Vincen wrote:Is the product of x and y greater than the sum of x and y?
(1) xy < 0
(2) x > -y
The OA is C.
I don't know how to use both statements together to get an answer. What can I conclude from the statement (2)? Experts, I'd appreciate your help. Thanks.
We have to determine if xy > x + y.
(1) xy < 0
=> One between x and y is negative and the other is positive.
Case 1: Say x = 1 and y = -1. Thus xy = -1*1 = - 1; x + y = -1 + 1 = 0. We see that xy < x + y. The answer is No.
Case 2: Say x = 1/10 and y = -10. Thus xy = -10*(1/10) = - 1; x + y = -10 + 1/10 = -9.90. We see that xy > x + y. The answer is Yes.
No unique answer. Insufficient.
(2) x > -y
Case 1: Say x = 2 and y = -1; (x > -y). Thus xy = -1*2 = - 2; x + y = -1 + 2 = 1. We see that xy < x + y. The answer is No.
Case 2: Say x = 10 and y = -1/10; (x > -y). Thus xy = -10*(1/10) = - 1; x + y = -1/10 + 10 = -9.90. We see that xy > x + y. The answer is Yes.
No unique answer. Insufficient.
(1) and (2) together
From (1), we have xy < 0 => xy is negative; from (2), we have x > -y => x + y > 0 => x + y is positive.
Thus, xy < x + y. The answer is No. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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