# Miscellaneous GMAT-Specific Strategies

## Shortest path graphic 2.png Note: This is article #3 in the multi-article series Are you doing it wrong?

In my previous article, we examined the strategy of testing the answer choices, which is just one of the ways to exploit the fact that the correct response to every GMAT Problem Solving question is hiding among the five answer choices.

In this article, we’ll examine 5 more ways to use the answer choices to our advantage:

• Testing solutions to given equations and inequalities
• Testing for equivalency
• Testing values that satisfy the given conditions
• Geometry by visual estimation
• Gut-driven probabilities

Let’s go!

1. Testing solutions to given equations and inequalities

The GMAT asks a lot of What Must Be True questions. These questions present us with some mathematical truth in the form of an equation or inequality, and we must determine which statement among the answer choices must also be true. Here’s an example from the GMAT Official Guide

If y + |y| = 0 which of the following must be true?

(A) y > 0

(B) y ≥ 0

(C) y < 0

(D) y ≤ 0

(E) y = 0

On GMAT Club, 35% of students get this question wrong. Most students will try to apply (with varying success) one or more mathematical properties to solve this question, whereas the faster (and more accurate) approach is to use the answer choices to our advantage.

If y + |y| = 0, we can easily see that it could be the case that y = 0

Now we’ll plug y = 0 into the five answer choices to see which one(s) is/are true:

A. 0 > 0. Not true. Eliminate.

B. 0 ≥ 0. True. Keep.

C. 0 < 0. Not true. Eliminate.

D. 0 ≤ 0. True. Keep.

E. 0 = 0. True. Keep.

We’re already down to options B, D and E.

Aside: When looking for solutions to a given equation or inequality, it's useful to first check whether 0 is a solution, since zero is such an easy value to work with.

Now we’ll test another y-value that satisfies the equation y + |y| = 0

We can see that y = -1 is another possible solution. So, we’ll plug y = -1 into the remaining three answer choices:

B. -1 ≥ 0. Not true. Eliminate.

D. -1 ≤ 0. True. Keep.

E. -1 = 0. Not true. Eliminate.

By the process of elimination, the correct answer is D.

This efficient strategy also works with 700+ level inequality questions like this one from the GMAT Club tests:

If (|x| - 2)(x + 5) < 0, then which of the following must be true?

(A) x > 2

(B) x < 2

(C) -2 < x < 2

(D) -5 < x < 2

(E) x < -5

On GMAT Club, this question has a success rate of 28%.

Let’s first find an x-value that satisfies the given inequality (|x| - 2)(x + 5) < 0.

It turns out x = 0 is a solution. Now plug x = 0 into the five answer choices:

(A) 0 > 2. Not true. Eliminate.

(B) 0 < 2. True. KEEP.

(C) -2 < 0 < 2. True. KEEP.

(D) -5 < 0 < 2. True. KEEP.

(E) 0 < -5. Not true. Eliminate.

We’re now down to choices B, C and D.

Now let’s find an “extreme” x-value that satisfies (|x| - 2)(x + 5) < 0.

x = -10 works. So, we’ll plug x = -10 into the remaining three answer choices:

(B) -10 < 2. True. KEEP.

(C) -2 < -10 < 2. Not true. Eliminate.

(D) -5 < -10 < 2. Not true. Eliminate.

By the process of elimination, the correct answer is B.

Here are a few more questions to practice with:

Sub 600 Level

600+ Level

2 - Testing for Equivalency

This next strategy can be applied to questions in which we’re given some algebraic expression, and we must identify an equivalent expression among the answer choices.

The GMAT-specific strategy for this question type relies on the following property:

If two algebraic expressions are equivalent, they must evaluate to the same value for every possible value of x.

For example, since the expression 2x + 3x is equivalent to the expression 5x, the two expressions will evaluate to the same number for every value of x. So, for example, when x = 7, the expression 2x + 3x = 2(7) + 3(7) = 14 + 21 = 35; likewise, the expression 5x = 5(7) = 35.

Let’s apply this strategy to the following question from the GMAT Official Guide

If k and n are positive integers such that n > k, then k! + (n - k)(k -1)! is equivalent to which of the following?

(A) (k)(n!)

(B) (k!)(n)

(C) (n - k)!

(D) (n)(k + 1)!

(E) (n)(k - 1)!

Since we’re told k and n are positive integers such that n > k, let’s first see what the given expression evaluates to when n = 3 and k = 2.

When we plug these values into the given expression, we get: k! + (n - k)(k -1)! = 2! + (3 - 2)(2 -1)! = 2! + (1)(1!) = 2 + 1 = 3.

So, when n = 3 and k = 2, the given expression evaluates to 3. This means the correct answer must also evaluate to 3, when n = 3 and k = 2

To find out, we'll plug n = 3 and k = 2 into the five answer choices:

(A) (k)(n!) = (2)(3!) = (2)(6) = 12. Eliminate.

(B) (k!)(n) = (2!)(3) = (2)(3) = 6. Eliminate.

(C) (n - k)! = (3 - 2)! = 1! = 1. Eliminate.

(D) (n)(k + 1)! = (3)(2 + 1)! = (3)(3!) = (3)(6) = 18. Eliminate.

(E) (n)(k - 1)! = (3)(2 - 1)! = (3)(1!) = (3)(1) = 3. Perfect!!

If more than one answer choice evaluated to 3 for n = 3 and k = 2, then we’d have to test another pair of values on the remaining answer choices.

