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