option is grammatically and logically correct. This is a promising choice.

(B) This option is a run-on sentence with a comma splice. This is incorrect.

(C) This option commits the famous missing-verb mistake. We get a main subject, “*a highly reactive metal*,” and this subject never gets a full verb. This is incorrect.

(D) This is grammatically correct but awkward. It makes the electron, rather than potassium the element, the focus of the sentence, which casts the entire sentence into the passive. This is far from ideal.

(E) This choice is logically incorrect. It implies that any “highly reactive metal that easily loses its outer electron” would be called potassium, as if potassium were the name of a category of metals with similar properties, rather than a single metal. While you don’t need to understand chemistry (see below), you do need to keep the meaning consistent with the prompt. The prompt identifies potassium as a single metal, so we have to stick with that interpretation.

Choice (D) is a questionable answer, so **(A)** is by far the best answer here.

BTW, this is more than you need to know for the GMAT, but if you are interested in the chemistry, then on the Periodic Table of the Elements, all the IA elements below hydrogen are highly reactive metals that easily lose an outer electron. These include lithium, sodium, potassium, rubidium, and caesium (a radioactive liquid that explodes on contact with air or water!) Potassium is the name of one metal in this category, not the name of the category. Sometimes the category is known as the **Alkali Metals** or the **IA Elements**.

4) A question about William Jennings Bryan and President William McKinley.

__Split #1__: the underlined section is followed by the appositive phrase “people who believed a silver-based economy would bring prosperity.” These people are the rural voters, so this modifier must touch “rural voters.” Where this modifier touches McKinley, it is a misplaced modifier, illogically equating this person to “people.” Choices (A) & (B) make this mistake.

Let’s look at the three remaining choices.

(C) This is grammatically and logically sound. This is a promising choice.

(D) This is an unidiomatic and awkward comparison, “*compared to A, B is more X.*” While technically correct, we can reject this because there are more elegant possibilities.

(E) This is an illogical comparison. We could say, “Unlike B, A is good at X,” which tells us that there is no question of degree: A is good at X, and B is not. Alternative, we could say ” A is better at X than is B,” which tells us that it’s a question of degree: both are good, but A is better. Choice (E) mixes elements of either comparison to create a logically ambiguous comparison: we get that Bryan is better, but was McKinley not good at all or simply not as good as Bryan?? Choice (E) is illogical and wrong.

The best answer is choice **(C)**.

5) This question contains a very subtle logical split. Let’s think about this. In this natural ecosystem outside of Vancouver, there are some number of riparian mammals living out in Nature, just doing what they are doing. Whether they live or die, thrive or fail, depends on a host of natural factors but most certainly does not depend on what the scientists know or don’t know. Thus, when scientific researchers make a new discovery, the actual number of mammals out in the world does not change—all that changes is our knowledge! It is the height of our arrogance as a species to think that some change in our knowledge actually changes anything in the natural world around us! The number of riparian mammals doesn’t change: all that changes is the number of __known__ riparian mammals. In other words, mammals that were there all along have crossed in our human scientific categories from unknown to known. The only choice that reflect his perspective is **(D)**, the OA.

6) One of the logic splits in this problem concerns the way Vietnam is mentioned. The problem discusses “East Asian information technology sectors” and wants to cite the specific example of the information technology sectors in Vietnam. Notice how this appears in the five choices.

(A) Here, “*the ones in Vietnam*” is a little informal but logically and grammatically correct. The overall passive structure of this choice makes it weak and mealy mouthed. It is technically correct but undesirable. We hope there is something better so that we don’t have to settle for this.

(B) The phrase “particularly Vietnam” is an illogical comparison: it makes Vietnam the country sound like nothing more than an information technology sectors. Choice (B) is illogical and incorrect.

(C) In this choice, the mention of Vietnam is fine, but the entire choice changes the meaning. The prompt suggested that the “developing East Asian information technology sectors” are one possibility for customers, but it doesn’t exclude the possibility that other potential customers are elsewhere in the world. The phasing in (C) makes the possibility exclusive, suggesting that these East Asian possibilities are the * only* possibilities for new customers. That’s an unwarranted change in meaning, so (C) is incorrect.

