Is x y ? (1) ax ay (2) a^2*x a^2*y

Question

Is  x > y  ?

(1)  ax > ay 
(2)  a^2 * x > a^2 * y

Aleehsgonji · Answer

1. ax > ay. The inequality between x and y depends on a, which can be either positive or negative.

2. a^2.x > a^2.y 
Though a is positive or negative a^2 will always be positive.
So we can conclude x > y.
2 alone is sufficient, where as 1 alone is not sufficient.
So answer is B

yezz · Answer

Is x > y ?

(1) ax > ay
(2) a^2 . x > a^2 . y

from 1

ax-ay>0

a(x-y)>0 we dont know whether a is -ve or +ve...insuff

from 2

a^2(x-y)>0 a^2 is +ve thus x-y is +ve thus x>y...suff

B

AshForGMAT · Answer

B it is ...

by squaring 'a' you are making it +ve ....

Bunuel · Answer

Is x > y ?

Is x > y? --> is x - y > 0?

(1) ax > ay --> ax-ay>0 --> a(x-y)>0 this equation holds true when both a and (x-y) has the same sign, meaning that they are both positive or both negative. So x-y can be negative or positive. Not sufficient.

(2) (a^2)*x > (a^2)*y --> a^2x-a^2y>0 -> a^2(x-y)>0 -> as a^2 is always positive (it cannot be zero as equation>0) --> (x-y) also must be positive for equation to hold true. Hence x-y>0. Sufficient

Answer: B.

jax91 · Answer

do we not need to consider complex values for a? i mean its not been specified that a is real.

Bunuel · Answer

On the GMAT all numbers are real, so x in even power is greater than or equal to zero.

Avh86 · Answer

What if a=sqrt(-1)?
a^2 will then be negative. I've seen another gmat question where it's tricky like that.

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Bunuel · Answer

Welcome to GMAT Club. Below is an answer to your question. First of all, the GMAT is dealing only with Real Numbers, so even roots from negative numbers are not defined . So, a^{even}\geq{0} . Is x>y? Question: is x-y> 0 (1) ax>ay --> a(x-y)>0 , two cases: A. a>0 and x-y>0 ; OR B. a<0 and x-y<0 ; Depending on a , x-y may or may not be greater than zero. Not sufficient. (2) a^2x > a^2y --> a^2(x-y)>0 --> since a^2>0 ( a^2 cannot be zero, since the product is more than zero) we can safely reduce by it: x-y>0 . Sufficient. Answer: B. Hope it's clear.

Bunuel · Answer

Is x>y? Question: is x-y> 0 (1) ax>ay --> a(x-y)>0 , two cases: A. a>0 and x-y>0 ; OR B. a<0 and x-y<0 ; Depending on a , x-y may or may not be greater than zero. Not sufficient. (2) a^2x > a^2y . Since a^2>0 ( a^2 can not be zero, because if a=0 , then the inequality won't hold true) we can safely reduce by it: x>y . Sufficient. Answer: B. Hope it's clear.

DivyanshuRohatgi · Answer

Hi Bunuel

What if question is

Is x = y

A) ax = bx
B ) a^2x = a^2y

Would then the answer be D

Regards

Bunuel · Answer

No, in this case the answer would be E. Consider: x=y=0 or a=b=0.

KarishmaB · Answer

Responding to a pm:

Is x > y?

(1) ax > ay

We don't know whether a is positive or negative.

Say a is positive.
Divide both sides by a. You get x > y

Say a is negative.
Divide both sides by a. You get x < y (the inequality sign will flip)

Is x > y? We cannot say. Not sufficient.

(2) a^2x > a^2y
a^2 cannot be negative since its the square of a real number. a^2 must be positive only. 
So when you divide both sides by a^2, you get x > y
Sufficient alone.

Answer (B)

chetan2u · Answer

A) ax>ay...
If a is positive, yes otherwise no
Insufficient
B)  a^2x>a^2y....x>y 
Sufficient

B

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Is x > y ? (1) ax > ay (2) a^2x > a^2y

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Is x > y ? (1) ax > ay (2) a^2*x > a^2*y