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Is xy> x/y ?

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Is xy> x/y ?

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Is xy> x/y ?

(1) 0 < y < 1
(2) xy > 1

OA : C

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NandishSS wrote:
Is xy> x/y ?

(1) 0 < y < 1
(2) xy > 1

OA : C
S1: Nothing about x; not sufficient

S2: Case 1: x = 2 and y =1: 2*1 is not greater than 2/1, so we get a NO.
Case 2: x = 1 and y = 2: 1*2 is greater than 1/2, so we get a YES; not sufficient

Together: Case 1: y = 1/2 x = 2: (1/2) * 2 is not greater than 2/(1/2), so we get a NO. We could continue to pick numbers, and see that the answer will always be NO to prove sufficiency.

Alternatively, we can use a little logic. S1 tells us that y is a fraction between 0 and 1. S2 tells us, in conjunction with S1, that x and y are both positive. In xy, we're multiplying some positive number (x) by a fraction between 0 and 1 (y) thus making the value smaller. In x/y, we're dividing some positive number (x) by a fraction between 0 and 1 (y) thus making the value bigger. Thus the xy will never be greater than x/y. Together the statements are sufficient. The answer is C.

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NandishSS wrote:
Is xy> x/y ?

(1) 0 < y < 1
(2) xy > 1

OA : C
We have to determine whether xy> x/y.

Statement 1: 0 < y < 1

All we can get from the inequality is that y is a positive fraction and is less than 1.

Say y =1/2, thus xy = x/2 and x/y = 2x

x/2 can be less than, equal to, or more than 2x since we do not know that value of x.

1. If x = 0, x/2 = 2x, the answer is No.
2. If x = a positive number, x/2 < 2x, the answer is No.
3. If x = a negative number, x/2 > 2x, the answer is Yes.

No unique answer. Insufficient.

Statement 2: xy > 1

The inequality tells that neither x nor y is 0 and both are of same sign: either both positive or both negative.

1. Say x = 2 and y = 1, then xy = 2 and x/y = 2, thus xy = x/y, the answer is No.
2. Say x = 1 and y = 2, then xy = 2 and x/y = 1/2, thus xy > x/y, the answer is Yes.

No unique answer. Insufficient.

Statement 1 & 2:

From Statement 1, we get that y is a positive fraction, thus from Statement 2, we get that x is also positive.

1. Say y = 1/2 and x = 4, then xy = 2 and x/y = 8, we see that xy < x/y, the answer is No.

2. Say y = 1/10 and x = 30, then xy = 3 and x/y = 300, we see that xy < x/y, the answer is No.

No matter what value of x and y you take, xy < x/y, thus, the answer is No. Sufficient!

The correct answer: C

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
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