M7MBA wrote: ↑Sun Apr 26, 2020 9:14 am
What is the value of \((x - y)^4?\)
(1) The product of \(x\) and \(y\) is \(7.\)
(2) \(x\) and \(y\) are integers
[spoiler]OA=C[/spoiler]
Source: Manhattan GMAT
Let's take each statement one by one.
(1) The product of \(x\) and \(y\) is \(7.\)
Certainly insufficient as x and y can take any values.
(2) \(x\) and \(y\) are integers.
Certainly insufficient as values for x and y are not given.
(1) and (2) together
Given that xy = 7 and x and y are integers, one of x and y is ±1 and the other is ±7.
Case 1: Say x = 1 and y = 7; thus, \((x - y)^4=(1-7)^4=6^4\); since the exponent (= 4) is even.
Case 2: Say x = 7 and y = 1; thus, \((x - y)^4=(7-1)^4=6^4\)
Case 3: Say x = –1 and y = –7; thus, \((x - y)^4=(–1+7)^4=6^4\)
Case 4: Say x = –7 and y = –1; thus, \((x - y)^4=(-7+1)^4=6^4\); since the exponent (= 4) is even.
We have a unique value of \((x - y)^4=6^4\). Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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