(D) This choice changes the meaning in a different way. The mention of Vietnam is logically correct, but the placement of “according to a consulting firm” makes it sound as if only the Vietnam case were the substance of the consulting firm’s recommendation, rather than the entire East Asian theater. In other words, the exact information provided by the consulting firm is different in this choice. This is also a change in meaning, so (D) is also incorrect.

(E) This choice is entirely correct, both logically and grammatically. It is direct, crisp, and clear, a powerful rhetorical statement. Notice that the mention of Vietnam elegantly uses a parallel structure that omits common words. This is a masterpiece of concision and clarity. This choice is much better than (A). Choice **(E)** is the best answer.

7) __Split #1__: One logical split in this problem concerns what actually troubled the city leaders? The innocent people themselves did not trouble the city leaders. The fact that innocent people were injured is what troubled the city leaders. Although both grammatically correct, choices (B) & (C) make the mistake of implying that the innocent people themselves were troubling: this is illogical, and these two choices are incorrect.

__Split #2__: pronoun problem. The pronoun “this” in choice (E) is problematic. Everything up to the second comma is fine, but then the pronoun “this” refers to the action of the previous clauses. Pronouns must have nouns as their antecedents: pronouns can’t refer to the action of a verb. This is an invalid use of pronouns, and choice (E) is incorrect.

__Split #3__: logical cohesion. Entirely grammatically correct, choice (D) presents the two facts side-by-side, (1) innocent people were injured, and (2) city leaders are troubled. The relationship between these two facts is not made clear, and we are left to infer this. It’s not hard to guess, but a rhetorically powerful sentence doesn’t leave its main point up to guesswork for the reader. Choice (D) is incorrect.

This leaves choice (A). Choice (A) may seem wordy, because it employs the emphatic structure of the empty “it.” This structure is justified by the subject, and this choice makes all the logically relationships explicitly clear. It is direct and powerful. Choice **(A)** is the best answer.

8) A sentence about the famous Treaty of Utrecht that mentions the Sun King, Louis XIV. The whole sentence is underlined, so we will go through each choice individually.

(A) This choice is grammatically and logically correct. This is a promising choice.

(B) This choice commits the famous missing-verb mistake. The Treaty appears to be the subject, but there is no bonafide verb in the entire sentence. Choice (B) is incorrect.

(C) This choice makes the rhetorically questionable move of making the bland phrase “series of documents” the main subject, while relegating the actual name of the treaty to a parenthetical mention. This strangely de-emphasizes the treaty that presumably is the focus of the sentence. Also, the second half of the sentence changes the logical relationship of Louis XIV’s actions. Choice (C) is incorrect.

(D) The prompt tells us one effect of the Treaty of Utrecht. Was this the only effect of this treaty? That’s unclear and outside the scope of the sentence, but the prompt leaves open the possibility that this treaty had many effects and it is discussing only one of these effects. Choice (D) implies that the effect discussed in the sentence is the only effect of the treaty, and this a change in meaning. Choice (D) is incorrect.

(E) The first half of the sentence focuses on one of the most powerful actors of 17^{th} century Europe, Louis XIV, making him the subject. All well and good, but now the Treaty of Utrecht is relegated to a small detail role in the sentence, so the focus is now completely different. Also, the ending of this is awkward and slightly different in meaning from the prompt. Choice (E) is incorrect.

The only possible answer is choice **(A)**.

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]]>If you’d like to see how we evaluated the passage, head over to our first Reading Comprehension video in this series.

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]]>The post Intro to GMAT Word Problems, Part 2: Assigning Variables appeared first on Magoosh GMAT Blog.

]]>1) Each month, after Jill pays for rent, utilities, food, and other necessary expenses, she has one fifth of her net monthly salary left as discretionary income. Of this discretionary income, she puts 30% into a vacation fund, 20% into savings, and spends 35% on eating out and socializing. This leaves her with $96 dollar, which she typically uses for gifts and charitable causes. What is Jill’s net monthly salary?

(A) $2400

(B) $3200

(C) $6000

(D) $6400

(E) $9600

2) Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/12 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 20%, then Al would have exactly $22 more than Eliot in his account. How much money does Eliot have in his account right now?

(A) $110

(B) $120

(C) $180

(D) $220

(E) $260

3) A pool, built with one edge flush against a building, has a length that is 5 meters longer than its width. The short width is against the building. A 4 meter wide path is built on three side around the pool, as shown in the diagram (the path is yellow). If the area of the path is 216 sq m, what is the width of the pool in meters?

