x, y

[vishwas.arora]

Problem:

If x^10 - y^10 = 0, what is the value of x^5 - y^5 ?

(1) x and y are both integers
(2) x^3 - y^4 = 0

OA after discussion.

Thanks

Vishwas

[Brent@GMATPrepNow]

Problem:

If x^10 - y^10 = 0, what is the value of x^5 - y^5 ?

(1) x and y are both integers
(2) x^3 - y^4 = 0

OA after discussion.

Thanks

Vishwas

We should begin by asking, "What conclusions can we make about x and y if we know that x^10 = y^10?"

Well, there are 3 cases to consider:
a) x=y (with several sub-cases)
b) x=1 and y=-1
c) x=-1 and y=1

Statement 1: This does not eliminate any cases (entirely).
If x=0 and y=0 (case a), then x^5 - y^5 = 0
If x=1 and y=-1 (case b), then x^5 - y^5 = 2
Since we cannot determine the value of x^5 - y^5 with certainty, statement 1 is not sufficient.


Statement 2: This eliminates case c and some sub-cases within case a.
However, there are still some cases that yield different answers to the target question.
If x=0 and y=0 (case a), then x^5 - y^5 = 0
If x=1 and y=-1 (case b), then x^5 - y^5 = 2
Aside: Notice that we used the same cases from statement 1
Since we cannot determine the value of x^5 - y^5 with certainty, statement 2 is not sufficient.

Statements 1 & 2:
Since we used the same counter-examples to show the insufficiency of each statement, we can conclude that the statements combined are not sufficient and the answer is E.

Cheers,
Brent

[tpr-becky]

exponent questions often deal with the concept of positive/negative/zero - this one certainly does.

if x^10 - y^10 = 0 then that tells us that the absolute value of x = absolute value of y.

When it asks about x^5 - y^5 it is asking about positive negative (because that is what is affected when you switch from even exponents to odd exponents).

Statment 1 - only tells us integers, which does not affect positive negative (so insufficient and your are left with BCE)

Statement 2 - tells us that x is positive or zero (becuase x^3 is negative when x is negative and y^4 is always positive a negative - a positive would always be a negative) But we don't have any information about the nature of y. insufficient, left with CE.

If you try them together you still know that x is positive or zero and have no real info about y - could be positive or negative. So it is insufficient and the answer is E.

[navami]

Thanks Brent

[czarczar]

Got E also.

Thanks Experts.