# GMAT DS Practice : Inequalities & Exponents

Concept: Inequality Data Sufficiency and Exponents

A GMAT DS question in Inequalities. Tests your understanding of rules of indices, positive and negative numbers. Gist of what is highlighted is one's ability to find a counter example to establish that a statement is not sufficient to answer the question.

Directions for Data Sufficiency

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 -

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

All numbers used are real numbers.

##### Figures

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.

##### Note

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: Is an > bn?

1. a > b
2. ab < 0

Video explanation will be added soon

#### What kind of an answer will the question fetch?

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

#### 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.

#### When is the answer Yes and when No?

If an > bn, the answer is Yes.

If an ≤ bn, the answer is No. Note that the answer is No if an = bn.

#### Statement 1: a > b.

Approach Counter Example

Example: a = 5, b = 2, n = 2
an = 25 and bn = 4.
an > bn

Counter Example: a = 2, b = -5 and n = 2
an = 4 and bn = 25.
an < bn

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
an = 25 and bn = 4.
an > bn

Counter Example: a = 2, b = -5 and n = 2
an = 4 and bn = 25.
an < bn

A counter example exists.

Statement 2 ALONE is NOT sufficient.

Eliminate choice B.
Choices narrow down to C or E.

#### Statement Together: a > b and ab < 0

Approach: counter example

Example: a = 5, b = -2, and n = 2
an = 25 and bn = 4.
an > bn

Counter Example: a = 2, b = -5 and n = 2
an = 4 and bn = 25.
an < bn

A counter example exists.

Together the statements are NOT sufficient.

Eliminate choice C.

Choice (E) is the answer.

FNZI A systematic way to identify counter examples is to follow this simple FNZI – look for counter examples in Fractions – Negative – Zero and finally 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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