(A) 12

(B) 14

(C) 16

(D) 18

(E) 20

4) Four friends, Saul, Peter, Quirinal, and Roderick, are pooling their money to buy a $1000 item. Peter has twice as much money as Saul. Quirinal has $60 more than Peter. Roderick has 20% more than Quirinal. If they put all their money together and spend the $1000, they will have $20 left. How much money does Peter have?

(A) $120

(B) $160

(C) $180

(D) $200

(E) $240

Full solutions will appear at the end of this article.

Most GMAT word problem concern real world quantities and are stated in real world terms, and we need to assign algebraic variables to these real world quantities.

Sometimes, one quantity is directly related to every other quantity in the problem. For example:

“Sarah spends 2/5 of her monthly salary on rent, 1/12 of her monthly salary on auto costs including gas and insurance, and 1/10 of her monthly salary automatically goes into saving each month. With what she has left each month, she spend she spends $800 on groceries and …”

In that problem, everything is related to “monthly salary,” so it would make a lot of sense to introduce just one variable for that, and express everything else in terms of that variable. Also, please don’t always use the boring choice of x for a variable! If we want a variable for salary, you might use the letter S, which will help you remember what the variable means! If we are given multiple variables that are all related to each other, it’s often helpful to assign a letter to the variable with the lowest value, and then express everything else in terms of this letter.

If there are two or more quantities that don’t depend directly on each other, then you may well have to introduce a different variable for each. Just remember that it’s mathematically problematic to litter a problem with a whole slew of different variables. You see, for each variable, you need an equation to solve it. If we want to solve for two different variables, we need two different equations (this is a common Word Problem scenario). If we want to solve for three different variables, we need three different equations (considerably less common). While the mathematical pattern continues to extend upward from there, more than three completely separate variables is almost unheard of on GMAT math.

When you assign variables, always be hyper-vigilant and over-the-top explicit about exactly what each variable means. Write a quick note to yourself on the scratch paper: T = the price of one box of tissue, or whatever the problem wants. What you want to avoid is the undesirable situation of solving for a number and not knowing what that number means in the problem!

Here’s an easier-than-the-GMAT word problem as an example:

“Andrew and Beatrice each have their own savings account. Beatrice’s account has $600 less than three times what Andrew’s account has. If Andrew had $300 more dollars, then he would have exactly half what is currently in Beatrice’s account. How much does Beatrice have?”

The obvious choices for variables are A = the amount in Andrew’s account and B = the amount in Beatrice’s account. The GMAT will be good about giving you word problems involving people whose names start with different letter, so that it’s easier to assign variables. We can turn the second & third sentences into equations.

second sentence: B = 3A – 600

Both equations are solved for B, so simply set them equal.

3A – 600 = 2(A + 300)

3A – 600 = 2A + 600

A – 600 = 600

A = 1200

We can plug this into either equation to find B. (BTW, if you have time, an excellent check is to plug it into ** both** equations, and make sure the value of B you get is the same!)

B = 3000

Thus, Andrew has $1200 in his account, and Beatrice, $3000 in hers.

If the foregoing discussion gave you any insights into assigning variables, it may well be worthwhile to look at those four practice problems again before preceding to the explanations below. If you join Magoosh, you can watch our 20+ video lessons on Word Problems.

1) Everything is in terms of Jill’s discretionary income, which is one-fifth of the net monthly rent. It makes sense to assign a variable to the former, solve for it, and then compute the latter. I will assign the letter D, to remind us that this represents the monthly discretionary income, not the answer to the question. We will not yet have the answer when we find the value of D.

vacation = 30% of D

savings = 20% of D

eating out & socializing = 35% of D

Together, those account for 85% of her monthly discretionary income. That leaves 15%. This 15% equals $96.

15% of D = $96

Divide by sides by 3.

5% of D = $32

Double.

10% of D = $64

Now, multiply by 10.

100% of D = D = $640

Remember, this is the value of D, the monthly discretionary income, not what the question asked. The question wanted monthly salary, which is five times this. Well, ten times D is $6400, so five times D would be half of that, $3200.

Answer = **(B)**

2) Names in this problem from a famous Al and a famous Eliot. Let’s start with two variables, A and E. The difference (A – E) is 1/12 the sum (A + B).

