# GMAT Math Questions | GMAT Inequalities Q8

#### Properties of Positive and Negative numbers | GMAT Sample Questions

A GMAT DS question in Inequalities. Tests your understanding of elementary number properties - specifically, positive and negative numbers. A GMAT 650 level data sufficiency sample question in inequalities.

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.
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 8: Is 'a' positive?

Statement 1: a - b > 0
Statement 2: 2a - b > 0

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### Explanatory Answer | GMAT Inequalities DS

#### Step 1: Decode the Question Stem

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".

#### Step 2: Evaluate Statement 1 ALONE

Statement 1: a - b > 0.

From this statement we can conclude that a > b. But we cannot gain any insight about whether 'a' is positive.
Here are two possible scenarios where the statement is true without helping us arrive at any conclusion.

Example: Both 'a' and 'b' could be negative and 'a' could be greater than 'b'.
For example, a = -5 and b = -10. a - b > 0. 'a' is negative.

Counter Example: Alternatively 'a' could be positive.
For example, a = 10 and b could be 3. a - b > 0 and 'a' is positive.
A counter example exists.

Statement 1 alone is NOT sufficient.
Eliminate answer options A and D.

#### Step 3: Evaluate Statement 2 ALONE

Statement 2: 2a - b > 0.

From this statement we can conclude that 2a > b. However, we cannot gain any insight about whether 'a' is positive.
Let us check out the following two scenarios.

Example: Let a = -3, b = -100, 2a = -6. 2a > b and 'a' is negative.
Counter Example: Let a = 10, b = 12. Therefore, 2a = 20. 2a > b and a is positive.

A counter example exists.
Statement 2 ALONE is NOT sufficient.
Eliminate option B. Choices narrow down to C or E.

#### Step 4: Evaluate statements together

Statement 1: a - b > 0.
Statement 2: 2a - b > 0.

Let us look at the following two examples.
Example: a = -3, b = -100 and 2a = -6. a > b and 2a > b. 'a' is negative.
Counter Example: a = 20, b = 15 and 2a = 40. a > b and 2a > b. However, 'a' is positive.
A counter example exists.
Even after combining the information in the two statements, we cannot conclude whether 'a' is positive.

Statements together are not sufficient.

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