A GMAT Inequality DS question. Tests your understanding of how exponents of a number compare at different intervals. A GMAT 650 level data sufficiency sample question.

This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwise), you must indicate whether -

- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- EACH statement ALONE is sufficient to answer the question asked.
- Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

All numbers used are real numbers.

A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2)

Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight

You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.

All figures lie in a plane unless otherwise indicated.

In data sufficiency problems that ask for the value of a quantity, the data given in the statement are sufficient only when it is possible to determine exactly one numerical value for the quantity.

Question 6: **Is a ^{3} > a^{2}?**

**Statement 1**: \\frac{1}{a}) > a

**Statement 2**: a^{5} > a^{3}

@ INR

**Q1. What kind of an answer will the question fetch?**

The question is an "IS" question. For "IS" questions, the answer is "YES" or "NO".

**Q2. When is the data sufficient?**

The data is sufficient if we are able to get a CONCLUSIVE YES or a CONCLUSIVE NO from the information in the statements.

If using the information in the statement(s), we arrive at an answer that is sometimes yes and sometimes no, the data is not sufficient.

**Q3. When is the answer yes?**

If a^{3} > a^{2}, the answer is YES.

**Q4. When is the answer no?**

If a^{3} ≤ a^{2}, the answer is NO.

**Statement 1**: \\frac{1}{a}) > a

For positive values of 'a' if \\frac{1}{a}) > a, a has to lie in the interval 0 < a < 1.

In this interval a^{3} < a^{2}

For negative values of 'a' a^{3} < a^{2} because odd powers of negative numbers are negative and even powers of negative numbers are positive.

Hence, from statement (1) we can conclude that a^{3} is not greater than a^{2}

Statement 1 ALONE is sufficient.

Eliminate choices B, C, and E. Choices narrow down to A or D.

**Statement 2**: a^{5} > a^{3}

For positive values of 'a' if a^{5} > a^{3}, a has to be greater than 1. In this interval a^{3} > a^{2}.

In such a possibility, the answer to the question is YES.

In this possibility, the answer to the question is NO.

We are not able to find a conclusive answer to the question using statement 2.

Hence, we will not be able determine whether a

Statement 2 is NOT sufficient.

__Eliminate answer option D__.

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