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!
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