Rephrasing the Target Question

In this article, we’ll examine how to make Data Sufficiency questions easier by simplifying the target question before examining the two statements. To set the stage, try solving the following question:

Is 4^(3x + y) = 8^(2x – y)?

1) xy < 0

2) y^x < 1

At first glance, the target question appears complex, but after some manipulation, we can see that it can be simplified significantly. Here’s how:

Get equivalent bases by rewriting 4 and 8 as 2^2 and 2^3 to get: Is (2^2)^(3x + y) = (2^3)^(2x – y)?

Apply Power of a Power rule: Is 2^(6x + 2y) = 2^(6x – 3y)?

Since the bases are equal, we can write: Is 6x + 2y = 6x – 3y?

Subtract 6x from both sides: Is 2y = –3y?

Add 3y to both sides: Is 5y = 0?

Solve: Is y = 0?

So, asking, “Is 4^(3x + y) = 8^(2x – y)?” is the same as asking, “Is y = 0?”

This rephrased target question is much easier than the original and, as a result, our question becomes:

Is y = 0 ?

1) xy < 0

2) y^x < 1

Now that we’ve rephrased the target question in simpler terms, we can handle the statements with relative ease.

Statement 1: If xy < 0, then y definitely does NOT equal 0. Since we can answer the rephrased target question with certainty, statement 1 is sufficient.

Statement 2: If y^x < 1, then there are several possible values for x and y. For example, it’s possible that x = 1 and y = 0, in which case y equals 0. Alternatively, it’s possible that x = 1 and y = -1, in which case y does not equal 0. Since we cannot answer the rephrased target question with certainty, statement 2 is not sufficient, and the correct answer is A.

TAKEAWAY: When answering Data Sufficiency questions, don’t be in a rush to analyze the two statements. Devoting extra time to simplifying the target question first can actually save you time in the long run.

So, as you prepare for the GMAT, watch out for complicated target questions that might benefit from rephrasing. At the same time, please note that we need not rephrase every target question. If the target question is already easily understood, then rephrasing it is unnecessary.

Here are a few examples of rephrased target questions I’ve spotted in the Beat The GMAT forums:

Target question: Is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?
Rephrased target question: Is n divisible by m?
Full question and solution: http://www.beatthegmat.com/how-to-solve-this-q-t216932.html

Target question: x is what fraction of y?
Rephrased target question: What is the value of x/y?
Full question and solution: http://www.beatthegmat.com/help-t171077.html

Target question: If x and y are positive integers,is (2+x)/(3+y) greater than (2+y)/(3+x)?
Rephrased target question: Is x > y?
Full question and solution: http://www.beatthegmat.com/ds-t157326.html

Target question: If x is an integer, does x have a factor n such that 1 < n < x?
Rephrased target question: Is x a non-prime integer?
Full question and solution: http://www.beatthegmat.com/data-sufficiency-t269564.html

Target question: Is p + pz = p?
Rephrased target question: Does pz = 0?
Full question and solution: http://www.beatthegmat.com/ds-3-t275284.html

Target question: Is point R equidistant from points (-3,-3) and (1,-3)?
Rephrased target question: Is point R on the line x = -1?
Full question and solution: beatthegmat.com/coordiante-plane-how-to-arrive-at-the-answer-t272785.html

Target question: Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?
Rephrased target question: Is integer p a composite number?
Full question and solution: http://www.beatthegmat.com/number-properties-how-do-i-even-start-t274723.html

I’ve also started a thread in the Data Sufficiency forum where students can post their own examples of target questions that benefit from rephrasing: http://www.beatthegmat.com/a-place-to-post-your-examples-of-rephrased-target-questions-t277300.html#722098

For more information about rephrasing the target question, you can watch our free video. Afterwards, you can practice your rephrasing skills by answering the following questions:

EASY

http://www.beatthegmat.com/which-operation-is-represented-t273470.html

http://www.beatthegmat.com/words-per-paragraph-t274055.html

http://www.beatthegmat.com/inequalities-sign-change-t271810.html

MEDIUM

http://www.beatthegmat.com/powers-and-inequalities-t277249.html

http://www.beatthegmat.com/each-of-a-b-and-c-is-positive-does-statement-1-state-t208331.html

http://www.beatthegmat.com/official-guide-question-73-t274523.html

http://www.beatthegmat.com/ds-query-t276597.html

HARD:

http://www.beatthegmat.com/sequences-and-primes-t273727.html

http://www.beatthegmat.com/distance-t273181.html