Is |x| 1 ? (1) x^y x (2) y = -1/2

Question

Is |x| > 1 ?

(1) x^y > x 
(2) y = -1/2

kntombat · Answer

aarish2102 , I did get the answer correct, but can you still provide the official explanation please ?

AndrewN · Answer

A simple question, but well designed. I am a proponent of starting with the easier looking statement, so I would start with  Statement (2) . It takes all of 2 seconds to realize that information on  y  only will not help us answer the question being asked, so  Statement (2) is NOT sufficient . Eliminate answer choices (B) and (D).

Statement (1)

x^y > x

For the inequality to hold,  x  cannot be equal to 0 or 1. It is not hard to see that positive integer values other than 1 for both  x  and  y  will yield a valid inequality. For instance,

2^3 > 2   √

We could then turn back to the original question, using 2 for  x :

|2| > 1

The answer is Yes. But can we find a way to break this inequality, in light of the fact that Statement (2) introduced us to the notion that  y  could be a negative non-integer? Experiment with the value given for  y . x^(-1/2) is the same as 1/x^(1/2), or 1/√x.

\frac{1}{\sqrt{x}} > x

A fraction between 0 and 1 will lead us to a valid inequality. For instance, 1/4 would eventually lead to 2 (since √(1/4) = 1/2, and 1/(1/2) = 2).

Clearly, 1/4 would not be greater than 1, so the answer to the question would be No, and conflicting results would lead us to the conclusion that  Statement (1) is NOT sufficient .

Together, the statements provide an exact value for  y , so we can deduce that we would be tracing the latter path from above, and the answer to the question would be No. A definitive No to the question provides a consistent answer, so   (C) must be correct  .

- Andrew

Kinshook · Answer

Asked: Is |x| > 1 ?

(1) x^y > x
If y=0; x<1
But if y=2: x^2 - x>0; x(x-1)>0; x>1 or x<0
Since y is unknown
NOT SUFFICIENT

(2) y = -1/2
There is no relationship between x & y.
NOT SUFFICIENT

(1) + (2)
(1) x^y > x
(2) y = -1/2
x^(-1/2) > x
\(\frac{1}{\sqrt{x}} >x\)
\(\frac{1}{\sqrt{x}} - x > 0\)
\((1 - x\sqrt{x})/\sqrt{x} > 0\)
0<x<1
|x| < 1
SUFFICIENT

IMO C

Devoshish · Answer

what if x is equal to 1

bumpbot · Answer

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Is |x| > 1 ? (1) x^y > x (2) y = -1/2

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