12(A – E) = A + E

12A – 12E = A + E

11A = 13E

Now, since we have related these variables, it doesn’t make sense to move through the rest of problem with two different variables. We could express E = (11/13)*A, and express everything in terms of A, but 11/13 is an especially ugly fraction. Here’s an alternative, using a little number sense. Clearly A equals 13 parts of something, and E equals 11 parts of something. Let’s say that P = the “part” in this ratio; then A = 13P and E = 11P. We can express everything in terms of P.

Al’s account increases by 10%:

New Al = 1.10*(13*P) = 14.3*P

Eliot’s account increases by 20%:

New Eliot = 1.20*(11*P) = 13.2*P

Difference = 14.3*P – 13.2*P = 1.1*P = $22

Multiply both sides by 10 to clear the decimal.

11*P = $220

We could solve for P at this point, but notice that what we want, Eliot’s amount, is already equal to 11*P. This is the answer! Eliot has $220 in his account.

Answer = **(D)**

3) Call the width W. Then the length is L = W + 5. The section of path to the left of the pool in the diagram is a rectangle L tall and 4 wide, so it’s area is

A1 = 4L = 4(W + 5)

In the upper-left hand corner of the path, there’s a 4 x 4 square, with area:

A2 = 16

Above the pool is a rectangle with a height of 4 and width of W, with an area:

A3 = 4W

Another 4 x 4 square in the upper right-hand corner:

A4 = 16

And finally, another rectangle on the right, equal to the one on the left

A5 = A1 = 4(W + 5)

All these pieces add up to 216.

Total = A1 + A2 + A3 + A4 + A5

Total = (4W + 20) + 16 + 4W + 16 + (4W + 20)

Total = 12W + 72 = 216

12W = 216 – 72 = 144

W = 12

The pool has a width of 12 m and a length of 17 m.

Answer = **(A)**

4) Saul appears to have the least money, so we will put everything in terms of his amount.

P = 2*S

Q = P + 60 = 2*S + 60

R = 1.2*Q = 1.2*(2*S + 60) = 2.4*S + 72

Total = S + P + Q + R

Total = S + 2*S + 2*S + 60 + 2.4*S + 72

Total = 7.4*S + 132 = 1020

7.4*S = 888

74*S = 8880

37*S = 4440

At this point, it’s very helpful to know that 3*37 = 111. This means that 12*37 = 444, and 120*37 = 4440. Thus, S = 120. Saul has $120. Notice, though, the question is not asking for what Saul has: it is asking for what Peter has. Peter has twice Saul’s amount, so Peter has $240.

Answer = **(E)**

This is beyond what you need to know for the test, but in this problem there’s a pattern encrypted in the names. The abbreviation of the four names spells out SPQR, which was the abbreviation in Latin for the name of the Roman Empire (*Senatvs Popvlvsqve Romanvs* = “The Senate and the People of Rome”). The four names are folks associated with the city of Rome in one way or another. In the Christian tradition, Saul (who became St. Paul) and St. Peter are believed to have lived and died in Rome. The somewhat obscure male name Quirinal was the name of a son of the god Mars, and it is also the name of the one of the seven hills of Rome. The name Roderick is an inside-joke from a Monty Python film set during Roman times.

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]]>

1) James Joyce wrote the novel *Ulysses* through the teens and published it in 1922, although in 1906, when he was finishing the short story collection *Dubliners*, __he had considered the addition of another story about the canvasser Bloom, who was Jewish and who later was the title Ulysses character.__

(A) he had considered the addition of another story about the canvasser Bloom, who was Jewish and who later was the title *Ulysses* character.

(B) he had been considering that he add an additional extra story, the Jewish canvasser Bloom, and to later make him the *Ulysses*‘ title character.

(C) considering the inclusion of the story of Bloom, the Jewish canvasser who would become the *Ulysses* title character later

(D) he considered including another story about the Jewish canvasser Bloom, who later would be the title character of the *Ulysses*

(E) he considered adding the Jewish canvasser Bloom’s story, and Bloom later would have become the *Ulysses* title character

2) Long before Thomas Edison made a long-lasting and commercially viable incandescent lightbulb, the British chemist Sir Humphry Davy __in 1802 created the first prototype of the lightbulb, that was__ too bright and burned out too quickly.

