If wxy ≠ 0, does x = y ?

Question

(1) w^x = w^y

(2) wxy ≠ xy

Bunuel · Accepted Answer

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
eq{0} , then this statement implies that  w
eq{1} . Not sufficient.

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

Answer: E.

Hope it's clear.

BrentGMATPrepNow · Answer

Target question :    Does x = y?

Given : wxy ≠ 0

IMPORTANT: When I scan the two statements, I can see that this question is testing us on our knowledge about when we can conclude that two exponents are equal. 
For statement 1, many students will conclude that, if w^x = w^y, then it must be true that x = y. 
HOWEVER,  this is true only if w does NOT equal 0, 1 or -1 
For example, if 1^x = 1^y, we can't then conclude that x = y 
Given all of this, we can jump straight to .....

Statements 1 and 2 combined    
There are many values of w, x and y that satisfy BOTH statements. Here are two: 
 Case a : w = -1, x = 2 and y = 2. These values work because (-1)^2 = (-1)^2. In this case, the answer to the target question is  YES, x = y 
 Case b : w = -1, x = 2 and y = 4. These values work because (-1)^2 = (-1)^4. In this case, the answer to the target question is  NO, x does NOT equal y 
Since we cannot answer the  target question  with certainty, the combined statements are NOT SUFFICIENT

Answer: E

WoundedTiger · Answer

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

Paris75 · Answer

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

EMPOWERgmatRichC · Answer

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:  E

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

pushkar633 · Answer

Please explain where i am wrong:

According to condition 1: 
=> w^(x-y) = 1
=> w^(x-y) * w = 1* w
=> w^(x-y+1) = w^1
=> x-y+1 = 1------ Comparing the powers as bases are same
Hence x=y

Can't we find the answer using condition 1 only?

EMPOWERgmatRichC · Answer

Hi pushkar633,

Data Sufficiency questions 'test' a number of different skills (more than just 'math' skills), so you have to be thorough with your thinking - and make sure that you're considering all of the possibilities. When dealing with Fact 1 in this particular prompt, what if W = 1? In THAT situations, couldn't each of X and Y be almost anything (and by extension, is it possible that X and Y are NOT equal?)?

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

Pritishd · Answer

Hi Rich. Would be great if you can elaborate on the highlighted text - How did you deduce that conclusion?

EMPOWERgmatRichC · Answer

Hi Pritishd,

In DS questions, the information in each of the two Facts is often 'restrictive' in some way - meaning that you can eliminate some possible values for your variables and/or narrow down how certain variables relate to one another. In this prompt, Fact 2 tells us:

2) wxy ≠ xy

In other words...

(W)(X)(Y) ≠ (X)(Y)

The one difference between the product on the 'left' and the product on the 'right' is the inclusion of a "W." We're told that those two products are NOT equal to one another.

IF.... W = 1, then we would have...

(1)(X)(Y) and (X)(Y)
(X)(Y) and (X)(Y)

Those two products are the exact SAME value, meaning that, when W = 1, those two products ARE equal to one another. Fact 2 tells us that THAT is not allowed though, so by extension, W CANNOT equal 1.

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

KanishkM · Answer

From 1  w^x = w^y

(-1)^2 = {-1}^4, x !=y, This answers the question No
(2)^2 = {2}^2, x =y, This answers the question Yes

From 2 wxy ≠ xy
again x and y can be any value, 
2*2*2 ≠ 4, but x=y,This answers the question Yes
-1*1*3 ≠ 3, x !=y, This answers the question No

When you combine both the statements we can use the same test cases

E

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If wxy ≠ 0, does x = y ?

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GMAT Data Sufficiency (DS) Questions

If wxy ≠ 0, does x = y ?

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