Rephrasing the target question

By Brent Hanneson - August 24, 2020

Consider this official GMAT question:

If x and y are both positive, is (x + 1)/(y + 1) > x/y ?

(1) x > 1

(2) x < y

The inequality in the target question is somewhat complex, but we can make things much easier by simplifying it before analyzing the statements. 

Take: (x + 1)/(y + 1) > x/y

Since y is positive, we can multiply both sides by y to get: (y)(x + 1)/(y + 1) > x

Likewise, since y is positive, we know that y+1 is positive, which means we can multiply both sides by (y+1) to get: (y)(x + 1) > x(y + 1)

Expand: xy + y > xy + x

Finally, subtract xy from both sides: y > x

So, the inequality y > x is equivalent to the original inequality, (x + 1)/(y + 1) > x/y. This means we can rephrase the target question as: Is y > x?

This makes our analysis much easier.

Statement 1: x > 1

Since we have no information about y, there’s no way to answer the rephrased target question (Is y > x?)

Statement 1 is insufficient.

Statement 2: x < y

Aha! The answer the rephrased target question (Is y > x?) is a definite YES.

So, statement 2 is sufficient.

Answer: B

Keep in mind that most target questions can’t be rephrased in a useful way. However, when they can be rephrased, doing so will usually make it easier to analyze the statements.  

To get you started, here’s a short list of examples of target questions that can be rephrased:

Target question: If x is positive, is x² < x?

Rephrased target question:  Is x < 1?

Explanation

Target question: If s and t are positive, is s/t less than st?

Rephrased target question:  Is 1 < t²?

Explanation

Target question: Does x + c = y + c ?

Rephrased target question:  Does x = y?

Explanation

Target question: Does a² + b²= 2ab?

Rephrased target question:  Does a = b?

Explanation

Target question: If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ?

Rephrased target question:  Does a +b = 0?

Explanation

Target question: If p, s, and t are positive integers, is |ps - pt| > p(s - t) ?

Rephrased target question:  Is s < t?

Explanation

Target question: If 2.00x and 3.00y are 2 numbers in decimal form with thousandths digits x and y, is 3(2.00x) > 2(3.00x)?

Rephrased target question:  Is 3X > 2Y?

Explanation

For more on this useful strategy, watch this.