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]]>Every GRE test is going to have a few math questions that are very difficult. Upon seeing them, you may become completely flustered and believe that there is no way you are able to solve such a question. Oftentimes this is not the case. Rather, you fall into any number of traps that prevent you from solving a problem that is well within your ability.

Below are five important points to keep in mind when you are dealing with a difficult GRE math problem.

It is very easy to become flustered on difficult math problems, especially word problems. One reason our normal breathing quickly changes to short, agitated breaths is we start reading and re-reading the same question over again. Hope that by the fourth read we will finally get it. At this point, re-reading is clearly an example of diminishing—and frustrating—returns. What to do?…

It often may take about 30-seconds—and a couple (and only a couple) of calm rereads of the question—to decipher a complicated math question. After all, it is complicated. Deciphering the question means understanding what the question is asking. Next, find the solution path. To do so, think—or even write down—the necessary steps to get to the solution.

A few pieces of good news: you can take longer on complicated questions. After all, there aren’t too many of them. Just make sure to solve the easy and medium questions quickly and accurately. Secondly, you can always come back to a question. Sometimes, it is easier to decode the second time around.

Sometimes a problem seems much more complicated than it actually is. The reason is we are misreading a word, or injecting or own word into the question. We spend several minutes laboring through difficult equations only to realize that none of the answer choices matches up with our answer. To avoid this **make you sure you don’t rush through the question**. Instead, read carefully, and know what the question is asking before attempting the question.

The great thing about the new GRE vs. the old format is that you can come back to questions. Sadly, many students do not take advantage of this and are unable to pull themselves from a question once they’ve bitten their teeth into it. But knowing when to unclench that jaw is very important. If a minute has gone by and you are unable to make sense of the question, move on! That question is worth the same number of points, so there is no point in wasting precious minutes on it.

The best thing about being able to come back to questions is your brain is able to make sense of the question a lot more easily the second time around. What seemed cryptic and inscrutable now seems much clearer.

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]]>The Revised GRE is a long, grueling test. To get a perfect score on the quantitative section (a 170) you will not only have to answer the difficult questions correctly, but you will also have to answer all of the easy ones. Nonetheless, I’ve focused on the difficult questions for the 170-challenge. I can’t promise a perfect correlation, but something tells me that if you can answer all five of these questions correctly in less than 10 minutes, you are well on your way to a perfect score.

Of course missing a few hardly precludes a perfect score. But make sure you learn from the ones you miss to make sure you don’t make similar mistakes in the future. And if time is a problem, remember the Magoosh GRE product has plently of questions to help you hone your chops—both from a pacing and a conceptual standpoint.

Good luck, and feel free to post your answers. Let’s see who the first perfect score will be!

1. If s and t are both primes, how many positive divisors of v are greater than 1, if v is an integer?

(A) two

(B) three

(C) five

(D) six

(E) eight

2. A quadrilateral has a perimeter of 16. Which of the following alone would provide sufficient information to determine the area of the quadrilateral. Choose ALL that apply.

[A] The quadrilateral contains equal sides

[B] The quadrilateral is formed by combining two isosceles right triangles

[C] Two pairs of congruent angles are in a 2:1 ratio

[D] The width is 4o% of the length and all angles are of equal measure

[E] If the perimeter was decreased by 50%, the area would decrease to 25% of the original

3. Product Question: Triangle in a Parabola

http://gre.magoosh.com/questions/2192

4. If x is an integer, and 169 < < 324, which of the following is the sum of all values of x?

(A) 61

(B) 62

(C) 75

(D) 93

(E) None of the above.

