The post Mental Math on the GRE appeared first on Magoosh GRE Blog.

]]>With the advent of the calculator on the GRE, some would say the days of knowing how to do mental math are obsolete. While you could rely on the calculator for the entire test, doing so may actually slow you down. Indeed a facility mental math will save you a lot of time, and may help you avoid any careless slip of the fingers.

Momentarily stepping out of the problem, so to speak, to attend to the calculator can interrupt the flow. You may forget exactly what the number pertained to. Was it the answer? Or was it one of many calculations you need to do to arrive at the answer? If it is the latter, then you may forget your place and have to start over.

By constantly relying on the calculator you can get a case of calculator-itis. Even easy computations has you running for the on-screen calculator. While you may be fast with your fingers, being able to calculations like 14 x 5 in your head will be a lot of faster. And with so many such calculations, those few seconds per calculation adds up to quite a lot over the course of the test.

Sure, we are all prone to mental math mistakes. But we are also prone to entering in the wrong numbers, especially under timed conditions. If it is a simple calculation, sharpen your calculator brain—don’t let 17 x 3 = 42, because of a simple slip of your finger.

Some questions may seem daunting, but with just a little mental approximation you can quickly get the answer. What is 15% of 50,200? Well, it’s a little bit greater than 7,500. If only one answer is close to 7,500 then you save yourself the time of having to enter the number into the calculator.

You may balk thinking that you’d prefer the accuracy, but remember working out your mental math muscle before the test will help you become far more adept at doing quick calculations in your head.

Using a calculator makes sense when you are dealing with big numbers, especially in the case of data input. But if you are dealing with smaller sums (say 20 x 12), then relying on math can save you a lot of time. And you won’t have to worry about any slippery fingers.

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]]>The post GRE Quantitative Comparison Tip #5 – Estimation with a Twist appeared first on Magoosh GRE Blog.

]]>Here’s the whole series of QC tips:

Tip #1: Dealing with Variables

Tip #5: Estimation with a Twist

In my last post, we solved the following question:

A. The quantity in Column A is greater

B. The quantity in Column B is greater

C. The two quantities are equal

D. The relationship cannot be determined from the information given

Our approach was to first recognize that two of fractions are approximately 1/2 and two are approximately 1/3.

Now if we had used these approximations, we would have been left with:

This would have made us conclude (incorrectly) that the answer is C.

To solve this question using approximation, we applied a twist. We recognized that 213/428 is a little bit less than 1/2, which we denoted as 1/2^{–}. We also noticed that 3007/9101 is a little bit less than 1/3, which we denoted as 1/3^{–}.

And so on.

With these little twists, we were able to simplify the two columns as:

From here, it was clear that the correct answer is B

Okay, now let’s see if you can apply this approximation with a twist to solve the following question:

Aside: before you read my solutions, see if you can find additional ways to solve this question.

Okay, first we’ll solve the question using approximation with a twist, and then we’ll solve it using different approaches.

First, let’s approximate as follows:

From here, we can drop 4 zeroes from each number to get:

At this point, I’ll apply a nice rule that says:

In other words, the product of two numbers is equal to the product of twice one number and half the other value.

So, in Column A, we’ll double 45^{+} and halve 64^{+} to get:

From here, when we compare the products in parts, we can see that Column A must be greater than Column B, so the answer is A.

As you might have guessed, the two original products are too large to work on a calculator. For example, (641,713)x(451,222)=289,555,023,286 and this number is too large for the GRE’s onscreen calculator. As such, the calculator would display an error message if you tried to perform this calculation.

There are, however, some ways to work around this constraint and still use the calculator.

For example, you could divide each number by 1000 to get:

** **

At this point, the products will still fit into the display of the onscreen calculator and you would clearly see that Column A is greater.

Another possible approach is to perform the same steps we performed earlier, but stop when we get to:

Originally, we applied that handy rule where we double one number and halve the other. However, we could also use the calculator at this point.

(64)x(45)=2880 and (90)x(32)=2880. This means that (64^{+})x(45^{+})=2880^{+} and (90^{–})x(32^{–})=2880^{–}.

So, we get:

Once again, we can see that the answer is A.

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]]>The post GRE Quantitative Comparison Tip #4 – Comparing in Parts appeared first on Magoosh GRE Blog.

