Essential Math Strategies for GRE Quant

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Essential Strategies for the GRE

Three Strategies You Must Know to Ace the

Quantitative Section of the GRE


The GRE is not simply a test of facts and memorization. In fact, knowing the

correct strategy for a question may allow you to solve a question correctly

without even understanding it! If this sounds dubious, stay tuned. In this brief

e-book we will show you the three most important strategies you need to get

a great Quant score on the GRE.


Ask yourself:

“Is the answer

choice reasonable?”

If you have no idea how to solve a multiple-choice

question, stop trying to solve and ask yourself a simple

question: Is the answer choice reasonable?

Since the GRE does not penalize you for wrong answers,

you must attempt every question. However, before taking

a wild guess, take a moment to look at the answer choices

- often, two or three of them will be completely

unreasonable! Eliminate those and guess one of the

others. Occasionally, four of the choices are absurd. When

this occurs, your answer is no longer a guess.

What makes a choice unreasonable? Well, let’s just say lots of things.

Here are a few. Even if you don’t know how to solve a problem you

may realize that:

1. The answer must be positive, but some of the choices are negative;

2. The answer must be even, but some of the choices are odd;

3. The answer must be less than 100, but some choices exceed 100;

4. A ratio must be less than 1, but some choices are greater than 1


Example:

Q. The average (arithmetic mean) of 5, 10, 15, and z is 20. What is z?

20

25

45

0

5 + 10 + 15 + 𝑤

4= 20

5 + 10 + 15 + 𝑤 = 20 × 4

→ 𝑤 = 80 − 30 = 50

Solution:

Start off by asking “Which answer choices are unreasonable?”

If the average of four numbers is 20, and three of them are less than 20, the

other one must be greater than 20. You can immediately see that answer

choices A and B are unreasonable and can be eliminated right away.

If you further realize that since 5 and 10 are a lot less than 20, z will

probably be a lot more than 20. You can eliminate C, as well. You now have

only two remaining answer choices with excellent odds of getting the right

answer.

Direct Solution:

Let’s face it. This problem is pretty easy to solve using simple algebra:

E is the Correct Answer

50


Let’s look at another example. Sometimes, the information provided with the problem is

intentionally insufficient to solve the problem; but you will still be able to determine that some

of the answers are absurd. In each case the “solution” will indicate which choices you should

have eliminated. At that point you would simply guess. Remember, when you guess on the GRE,

don’t agonize. Just guess and move on!

Example:

Q. If 25% of 260 equals 6.5% of a, what is a?

65

100

130

10

Solution:

The problems says that 6.5% of a equals 25% of 260. Based on

this information, we can comfortably say that, a must be greater

than 260. Why? Because 6.5% is lower than 25% and since a

lower percentage of a equals 25% of 260, we can safely say

𝑎 > 260 . Eliminate A, B, C, and D. The answer must be E!

1000

This example illustrates an important point. Even if you know how to

solve a problem, if you immediately see that four of the five choices

are absurd, just pick the fifth choice and move on.


“

Pick Your Numbers

.

Mastery of this technique is critical

for anyone developing good test-

taking skills. This tactic can be used

whenever the five choices involve

the variables in the question.

The Approach:

This strategy contains three steps:

1. Replace each letter or variable with an easy-to-use number.

2. Solve the problem using those numbers.

3. Evaluate each of the five choices with the numbers you picked to see which choice is equal

to the answer you obtained.

“


This strategy works very well when easy-to-use numbers are chosen. Here are some guidelines for using convenient numbers:

• Use nice, round numbers whenever possible. The best choices

are 1, 0, and –1. • Fractions between 0 and 1 and/or -1 and 0. • “Large” convenient numbers such as 10 or 100. • In problems involving fractions and ratios, use the least

common denominator of all the fractions. • In problems involving percents, use 100.

Always make sure you check the limitations stated

in the question if there are any. Do not impose any conditions not specifically stated in the problem e.g. if the question pertains to negative integers, do not pick your numbers as 1, 2, etc.

Let's solve an example GRE question where this strategy can be seen in action.


Example:

If the sum of five consecutive even integers is t, then, in terms of t, what is the greatest of these integers?

𝑡 = 2 + 4 + 6 + 8 + 10 = 30

Solution:

1. Pick five easy-to-use consecutive even integers e.g. 2, 4, 6, 8 and 10.

2. Solve the problem with these numbers: the greatest of these

integers is 10.

3. When t = 30, the five choices are: 10

5,

20

5,

30

5,

40

5 and

50

5. Out of

these choices only 50

5= 10

E is the Correct Answer.

𝑡+20

5

𝑡−10

5

𝑡

5

𝑡+10

5

𝑡−20

5

Direct Solution:

Of course, this question can be solved without using this strategy if your algebra skills are good. Here is the solution to this problem using algebra:

1. Let n be the highest integer. Therefore n - 8, n - 6, n - 4, n - 2 and n are the five consecutive even integers. Since their sum is t, we can write:

t = n + (n - 2) + (n - 4) + (n - 6) + (n - 8) = 5n - 20

2. Therefore 𝑛 =𝑡+20

5

E is the Correct Answer.


Plug and Chug

This strategy, often called backsolving, is useful when you are asked to solve for an unknown and you understand what needs to be done to answer the question, but you want to avoid doing the algebra. The idea is simple: test the various answer choices to see which one is correct.

On the GRE, the answers to virtually all numerical multiple-choice questions are listed in either increasing or decreasing order. Consequently, C is the middle value, and in applying this tactic, you should always start with C.

For example, assume that choices A, B, C, D, and E are given in increasing order. Try C. If it works, you’ve found the answer. If C doesn’t work, you may know whether you need to test a larger number or a smaller one, and that permits you to eliminate two more choices. If C is too small, you need a larger number, and so A and B are out; if C is too large, eliminate D and E, which are even larger.


Example:

If the average (arithmetic mean) of 5, 6, 7, and w is 10, what is the value of w?

5 + 6 + 7 + 18

4=

36

4= 9

5 + 6 + 7 + 22

4=

40

4= 10

Solution:

1. Plug in Choice C: w = 18. Is the average of 5, 6, 7, and 18 equal to 10? The answer is No. The answer 9 is too small:

2. Eliminate C, and, since for the average to be 10, w must be greater than 18. Therefore you can eliminate A and B as well.

3. Try D: w = 22. Is the average of 5, 6, 7 and 22 equal to 10? The answer is yes.

D is the Correct Answer.

28

13

18

22

8

Here are two direct methods for solving the example problem, each of which is faster than backsolving. If you know either method you should use it, and save this technique for those problems that you can’t easily solve directly.

DIRECT SOLUTION 1. If the average of four numbers is 10, their sum is 40. Therefore, 5 + 6 + 7 + w = 40 18 + w = 40 w = 22.

DIRECT SOLUTION 2. Since 5 is 5 less than 10, 6 is 4 less than 10, and 7 is 3 less than 10, to compensate, w must be 5 + 4 + 3 = 12 more than 10. Therefore, w = 10 + 12 = 22.

Every problem that can be solved in this way can be solved directly, often in less time. So we stress: if you are confident that you can solve a problem quickly and accurately, just do so.


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Essential Math Strategies for GRE Quant