If \(x\) and \(y\) are integers, is \(x/y\) an integer?

[AAPL]

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

[Jay@ManhattanReview]

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

Let's take each statement one by one.

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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[Brent@GMATPrepNow]

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

Given: x and y are integers

Target question: Is x/y an integer?

When I SCAN the two statements, they both feel insufficient, AND I'm pretty sure I can identify some cases with conflicting answers to the target question. So, I'm going to head straight to......

Statements 1 and 2 combined
There are several values of x and y that satisfy BOTH statements. Here are two:
Case a: x = 28 and y = 7. In this case, x/y = 28/7 = 4. So, the answer to the target question is YES, x/y is IS an integer
Case b: x = 28 and y = 40. In this case, x/y = 28/40 = 7/10 = 0.7. So, the answer to the target question is NO, x/y is is NOT an integer
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent