Data Sufficiency

If wxy ≠ 0, does x = y ?

(1) w^x = w^y

(2) wxy ≠ xy


I need some clarification on stm1....

Hi,

Stmt 1:

Taking logarithm on both sides;

log (w^x) = log (w^y)

Using power rule,

x times log (w) = y times log (w)

* Edited once *

Dividing throughout by log(w) can be done only if it is not equal to 0. log(w) will become 0 if w equals 1.

Hence, we are not able to divide on both sides by log(w) in the absence of additional information about w.

Thanks.

4gmat i was thinking same like you except i used the rule of exponent for like bases. However according to the solution we are both wrong..

Hi ...

My bad ... The logic for statement 1 falls apart when log (w) = 0; that is, if w = 1.

Statement 2 gives the info that w is not equal to 1.

Is the answer C by any chance ...

official answer is E...

Respect ! <Bow> !!

1 & 2 Together: w must be equal to -1 and in that case x and y can be any even integers (not necessarily same integer).

Not sufficient.

@ Rahul,
Why should the x and y be any even integer.
Infact it can be any integer.
By the conditions given,
1> w^x = w^y
Here w can be one, and x and y can be any positive integer.

2> wxy is not equal to xy..=> w is not equal to 1.

In essense we find w not equal to 0 and 1.

So w can be -1.

1> w^x = W^y

(-1)^1 = (-1)^3
We get x as 1 and y as 3. But infact x and y also can be the same to yield the same answer.

X and y can be anything and not just any even integer.