(A) in 1802 created the first prototype of the lightbulb, that was

(B) made the first prototype in 1802, but it was

(C) had created in 1802 the first prototype of the lightbulb, although this would be

(D) had created the 1802 prototype, the first one, which had been

(E) in 1802 had made the first prototype, but this would be

3) __In 1871, Charles Darwin published The Descent of Man, and before that, Gregor Mendel already had discovered the principles of genetics, using his famous pea plant experiments, and ultimately they would explain and justify Darwin’s conclusions__.

(A) In 1871, Charles Darwin published *The Descent of Man*, and before that, Gregor Mendel already had discovered the principles of genetics, using his famous pea plant experiments, and ultimately they would explain and justify Darwin’s conclusions

(B) By the time Charles Darwin published *The Descent of Man* in 1871, Gregor Mendel already had discovered, during his famous pea plant experiments, the genetic principles that ultimately would explain and justify Darwin’s conclusions

(C) Gregor Mendel already discovered the principles of genetics during his famous pea plant experiments, and although later Charles Darwin published *The Descent of Man* in 1871, these principles ultimately would explain and justify the conclusions of Darwin.

(D) With Charles Darwin publishing *The Descent of Man* in 1871, Gregor Mendel discovered already before this the principles of genetics during his famous pea plant experiments, principles that ultimately would explain and justify the conclusions of Darwin

(E) Before Charles Darwin publishing *The Descent of Man* in 1871, already Gregor Mendel had conducted the famous pea plants experiments and had discovered the principles of genetics, but these principles ultimately would explain and justify Darwin’s conclusions

4) __Had the quantitative skills of Boustrophedon’s CEO been on par with his extraordinary intuition in negotiations__, he would not have needed such a brilliant expert in finance as his CFO.

(A) Had the quantitative skills of Boustrophedon’s CEO been on par with his extraordinary intuition in negotiations

(B) If the Boustrophedon’s CEO’s quantitative skills equaled his extraordinary negotiation intuition

(C) In the case that the quantitative skills of Boustrophedon’s CEO were comparable to his extraordinary skill of using intuition in negotiations

(D) If Boustrophedon’s CEO’s skills for quantitative material were on par to his extraordinary intuition in negotiations

(E) If the quantitative skills of Boustrophedon’s CEO were a comparable ability for his extraordinary intuition in negotiations

Complete explanations will follow this article.

First of all, here are two previous posts:

GMAT Verb Tense: The Perfect Tense

As you may remember, or as may have been reminded in reading one of those two blogs, the pat perfect tense indicates an action that precedes another past action. It is one way to indicate a sequence of events, all of which are in the past. For example

5)* George Washington was a skilled military commander at the outset of the American Revolution because he had gained extensive battlefield experience in the French and Indian War*.

In this example sentence, the verb “had gained” is in the past perfect, to make clear that it indicates an action before the time of the verb “was.” If you know American history, you might have known that the French and Indian War ended about a decade before the American Revolutionary War began. That knowledge is outside this sentence, and of course, such outside knowledge is not required to understand GMAT SC questions, so if sentence #5 were a sentence in a GMAT SC question, the use of the past perfect would tell us all we need to know about which action came first.

The past perfect tense is definitely one way to indicate that one past action was before another, but it’s not the only way to do so. Consider this sentence,

6a) *Richard Nixon was elected US President in 1968, but as the incumbent Vice President he had run in 1960 and had been defeated by John F. Kennedy. *

Notice that this sentence gives us two different ways to know that the events in the second half of the sentence were earlier in time. One is use of the past perfect, and the other is simply the dates given. We know that 1960 happened before 1968: unlike sentence #5, this sentence supplies us with the exact historical information so we know the years when events happened. We don’t need outside knowledge, as we would have with #5.

In a way, this is a kind of redundancy, because the information about which event was earlier is given in two different ways. It’s not as glaring as other forms of redundancy, but it’s certainly suspicious to the GMAT. The GMAT will often consider use of the past perfect tense incorrect if there are other clear indicators of time sequence in the sentence. In all likelihood, the GMAT would prefer this version:

6b) *Richard Nixon was elected US President in 1968, but as the incumbent Vice President he ran in 1960 and was defeated by John F. Kennedy.*

This version, with the verbs of the second half in the simple past tense, is no longer redundant: only the dates given indicate the sequence. As a general rule, if dates or other indications in the sentence clearly let us know the sequence of events, then the use of the past perfect is certainly not necessary and may be considered redundant and incorrect.

