GMAT Prep From Platinum GMAT

GMAT Prep Materials

GMAT Practice Questions

Problem Solving · Data Sufficiency · Sentence Correction · Reading Comprehension · Critical Reasoning

GMAT Study Guide

Number Properties · Combinatorics · AWA Essay Template · GMAT Idioms

MBA Admissions

Average Scores & GPAs · Rankings · School Profiles

About Us

Platinum GMAT Prep provides the best GMAT preparation materials available anywhere, enabling individuals to master the GMAT and gain admission to any MBA program. We also provide hundreds of pages of free GMAT prep content, including practice questions, study guides, and test overviews.

rss GMAT Practice Question (One of Hundreds)
If x and y are both integers, which is larger, xx or yy?
  1. x = y + 1
  2. xy > x and x is positive.
Correct Answer: C
For Statement (1), try plugging in negative values for x.
  1. The problem deals with properties of exponents. Analyzing the different cases where x is positive and y is positive, for example, is the key to this problem.
  2. Evaluate Statement (1) alone.
    1. Since x = y + 1, substitute for x in xx.
      xx = (y + 1)(y + 1)
    2. Since x is one number larger than y, it may appear that xx must be larger than yy. However, consider the table below.
      xyxxyy
      -1-2-11/4
      -2-31/4-1/27
      -3-4-1/271/256
    3. When x = -1 and y = -2, xx is smaller. However, when x = -2 and y = -3, yy is smaller. Whether xx or yy is larger depends on the values of x and y.
    4. Statement (1) is NOT SUFFICIENT.
  3. Evaluate Statement (2) alone.
    1. Given the inequality from Statement (2),
      xy > x
      Divide both sides by x.
      x(y - 1) > 1
    2. First consider this inequality when y = 1. Then x(y - 1) = x(1 - 1) = 1. But this violates the inequality because it is not true that x(1 - 1) > 1. Therefore, y may not be 1.
    3. Next consider the case where y < 1. Then x(y - 1) = x-k, where -k is some negative number. And x-k = 1 / xk, which is less than 1 no matter the value of x; this violates the inequality, too, since x(y - 1) is supposed to be greater than 1. For example, if y = -3 and x = 2, then x(y - 1) = 2(-3 - 1) = 1 / 24 = 1/8, which is less than 1.
    4. Since it cannot be that y = 1 or y < 1, the only option that remains is y > 1. From this conclusion and the information given in Statement (2), we conclude that x > 0 and y > 1. However, this is not enough information to determine whether xx or yy is larger. For example, it could be that x = 4 and y = 6; in this case, yy would be larger. It could be that x = 7 and y = 3; in this case, xx would be larger.
    5. Statement (2) is NOT SUFFICIENT.
  4. Evaluate Statement (1) and (2) together.
    1. The conclusion reached in examining Statement (2) was that y > 1 and x > 0. Combine this with Statement (1), which says that x is one number larger than y. Thus, xx will always be larger than yy. For example, if y = 2, then x = 3; yy = 22 = 4 and xx = 33 = 27.
    2. Statement (1) and (2) together are SUFFICIENT.
  5. Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is NOT SUFFICIENT yet Statements (1) and (2), when taken together, are SUFFICIENT, answer C is correct.