# GMAT Inequalities - Data Sufficiency

Inequalities and Data Sufficiency are favorite combinations in the GMAT quant section.

Here is a relatively easy question

Is 'a' positive?
1. a - b > 0
2. 2a - b > 0

Correct Answer is Choice E. The data is insufficient.

Let us evaluate statement 1 alone.  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.

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

Alternatively a could be positive. For instance, a = 10 and b could be 3. a - b > 0 and 'a' is positive.

So, statement 1 alone is NOT SUFFICIENT.

Now, let us evaluate statement 2 alone. 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.
1. Let a = -3, b = -100, 2a = -6. 2a > b and a is negative.
2. Let a = 10, b = 12 and therefore, 2a = 20. 2a > b and a is positive.

So, statement 2 alone is NOT SUFFICIENT.

Combining the two statements, we know a - b > 0 and 2a - b > 0.
Let us look at the following two scenarios.
1. a = -3, b = -100 and 2a = -6. a > b and 2a > b. a is negative.
2. a = 20, b = 15 and 2a = 40. a > b and 2a > b. However, a is positive.

Even after combining the data in the two statements, we cannot conclude whether a is positive.

Hence, Choice E is the correct answer.

You can find additional GMAT Inequalities Practice questions here.