The past perfect tense involves the use of the auxiliary verb “had” before the past participle form of the main verb. In formal writing, this opens up an alternative possible structure for conditionals.

Typically, conditional statements start with the word “if.” If the verb employs the auxiliary verb “had,” “should,” or “were,” we can construct a conditional statement by omitting the word “if” and putting the auxiliary verb before the subject. Consider this standard conditional sentence.

7a) *If I had known beforehand about the full cost of the program, I never would have joined.*

That is a 100% grammatical correct sentence, but it is a bit prosaic. It is completely factual and lacking in elegance. By contrast, consider this sophisticated rewrite.

7b) *Had I known beforehand about the full cost of the program, I never would have joined. *

This conveys precisely the same factual information, but unlike it’s prosaic partner #7a, this version has an air of sophistication. Similarly,

8) *Should he win the first round, he will find the competition in the second round considerably more daunting. *

9) *Were I President of the US, I would make “My Country, ‘Tis of Thee” the national anthem. *

These are further examples of conditional statements in which the word “if” has been dropped and the auxiliary verb moved to the beginning of the sentence. Again, this is a very sophisticated structure, typical of high quality writing. Don’t be surprised to find this on the GMAT Sentence Correction.

If the ideas discussed here gave you any insights into the practice questions at the top, you may want to look at them again before reading the explanations below. As you read GMAT RC practice and sophisticated reading unrelated to the GMAT, notice when the past perfect is and isn’t used, and notice the sophisticated conditional structure discussed in the last section.

1) A question about Mike’s favorite author, James Joyce, and his favorite novel, *Ulysses*. The main character is Leopold Bloom, and the book is celebrated on Bloomsday.

Because we have years, the past perfect tense is not necessary.

(A) This is grammatically correct but long-winded and a bit awkward. Also, the phrasing “title *Ulysses* character” is very awkward and unnatural. This is incorrect.

(B) This is a a disaster. The progressive tense “considering” is unnecessary. Having a “that” clause following this is a wordy and awkward way to convey this information. The big mistake: this version has a failure in parallelism: “that he add . . . and to later make.” Finally, just a detail, but that last infinite is a split infinitive, a gaff that would not appear on the correct answer of a GMAT SC problem. This is incorrect.

(C) This commits the famous missing verb mistake. The “although” clause should have a full subject + verb after the “when” clause, but all we get here is a participle. This is a gigantic grammatical failure. This is incorrect.

(D) Elegant and mistake free. This is promising.

(E) The phrasing “the Jewish canvasser Bloom’s story” is a little awkward, and the hypothetical phrasing in the second half changes the meaning, seeming to suggest that Bloom did not become the title character of the *Ulysses*. This meaning is different from that of the prompt. This is incorrect.

The only possible answer is **(D)**.

2) A sentence that mentions the inventor Thomas Edison (1847 – 1931) and the scientist Sir Humphry Davy (1778 – 1829).

(A) This has no major mistake but it is awkward. It is awkward that the sentence uses “that” for a non-restrictive modifier. Also, it’s not necessary to repeat the word “lightbulb,” since this is the topic of the sentence. This is incorrect.

(B) This is elegant and promising.

(C) The past perfect tense is not necessary and somewhat redundant, because time sequence is already double indicated by the “long before” phrase and the years. The hypothetical tone at the end is not appropriate. This is incorrect.

(D) Again, the past perfect is not necessary. Also, the phrasing “the 1802 prototype, the first one” is quite awkward and unclear. This is incorrect.

(E) Again, the past perfect is not necessary. Again, the hypothetical tone at the end is not appropriate. This is incorrect.

The only possible answer is **(B)**.

3) A sentence about two great scientists, Charles Darwin (1809 – 1882) and Gregor Mendel (1822 – 1884). The whole sentence is underlined, so we have to look at each choice separately.

(A) The “before that” and use of the past perfect could be considered redundant. Also, the pronoun “they” in the last clause is ambiguous in its referent. This is incorrect.

(B) This correctly uses the past perfect tense as the only indication of time sequence. This is elegant and mistake-free—a promising choice.

(C) This is grammatically correct but awkward. The “already” in the first clause would seem to establish a connection with other actions, but this expectation is not met. Also, the huge logical shift created by “although” makes the logical relationship of the second clause to the first clause quite unclear. This is incorrect.

