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
x, y
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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
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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.
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.
Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA
Master GMAT Instructor
The Princeton Review
Irvine, CA