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What is the value of (x - y)^4? (1) The product of x and y is 7

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What is the value of (x - y)^4? (1) The product of x and y is 7 [#permalink] New post   27 Dec 2010, 14:10
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What is the value of (x - y)^4 ?

(1) The product of x and y is 7.
(2) x and y are integers.
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What is the value of (x - y)^4? (1) The product of x and y is 7 [#permalink] New post   27 Feb 2012, 09:20
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What is the value of (x - y)^4?

(1) The product of x and y is 7.

    Well, this one is clearly insufficient: if \(x=7\) and \(y=1\) then \((x-y)^4=6^4\) and if \(x=14\) and \(y=\frac{1}{2}\) then \((x-y)^4=(\frac{27}{2})^4\), two different answers, hence not sufficient.

(2) x and y are integers. Also insufficient.

(1)+(2) Since \(x\) and \(y\) are integers and \(xy=7\) then either \(x\) and \(y\) are 1 and 7 (or vise-versa) or -1 and -7 (or vise-versa) in any case because of even power: \((x-y)^4=(7-1)^4=(1-7)^4=(-7+1)^4=(-1+7)^4=6^4\). Sufficient.

Answer: C.
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Re: What is the value of (x - y)^4? (1) The product of x and y is 7 [#permalink] New post   16 Jan 2015, 21:03
why can't x = -1 and y = -7 or vice versa?
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Re: What is the value of (x - y)^4? (1) The product of x and y is 7 [#permalink] New post   17 Jan 2015, 12:21
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Hi cg0588,

You ask a good question. X and Y CAN be -1 and -7 (or vice versa). Thankfully, it's easy to prove what happens when either of those options occurs:

(X - Y)^4

First, the positive options:
X = 1, Y = 7
(1 - 7)^4 = (-6)^4 = 1296

X = 7, Y = 1
(7 - 1)^4 = (6)^4 = 1296

Now, the negative options:
X = -1, Y = -7
(-1 -[-7]) = (6)^4 = 1296

X = -7, Y = -1
(-7 - [-1]) = (-6)^4 = 1296

The result stays the SAME.

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Re: What is the value of (x - y)^4? (1) The product of x and y is 7 [#permalink] New post   06 Apr 2020, 13:54
Bunuel wrote:
What is the value of (x - y)^4?

(1) The product of x and y is 7, well this one is clearly insufficient: if \(x=7\) and \(y=1\) then \((x-y)^4=6^4\) and if \(x=14\) and \(y=\frac{1}{2}\) then \((x-y)^4=(\frac{27}{2})^4\), two different answers, hence not sufficient.

(2) x and y are integers. Also insufficient.

(1)+(2) As \(x\) and \(y\) are integers and \(xy=7\) then either \(x\) and \(y\) are 1 and 7 (or vise-versa) or -1 and -7 (or vise-versa) in any case because of even power: \((x-y)^4=(7-1)^4=(1-7)^4=(-7+1)^4=(-1+7)^4=6^4\). Sufficient.

Answer: C.


But what if the question is formulated in another way:
If x and y are integers, what is the value of (x - y)^4?
(1) The product of x and y is 7.
(2) The sum of x and y is -8.

will the answer be A?
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Re: What is the value of (x - y)^4? (1) The product of x and y is 7 [#permalink] New post   06 Apr 2020, 14:07
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frombelarus wrote:
Bunuel wrote:
What is the value of (x - y)^4?

(1) The product of x and y is 7, well this one is clearly insufficient: if \(x=7\) and \(y=1\) then \((x-y)^4=6^4\) and if \(x=14\) and \(y=\frac{1}{2}\) then \((x-y)^4=(\frac{27}{2})^4\), two different answers, hence not sufficient.

(2) x and y are integers. Also insufficient.

(1)+(2) As \(x\) and \(y\) are integers and \(xy=7\) then either \(x\) and \(y\) are 1 and 7 (or vise-versa) or -1 and -7 (or vise-versa) in any case because of even power: \((x-y)^4=(7-1)^4=(1-7)^4=(-7+1)^4=(-1+7)^4=6^4\). Sufficient.

Answer: C.


But what if the question is formulated in another way:
If x and y are integers, what is the value of (x - y)^4?
(1) The product of x and y is 7.
(2) The sum of x and y is -8.

will the answer be A?


Hi frombelarus,

Yes - if you changed the prompt in the way that you wrote (re: we're told that X and Y have to be INTEGERS), then Fact 1 would lead to just one solution (re: 1296) - so it would be SUFFICIENT and Fact 2 would lead to several possible solutions (re: 1296 and 4096, among others) - so it would be INSUFFICIENT. In this situation, the final answer would be A.

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Re: What is the value of (x - y)^4? (1) The product of x and y is 7 [#permalink] New post   06 Apr 2020, 14:08
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frombelarus wrote:
Bunuel wrote:
What is the value of (x - y)^4?

(1) The product of x and y is 7, well this one is clearly insufficient: if \(x=7\) and \(y=1\) then \((x-y)^4=6^4\) and if \(x=14\) and \(y=\frac{1}{2}\) then \((x-y)^4=(\frac{27}{2})^4\), two different answers, hence not sufficient.

(2) x and y are integers. Also insufficient.

(1)+(2) As \(x\) and \(y\) are integers and \(xy=7\) then either \(x\) and \(y\) are 1 and 7 (or vise-versa) or -1 and -7 (or vise-versa) in any case because of even power: \((x-y)^4=(7-1)^4=(1-7)^4=(-7+1)^4=(-1+7)^4=6^4\). Sufficient.

Answer: C.


But what if the question is formulated in another way:
If x and y are integers, what is the value of (x - y)^4?
(1) The product of x and y is 7.
(2) The sum of x and y is -8.

will the answer be A?


Yes, if we were given that x and y are integers, then the answer would be A. In this case from (1) we'd have that (x, y) could be (1, 7), (7, 1), (-1, -7) or (-7, -1). Each of those cases give the same value for (x - y)^4.
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Re: What is the value of (x - y)^4? (1) The product of x and y is 7 [#permalink] New post   18 Oct 2022, 22:59
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