A GMAT DS question in Inequalities. Tests your understanding of elementary number properties - specifically, laws of exponents and rules of indices. 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 9: **Is a ^{n} > b^{n}?**

**Statement 1**: a > b

**Statement 2**: ab < 0

From 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?**

If we get a conclusive Yes or conclusive No from the information in the statement(s), the data is sufficient. Note, a conclusive No means that the data is sufficient.

Conversely, if we end up getting Yes in some instances and No in others using the information in the statements, the data is NOT sufficient.

**Q3. When is the answer Yes and when No?**

If a^{n} > b^{n}, the answer is Yes.

If a^{n} ≤ b^{n}, the answer is No. Note that the answer is No if a^{n} = b^{n}.

**Statement 1**: a > b

**Approach Counter Example**

**Example:** a = 5, b = 2, n = 2. Satisfies the condition that a > b.

a^{n} = 25 and b^{n} = 4.

a^{n} > b^{n}

Answer to the question: YES

**Counter Example**: a = 2, b = -5 and n = 2. Satisfies the condition that a > b

a^{n} = 4 and b^{n} = 25.

a^{n} < b^{n}

Answer to the question: NO

A counter example exists.

Statement 1 ALONE is NOT sufficient.

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

**Statement 2**: ab < 0

One of a or b is positive and the other is negative.

**Approach**: Counter Example

Example: a = -5, b = 2, n = 2. Satisfies the condition that ab < 0

a^{n} = 25 and b^{n} = 4.

a^{n} > b^{n}

Answer to the question: YES

**Counter Example**: a = 2, b = -5 and n = 2. Satisfies the condition that ab < 0

a^{n} = 4 and b^{n} = 25.

a^{n} < b^{n}

Answer to the question: NO

A counter example exists.

Statement 2 ALONE is NOT sufficient.

__Eliminate answer option B__.

**Statement 1**: a > b

**Statement 2**: ab < 0

**Approach**: counter example

**Example**: a = 5, b = -2, and n = 2. Satisfies a > b and ab < 0

a^{n} = 25 and b^{n} = 4.

a^{n} > b^{n}

Answer to the question: YES

**Counter Example**: a = 2, b = -5 and n = 2. Satisfies a > b and ab < 0

a^{n} = 4 and b^{n} = 25.

a^{n} < b^{n}

Answer to the question: NO

A counter example exists.

Statements together are not sufficient.

__Eliminate answer option C__.

FNZI A systematic way to identify counter examples

FNZI – look for counter examples in (F)Fractions – (N)Negative – (Z)Zero and finally (I)Integers.

More often than not, we think of integers when we think of numbers. Break that habit – success in data sufficiency depends a lot on breaking this habit.

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