(D) This choice uses the “with” + [noun] + [participle] structure, and uses it to encapsulate action by an actor other than the subject of the sentence. That’s too much action inside a prepositional phrase and Mendel did not do what he did “with Darwin.” Also, the phrase “already before this” is extremely awkward. This is incorrect.

(E) This choice commits the famous missing verb mistake in the opening subordinate clause. After the subordinate conjunction “before,” we need a full noun + verb structure, and rather than a full verb, we get only a participle. The “but” before the final clause is illogical. This is incorrect.

The only possible answer is **(B)**.

4) (A) This first option employs the sophisticated conditional structure discussed in the section on “Conditionals” in this blog. This is grammatically and idiomatically correct, and it makes use of an elegant structure. This is a promising choice.

(B) This is awkward. First of all, the phrases “the Boustrophedon’s CEO’s quantitative skills” and “his extraordinary negotiation intuition” are both awkward insofar as they pile too many nouns together at once. Also, the word “equaled” is too strong: it suggests that two things are are entirely equivalent, such that one could substitute for the other, and this reading changes the meaning from the prompt. This is incorrect.

(C) This is grammatically correct but very long, wordy, and awkward. At every instance, this option chooses an especially wordy way to phrase something, so the whole thing is a rambling disaster. This is incorrect.

(D) The double possessive, “Boustrophedon’s CEO’s skills,” is somewhat awkward: this is a structure unlikely to appear as part of a correct answer on an official GMAT SC question. Also, the phrase “on par to” is idiomatically incorrect; the correct idiom is “on par with.” This is incorrect.

(E) The phrase “were a comparable ability for” is not idiomatically correct to convey a comparison. This phrase could be correct if the object of “for” were something other than the second term in the comparison. This is incorrect.

The only possible answer is **(A)**.

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]]>The post Intro to GMAT Word Problems, Part 1: Translating from Word to Math appeared first on Magoosh GMAT Blog.

]]>1) Seven more than a number is 2 more than four times the number. What is the number?

(A) 1

(B) 2/3

(C) 3/5

(D) 4/7

(E) 5/3

2) If $40,000 less than John’s salary is $5,000 more than 25% more than half his salary, then what is John’s salary?

(A) $80,000

(B) $100,000

(C) $120,000

(D) $135,000

(E) $140,000

3) Twice a number is 3 times the square of the number less than one. If the number is positive, what is the value of the number?

(A) 1

(B) 1/2

(C) 1/3

(D) 2/3

(E) 3/2

4) The original price of an item is discounted 20%. A customer buys the item at this discounted price using a $20-off coupon. There is no tax on the item, and this was the only item the customer bought. If the customer paid $1.90 more than half the original price of the item, what was the original price of the item?

(A) $61

(B) $65

(C) $67.40

(D) $70

(E) $73

It’s one thing to understand algebra in the abstract, and quite another to think about where the rubber meets the road. The reason human beings created algebra was to solve problems about real world situations, and the GMAT loves asking math problems about numbers and about real world situations, a.k.a. **word problems**! Even folks who can do algebra in the abstract sometimes find word problems challenging. In this blog and the next, we present a rough-and-ready guide to what you need about word problems.

Suppose we have the following sentence in a word problem:

“Three-fifths of x is 14 less than twice y squared.”

How do we change words to math? Here’s a quick guide

1) the verb “is/are” is the equivalent of an equal sign; the equal sign in an equation is, in terms of “mathematical grammar,” the equivalent of a verb in a sentence. Every sentence has a verb and every equation has an equal sign.

2) The word “of” means multiply (often used with fractions and percents). Ex. “26% of x” means (0.26x)

3) The words “more than” or “greater than” mean addition. Ex. “5 greater than x” means (x + 5) and “7 more than y” means (y + 7)

4) The words “less than” means subtraction. Ex. “8 less than Q” means (Q – 8). Notice that the **first element** is always **subtracted**: in other words, “J less than K” means (K – J).

With that in mind, let’s go back to the sentence from the hypothetical problem above.

“three fifths of x” means [(3/5)*x]

“is” marks the location of the equal sign

“twice y squared” means 2(y^2)

“14 less than twice y squared” means 2(y^2) – 14

Altogether, the equation we get is:

Using this strategy, it’s straightforward to translate from a verbal statement about numbers to an equation.