5. x = 350,000

y = 45,000

Column A | Column B |
---|---|

The total number of positive divisors of x | The total number of positive divisors of y |

- The quantity in Column A is greater
- The quantity in Column B is greater
- The two quantities are equal
- The relationship cannot be determined from the information given

[Note from our intern, Dylan: “I can do multivariable calculus, and got 2/5 on these in 10 minutes. These guys are tricky. :P”]

https://www.youtube.com/watch?v=BxkB8R7esB4

https://www.youtube.com/watch?v=jZdxqajkZtw

http://gre.magoosh.com/questions/2192

https://www.youtube.com/watch?v=pwzlclrvqWU

https://www.youtube.com/watch?v=–U8aDmLNzE

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]]>Have a go at a type of problem that “freaks out” (my students’ own words) test-takers:

Which of the following must be greater than , where ? Choose ALL that apply.

This is a very difficult, time-consuming problem. Unfortunately, there will be a few such problems on the new GRE math section. The good news is that the new GRE will not have too many problems that are multiple answer questions. Out of the 20 questions on the quant section, you will only have about one or two such questions.

**Choose Numbers**

When dealing with variables in the answer choices, you should always plug-in your own numbers. Starting with (A), we can see that we will have a negative fraction: multiplying a negative times itself three times will yield a negative: . The question is will this fraction be greater or smaller than ?

Let’s plug in

On a number line, is closer to zero than . Therefore, will be greater than . This will hold in each case, because as you take any fraction between and to an odd power, you will always make this number approach zero. ONE ANSWER.

For (B), the opposite is true. Taking a cube root of a fraction between and will make that number more negative. At first, you may be hard-pressed to find a fraction in which you can easily take the cube root. From above, we cubed to get . Therefore, the cubed root of is . We are reversing what we did with answer choice (A); therefore, (B) will always be higher, not lower, than .

**Test Both Ranges**

With (C), we can plug in for , giving us . In this case, the answer choice is greater than . You shouldn’t stop there, but test using different numbers. I would suggest numbers closer to the far end of the range, i.e. numbers close to or . Once you’ve established that this relationship holds true at both ends of the range, in this case, is the lowest and the highest, then you’ve done enough plugging in and can include (C) as one of the answers. ANOTHER ANSWER.

A more logical (and optimal) approach is to note that will always be positive. Since you are adding a positive number to , which is negative, will become less negative. There has to be positive. is negative, but since you are subtracting this negative fraction, it is the same as adding it. Therefore, a positive plus a positive must be positive. For instance, plugging in for : is clearly positive. YET ANOTHER ANSWER.

Finally, we have answer choice (E). Let’s start with .

. Just because we found value where that is the case does not mean that it holds true for all values. Let’s plug in for . We get

What happens when we make more negative? Well, let’s work from extremes: must be less than . But let’s say is equal to . Plugging in , we get . On the other extreme, could be zero. Here we would get . Therefore, the range of when we plug in into the equation must be between -1 and 1.

**Final Answers**: A, C, D, and E

Again, this is a very difficult problem, and you probably will only see a couple such time-consuming problems. The takeaways from this problem, however, can be applied to quantitative comparison problems that ask you to reason with fractions and negative fractions. As for quantitative comparison questions, they will comprise roughly 40% of the 20 math questions you will see on each of the Revised GRE math questions. So, make sure you are able to confidently handle thorny problems like the one above.

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]]>The post The Revised GRE– What’s New on the Math Front? appeared first on Magoosh GRE Blog.

]]>Concept-wise, I would say the math section is business as usual, save for two things: coordinate geometry and the quadratic equation.

While parabolas are tested on the current GRE, they are oddball questions, geometry outliers in the usually slew of right triangle and circle problems. In the revised GRE book, an entire section is devoted to understanding not only parabolas but also absolute value graphs (they are represented in a V-shape that can be placed in a horizontal or a vertical position. Such focus leads me to think that we’ll have a greater proportion of these questions compared to before (a good way to practice these is via SAT prep books—the SAT has many parabola questions.)

As for the quadratic equation, it is only employed to help us derive the intersection of a parabola and a line. (See page 240). Still, now that ETS is requiring us to know the quadratic equation, it is fair game for simple polynomial expressions. For instance try the problem below:

What are the two values of x that satisfy the equation above? If you haven’t learned the quadratic equation then definitely add it to your arsenal.

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