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555-605 (Medium)|   Algebra|      
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eresh
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What is the value of (x - y)^4? Updated on: 03 Jul 2013, 00:34
Originally posted by eresh on 15 Oct 2009, 15:58.
Last edited by Bunuel on 03 Jul 2013, 00:34, edited 1 time in total.
Edited the question and added the OA
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C
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Difficulty:

25% (medium)

Question Stats:

66% (00:59) correct 34% (01:14) wrong based on 156 sessions

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-value-of-x-y-128238.html
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C
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yangsta8
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What is the value of (x - y)^4? 15 Oct 2009, 16:08
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Statement 1)
If xy = 7 then considering the following two scenarios
x = 7 y =17 then (x-y)^4 = 6^4
x = 14 y = ½ then (x-y)^4 = 13.5^4
Not suff.

Statement 2)
X and Y are integers means that x=1 y=7 or y=1 x=7, since 7 is prime it’s only factors are 1 and itself.
(1-7)^4 = -6^4
(7-1)^4 = 6^4
These are both equal hence sufficient.

ANS = B
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What is the value of (x - y)^4? 15 Oct 2009, 16:22
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x and y are integers only 7 and 1 is valid.. so its cannot be B.

both statements are required to solve the problem
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yangsta8
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What is the value of (x - y)^4? 15 Oct 2009, 16:40
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pittgreek
x and y are integers only 7 and 1 is valid.. so its cannot be B.

both statements are required to solve the problem
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Sorry my working for B was actually assuming that the integers xy = 7 which actually implies ANS = C.

Silly mistake :shock:
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Economist
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What is the value of (x - y)^4? 15 Oct 2009, 23:06
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yangsta8
pittgreek
x and y are integers only 7 and 1 is valid.. so its cannot be B.

both statements are required to solve the problem

Sorry my working for B was actually assuming that the integers xy = 7 which actually implies ANS = C.

Silly mistake :shock:
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When I saw your first post..I was like WTF...what am I doing today !! :) Answer SHOULD be C :)
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yangsta8
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What is the value of (x - y)^4? 15 Oct 2009, 23:26
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Economist

When I saw your first post..I was like WTF...what am I doing today !! :) Answer SHOULD be C :)
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yep Friday is not a good day for brain activity hehe :)

Posted from my mobile device
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What is the value of (x - y)^4? 16 Oct 2009, 01:07
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eresh
What is the value of \((x - y)^4\)?
(1) The product of x and y is 7.
(2) x and y are integers.

Please answer what should be the best approach trying this kind of problem?
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we would need both statements to solve. would go with C
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What is the value of (x - y)^4? 03 Jul 2013, 00:29
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[quote="eresh"]What is the value of \((x - y)^4\)?
(1) The product of x and y is 7.
(2) x and y are integers.

ANSWER 1 ALONE SUFFICIENT

1) THE INTEGERS CAN BE 1 AND 7 OR -1 AND -7
(1-7) POWER 4 =-6 POWER 4. Therefore the value is 1296

If they are -1 and -7 still (-1-(-7)) = -1+7 = 6 (POWER 4) =1296. Therefore 1 alone sufficient.

2) Clearly insufficient.
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What is the value of (x - y)^4? 03 Jul 2013, 00:37
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dasikasuneel
eresh
What is the value of \((x - y)^4\)?
(1) The product of x and y is 7.
(2) x and y are integers.

ANSWER 1 ALONE SUFFICIENT

1) THE INTEGERS CAN BE 1 AND 7 OR -1 AND -7
(1-7) POWER 4 =-6 POWER 4. Therefore the value is 1296

If they are -1 and -7 still (-1-(-7)) = -1+7 = 6 (POWER 4) =1296. Therefore 1 alone sufficient.

2) Clearly insufficient.
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Unfortunately that's not correct. Notice that we are NOT told that x and y are integers.

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-value-of-x-y-128238.html
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