Here are a few practice questions:

Sub 600 Level

600+ Level

3 - Testing values that satisfy the given conditions

Another GMAT-specific strategy is testing values that adhere to the conditions provided in the question. This strategy works especially well with Integer Properties questions such as this one from the Official Guide:

If n = 4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n?

(A)    Two

(B)     Three

(C)     Four

(D)     Six

(E)     Eight

On GMAT Club, this question has a 700+ rating. Having reviewed it with dozens (perhaps hundreds) of students, I know that many try to apply logic that goes something like this:

If p is a prime greater than 2, then p is odd. If p is odd, then 2p is even and, since 2p is a divisor of 4p, we know that 2p must be an even divisor of 4p. Similarly, 4p will be another even divisor of 4p, . . . etc.

This approach (although admirable) pales in comparison to simply testing a value of n that satisfies the given information.

Since p is a prime number greater than 2, it could be the case that p = 3.

Substitute into given equation to get: n = 4p = 4(3) = 12

If n = 12, the positive divisors of n are 1, 2, 3, 4, 6 and 12. Among these divisors, four are even (2, 4, 6, and 12), which means the correct answer is C.

Here’s another official GMAT question:

At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?

(A) 1/2

(B) 2/5

(C) 3/5

(D) 4/5

(E) 5/8

Since each night crew worker loaded 3/4 as many boxes as each day crew worker, it could be the case that each day crew worker loaded 4 boxes, and each night crew worker loaded 3 boxes.

Since the number of night crew workers is 4/5 the number of day crew workers, it could be the case that there are 5 day crew workers, and 4 night crew workers.

If there are 5 day crew workers, and each day crew worker loaded 4 boxes, then the day crew loaded a total of 20 boxes.

Similarly, if there are 4 night crew workers, and each night crew worker loaded 3 boxes, then the night crew loaded a total of 12 boxes.

20 + 12 = 32, which means the two crews loaded a total of 32 boxes.

Since the day crew loaded 20 boxes, the required fraction = 20/32 = 5/8

Here are some questions to practice the above strategy:

Sub 600 Level

600+ Level

4 - Geometry by visual estimation

Another area where we can use the answer choices to our advantage involves an important feature regarding the geometric figures accompanying GMAT Problem Solving questions.

Consider this question from the Official Guide

## Geometry-visual-estimation-Q.png The key ingredient of this strategy is the fact that the geometric diagrams in GMAT Problem Solving questions are drawn to scale unless stated otherwise. So, in some cases, we may be able to identify the correct answer through visual approximation alone.

Here, the question tells us the diameter = 2, which means PO (the radius) has length 1.

When we compare the lengths of PO and RT, we see that RT is slightly longer, which means RT is slightly longer than 1.

Now let’s evaluate each answer choice by replacing √3 with its approximate value of 1.7

Tip: Before test day, be sure to memorize the following approximations: √2 ≈ 1.4, √3 ≈ 1.7, and √5 ≈ 2.2. These values come in handy A LOT.

When we replace √3 with 1.7, we get:

A) 1/2 = 0.5

B) 1/1.7 = a number that’s less than 1.

C) 1.7/2 = a number that’s less than 1.

D) 2/1.7 = a number that’s a little bit bigger than 1.

E) 1.7 = a number that’s 70% bigger than 1.

We can see that answer choice D is the only one that suits our approximation.

The test-makers know that some students will bypass geometric reasoning altogether and attempt to answer the question by estimating the length of RT. Given this, you’d think they’d have more than just one answer choice that’s slightly greater than 1, but they didn’t. Another gift from our benevolent test-makers!

Here’s another official question where we can easily identify the correct answer solely through visual approximation (my solution here).

Can all GMAT geometry questions be solved by visual approximation?

Absolutely not. In fact, most can’t be solved this way. That said, there are many questions where we can visually estimate the answer and then eliminate 2 or 3 options, which makes for an expedient guess if you’re behind time, or you have no idea how to solve the question.

It’s also worth noting that, even if we solve a geometry question via conventional strategies, we can still use visual approximation to confirm our solution.

For example, in this question from the Official Guide, we must determine what fraction of the larger circle is shaded. If your calculations yielded an answer of 1/2 (answer choice E), a quick visual inspection of the given diagram would be enough to tell you your calculations were incorrect.

Here are a few more examples to try:

600+ Level

5 - Gut-driven probabilities

This last strategy relies on our innate ability to estimate the likelihood of an event. For example, even if we know nothing about probability rules, we still have a “gut feeling” about the probability of randomly selecting 2 queens from a deck of playing cards in two draws. We certainly know the probability is less than 1/5, which means we can eliminate any answer choices greater than 1/5. This isn’t to say you’ll be able to eliminate 4 answer choices, but in many cases, you’ll be able to eliminate some answer choices, which is better than a 1-in-5 guess.

For example, consider this official GMAT question:

A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushes at random, one at a time, and plant them in a row, what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes?

A. 1/12

B. 1/6

C. 1/5

D. 1/3

E. 1/2

Check out the extremes. Do you think the two middle rosebushes will be red half the time? Seems unlikely, so we can eliminate E. What about 1/12? And so on.

Here’s my full solution to that question.

Test out your gut feeling “skills” with these questions:

Sub 600 Level

600+ Level

Final Words

As you can see, the test-makers often provide opportunities to use time-saving (and error-reducing strategies). Always remember that the every GMAT quantitative question is testing your ability to identify the correct answer in the most efficient manner. Sometimes, conventional strategies are more efficient, and sometimes GMAT-specific strategies are.

So, as you practice with official questions, practice identifying the most efficient approach. Afterwards, you can try answering the question via the other approach.