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Source: — Data Sufficiency |
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by Uva@90 » Thu Nov 14, 2013 5:17 am
[email protected] wrote:If x is different from 0, is |x| < 1 ?

(1) x |x| < x

(2) |x| > x
Question ask us whether x is 1 distance away from o, i.e.

----------(-1)-------0---------(1)-----------

whether x lies at either on GREEN or BLUE region or not ?(YES/NO Question)

Statement 1: x |x| < x

it says x<-1 and between 0 and 1

i.e

--------(-1)------0-------(1)-------

So, insufficient.

Statement 2:|x| > x

It says x < 0

--------(-1)---------0---------(1)-----------

Combining 1 and 2 we get

----------(-1)---------0---------(1)---------


Hence sufficient to say NO.

Hope it helps you.

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Uva.
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by [email protected] » Thu Nov 14, 2013 1:36 pm
Hi shibsriz,

This DS question is perfect for TESTing Values.

We're told that X cannot be 0. We're asked "is |X| < 1?" This is a YES/NO question.

Fact 1: X|X| < X

Here, X CANNOT be >= 1
If X = 1/2, then the answer to the question is YES
If X = -2, then the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: |X| > X

Here, X CANNOT be >= 0; X MUST be NEGATIVE.
If X = -1/2, then the answer to the question is YES
If X = -2, then the answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we know that X MUST be NEGATIVE (from Fact 2), but X CANNOT be a NEGATIVE FRACTION (from Fact 1).
The ONLY values that we can use are NEGATIVE and less than -1
This means that the answer is ALWAYS NO.
Combined, SUFFICIENT

Final Answer: C

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Rich
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