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If wxy ≠ 0, does x = y ?

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If wxy ≠ 0, does x = y ? [#permalink]

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If wxy ≠ 0, does x = y ?

(1) w^x = w^y

(2) wxy ≠ xy
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 Dec 2013, 05:40, edited 1 time in total.
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Re: If wxy ≠ 0, does x = y ? [#permalink]

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If wxy ≠ 0, does x = y ?

wxy ≠ 0, means that neither of three is 0. The question asks whether x-y=0.

(1) w^x = w^y --> \(w^{x-y}=1\). Three cases:

\(w=1\) and \(x-y\) is any number;
\(w=-1\) and \(x-y=even\).
\(x-y=0\) and w is any number

Not sufficient.

(2) wxy ≠ xy --> since we know that \(xy\neq{0}\), then this statement implies that \(w\neq{1}\). Not sufficient.

(1)+(2) Since from (2) \(w\neq{1}\), then from (1) we are left with second and third cases. Not sufficient.

Answer: E.

Hope it's clear.
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Re: If wxy ≠ 0, does x = y ? [#permalink]

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New post 08 Dec 2013, 22:14
gmatgambler wrote:
If wxy ≠ 0, does x = y ?

(1) w^x = w^y

(2) wxy ≠ xy


Hello,

Given that w,x and y ≠ 0. we need to find whether x=y

From st 1, we have W^x=W^y

If W = 2 then x=y=2 then yes because different values of x=y will prove st1 to be insufficient in this case
Consider w=1, then x and y can have any values as 1^(Some Power) = 1 Hence no St 1 is not sufficient.
Consider w= -1 then x and y have same values for ex x=y=-3 or or x=-3 and y = -5.

Hence A and D ruled out

Consider st 2, we get w ≠1 still not sufficent....

Combining the 2 statements we get that there are still cases possible for w=-1 for which x ≠y and x=y

Ans E.

Actually if you look at st 2, it gives you ample hint to check for what values of w
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Re: If wxy ≠ 0, does x = y ? [#permalink]

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New post 26 Dec 2013, 01:13
The main example here is if you use W= -1

Than you will see that X=2 and Y=4 could be correct

Ans E
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Re: If wxy ≠ 0, does x = y ? [#permalink]

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New post 31 Jan 2015, 12:37
Hi All,

This DS question can be solved by TESTing VALUES (although recognizing the built-in Number Properties would help make solving this problem easier).

We're told that WXY is not = 0, so NONE of those variables can = 0. We're asked if X = Y. This is a YES/NO question.

To start, it's interesting that this prompt has 3 variables, but the question focuses on just 2 of them. That almost always means that the third variable (in this case, the W) will play a role in defining the other two variables.

Fact 1: W^X = W^Y

Since the 'base' on both sides of this equation are Ws, it might be tempting to think that this X = Y. However, you have to be thorough with your thinking....

IF...
W = 2
X = 3
Y = 3
2^3 = 2^3 and the answer to the question is YES.

But what happens if W = 1 or W = -1? Do the exponents even matter at that point?

IF...
W = 1
X = 1
Y = 5
1^1 = 1^5 and the answer to the question is NO.
Fact 1 is INSUFFICIENT

Fact 2: WXY is NOT = XY

This pinpoints one specific restriction about W....W CANNOT = 1. Unfortunately, it doesn't tell us anything about X and Y

IF....
W =2
X = 1
Y = 1
The answer to the questions is YES.

IF...
W = 2
X = 1
Y = 3
The answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we know...
W^X = W^Y
W CANNOT = 1

IF....
W = 2
X = 3
Y = 3
2^3 = 2^3 and the answer to the question is YES.

IF....
W = -1
X = 1
Y = 3
(-1)^1 = (-1)^3 and the answer to the question is NO.
Combined, INSUFFICIENT.

Final Answer:
[Reveal] Spoiler:
E


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Re: If wxy ≠ 0, does x = y ? [#permalink]

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Re: If wxy ≠ 0, does x = y ?   [#permalink] 23 Feb 2017, 02:25
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