]]>To set up today’s Quantitative Comparison (QC) strategy, please solve the following question:

A. The quantity in Column A is greater

B. The quantity in Column B is greater

C. The two quantities are equal

D. The relationship cannot be determined from the information given

There are several different ways to solve this question. For example, we could add the fractions in each column, and then rewrite both sums with a common denominator and then compare them (yikes!). Or, we could use the onscreen calculator to convert each fraction to a decimal and find the sum in each column (yeesh!).

Both of these approaches would take a long time.

Fortunately, we already know that, since the test-makers are reasonable, there MUST be an easier way to solve this question (please read my previous post: The Reasonable Test-Maker).

The fastest way to solve this question is to estimate and compare the columns in parts.

Here’s how it works.

First notice that 213/428 is approximately 1/2. Now, for this question, we need to be a little more accurate than that. Notice that, since 214/428 = 1/2, it must be the case that 213/428 is a little bit less than 1/2, which we’ll denote as 1/2-.

Using similar logic, we can see that, since 3007/9021 = 1/3, it must be the case that 3007/9101 is a little bit less than 1/3, which we’ll denote as 1/3^{–}.

Next, since 731/1462 = ½, it must be the case that 741/428 is a little bit more than 1/2, which we’ll denote as 1/2+.

Using the same logic, we can see that 208/597 is a little bit more than 1/3, which we’ll denote as 1/3^{+}.

At this point, we can simplify the two columns as:

From here, we can compare the two sums in parts.

Since 1/2+is greater than 1/2-, and since 1/3^{+} is greater than 1/3^{–}, the sum of 1/2+ and 1/3^{+} must be greater than the sum of 1/2- and 1/3^{-.}

As such, the answer must be B.

Heres’ the whole series of QC tips:

Tip #1: Dealing with Variables

Tip #5: Estimation with a Twist

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]]>The post GRE Math Techniques – The Power of Estimation appeared first on Magoosh GRE Blog.

]]>Many of us, when we first see a math question, hone in on it with laser-like focus. We make sure we read all the relevant parts, and then work out a solution to the problem. Only then do we look at the answers.

There is nothing inherently wrong with approaching a math problem this way; often times, it yields the right answer. But the GRE is a timed test, and solving for the exact answer to every problem is only going to eat up time.

Is there another—almost magical—way of solving a GRE math problem? Well, yes, depending on how you define magic. Once I show you the following technique, and you are able to apply it, you may very well think it magical.

First off, try the following problem.

*1. **If Machine X can make 40 widgets in 8 minutes, how many widgets can it make in 1 hour?*

* *

*(A) **90*

*(B) **180*

*(C) **240*

*(D) **300*

*(E) **320*

Okay, did you find yourself reading the question, setting up a proportion and then solving for the unknown? If so, no worries. You are simply taking the long approach.

Let’s instead look at the answer choices as soon as we’ve finished reading the question. There is quite a spread between the answer choices, as is often the case with GRE math problems. The range is 90 to 320. If the machine is already pumping up 40 widgets in 8 minutes, it’s definitely going to make more than 90 in 60 minutes. In fact, 60 minutes is almost 8 times as great as 8 minutes. Therefore the machine is going to make almost 8 times more than 40. Well, 8 x 40 = 320 (E), so that’s too big. So, which is number is slightly smaller? (D) 300. And there’s your answer.

This technique is called estimation. Learning to apply it accurately will save you time. It will also help with those more difficult questions, on which you really need your laser-like focus.

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]]>The post GRE Math Strategies Part V of VI: Estimation appeared first on Magoosh GRE Blog.

]]>**Example #1:**

Which of the following is nearest to

(A) 20

(B) 15

(C) 10

(D) 5

(E) 1

**(E) is the correct answer.**

The numerator of the first factor and denominator of the second factor are nearly equal, approximately 100, and can be cancelled. Then the remaining expression can be easily estimated.

Some questions may involve unfamiliar symbolism and minor calculations yet are still good candidates for Estimation.

**Example #2:**

(A)

(B)

(C)

(D)

(E)

**(C) is the correct answer.**

Because and , we can estimate the expression as , which is very close to

**Note:**

Textbook Approach: If you remember this formula, the problem is easily solved: , so

The post GRE Math Strategies Part V of VI: Estimation appeared first on Magoosh GRE Blog.

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