1. x=2 and y=1 xy=2 will satisfy but x=-4 and y=-3 gives xy as 12 which does not satisfy the given equation. So A or D is ruled out
2. Now x= 0.66 and y=2.4 etc then xy <6. Even if y < 0 i.e if y=-2.4 then also x will be +ve (given) hence xy will still be <0 hence satisfies.
So the answer is B.) alone
- Deepak
xy < 6
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Target question: Is xy < 6?
Statement 1: x < 3 and y < 2
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 0 and y = 0. In this case, xy = (0)(0) = 0. So, the answer to the target question is YES, xy IS less than 6
Case b: x = -5 and y = -5. In this case, xy = (-5)(-5) = 25. So, the answer to the target question is NO, xy is NOT less than 6
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 1/2 < x < 2/3 and y² < 64
Let's see if we can find the greatest possible value of xy.
Since we can see that x is POSITIVE, the maximum value of xy will be achieved when y is also POSITIVE
From the inequality y² < 64, we can conclude that y < 8
He also know that x < 2/3
(8)(2/3) = 16/3 = 5 1/3 (which is less than 6)
Since x < 2/3 and y < 8, we can be certain that xy is less than 6
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