When all the answer choices are numerical, one further strategy we have at our disposal is backsolving. Using this strategy, we can pick one answer, plug it into the problem, and see whether it works. If this choice is too big or too small, it guides us in what other answer choices to eliminate. Typically, we would start with answer choice (C), but if another answer choice is a particularly convenient choice, then we would start there.

If the strategies discussed here gave you any insights, you may want to give the problems above another look before turning to the solutions below. Look for the second article on Assigning Variables in Word Problems.

1) Translate this one step at a time. Let N be the number we seek.

“seven more than a number” = N + 7

The “is” is the equal sign.

“two more than four times the number” = 4N + 2

Answer = **(E)**

2) We will say that S is John’s salary. “$40,000 less than John’s salary” is (S – 40000). The second part is tricky: “25% more than half his salary” is (1.25*(1/2)*S), so “$5,000 more than 25% more than half his salary” would be that plus 5000. We can write the whole first part of the prompt sentence as

Multiply both sides by 8 (we don’t have to perform the numerical multiplication yet)

8S – 8*45000 = 5S

3S = 8*45000

S = 8*15000 = 4*30000 = 120,000

Notice the use of the doubling and halving trick to perform the multiplication in the last line. John’s salary must be $120,000.

Answer = **(C)**

3) Call the number x. Of course, “twice the number” equals 2x. The part after the word “is” can be tricky. Remember that the information of the form “J less than K” takes the mathematical form (K – J), in which the first part is the part that’s subtracted. What we have here is “3 times the square of the number less than one.” That would be one minus 3 times x squared. Now we can translate that entire first sentence of the prompt into math:

This is a quadratic. We need to get all the terms on one side, equal to zero, and then factor.

Because the prompt tells us that the number must be positive, we can reject the negative root. The number must be +1/3.

Answer = **(C)**

4) We will show two solutions for this: (i) backsolving, and (ii) the full algebraic solution.

For the backsolving solution, notice that (C) is an ugly number. (B) and (D) are nicer numbers. Let’s start with (D).

Original price = $70

10% of price = $7, so

20% of price = $14.

After discount, the price is 70 – 14 = $56. The customer then uses a $20-off coupon, so this customer pays $36.

How does this price compare to half the original price? Well, half the original was $35, so the customer paid exactly $1 more than half the original price.

First of all, we know that answer choice (D) does not work. We know we need a bigger difference, so we need a bigger price. The only price bigger is (E). This must be the answer.

Answer = **(E)**

Now, a full algebra solution. Let the original price be P. Then, 20% off would be 0.8*P. Then, if we subtract $20, that’s (0.8*P – 20). That is the price the customer paid, which equals “$1.90 more than half the original price,” or (0.5P + 1.9). We will set these equal.

08*P – 20 = 0.5*P + 1.9

0.3*P = 21.9

3P = 219

P = 73

The original price was $73. Answer = **(E)**

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]]>Be excellent to the universe!

Here’s this week’s board!

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]]>The post Admission Tips: Countering a Low Verbal Score appeared first on Magoosh GMAT Blog.

]]>Here are three simple ways to show the adcoms that your scores are not showing the full picture, and that you’re still a competitive candidate worthy of that golden acceptance.

The easiest way to prove a single score wrong is by having other grades that tell a different story. Consider taking additional classes that will highlight your strong verbal/communication skills. Take communications classes at a local college, participate in a local debate club, take a public speaking course – and then, of course, get straight A’s or rave reviews in all of them! – to balance out the poor verbal score.

This is a good tip for anyone who scored low on their GMAT, but is even more important if you already have poor English grades on your transcript.

Another proven way to counter a poor verbal GMAT score is to illustrate that you can actually write eloquently and persuasively. Construct a flawless application essay, complete with examples, details, and stories that will adequately convey how well you handle your communications skills. Bringing Including real life examples of your abilities will speak much more strongly for your skills than just another well-written essay.

Speak to each one of the people you’ve asked to write a recommendation for you, and ask them to highlight some of your stronger verbal or communications skills. Once again, bringing in actual examples of instances or areas that you have developed and utilized these skills will help to build the argument even more.

The GMAT is just one element in a grander picture, so make sure the adcoms are seeing the wider view of your capabilities by using some of these useful tips when you apply to b-school. For more advice, view our on-demand webinar, Get Accepted to B-School with Low Stats.

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