Data Sufficiency

gmattoend wrote:Is y^3 < |y|

(1) y < 1

(2) y < 0

OA: B

Dear Sirs,

How can I solve this problem with algebra?

This question can be solved logically. There is no need to go the Algebraic way.

Question: Is y^3 < |y|?

We see that RHS, |y| is either a positive quantity or zero, while y^3 can be anything positive, negative, or zero.

So, if y = 0, the answer is No. y^3 = |y|; however, if y < 0, the answer is yes, y^3 < |y|.

Statement 1: y < 1

y < 1 has three ranges.

1. 0 < y < 1: It implies that y is a positive fraction. Cube of a positive fraction that is less than 1 is always less than the number itself. Ex.: Say y = 1/2, then y^3 = 1/8 and |y| = 1/2. Here. 1/8 < 1/2. The answer is Yes.

2. y = 0: We have already seen that @ y = 0, y^3 = |y|. The answer is No. No unique answer. Insufficient.

Though we concluded that Statement 1 is not sufficient, let's take the third range too for the sake of understanding.

3. y < 0: It implies that y is negative. We already saw that if y is negative, y^3 < |y|. The answer is Yes.

Statement 2: y < 0

We have discussed this above. Thus, Statement 2 is sufficient. The answer is Yes.

The correct answer: B

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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Hi gmattoend,

The Quant section of the GMAT is NOT a 'math test' - it's a 'critical thinking' test that will involve lots of little calculations as you work through it. As such, you have to be careful about taking a "just do math" approach to this section of the GMAT (since you will likely end up making the section harder than it actually is and limiting how high you score). Most GMAT questions can be approached in more than one way, so one of your goals during your studies should be to learn the various approaches - so that you can use the most efficient approach for each question that you face. With this prompt, TESTing VALUES or using Number Properties would almost certainly be faster and easier than doing Algebra.

GMAT assassins aren't born, they're made,
Rich