Let's take each statement one by one.AAPL wrote:Economist GMAT
If \(x\) and \(y\) are integers, is \(x/y\) an integer?
1) Both \(x/4\) and \(x/7\) are integers.
2) \(y/28\) is not an integer.
OA E
1) Both \(x/4\) and \(x/7\) are integers.
All we can deduce that x is a multiple of 4 and 7; thus, x is a multiple of 28; however, we cannot deduce that \(x/y\) an integer. Insufficient.
2) \(y/28\) is not an integer.
Certainly insufficient.
(1) and (2) together
From (1), we have x = 28p, where p is an integer; thus, x/y = 28p/y = 28(p/y). Thus, for x/y to be an integer, p/y must be an integer. From (2), we know that y is not a multiple of 28.
Case 1: Say p = y = 1, we see that x/y = 28(1/1) = 28, an integer. The answer is yes.
Case 2: Say p = 1 and y = 11, we see that x/y = 28(1/11) = fraction, not an integer. The answer is no.
No unique answer. Insufficient.
The correct answer: E
Hope this helps!
-Jay
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