Data Sufficiency

VJesus12 wrote:Is |xy| = 12?

(1) (y+4)(x-3) = 0
(2) y=4

The OA is the option C.

I don't understand. From the statement (1) we can get that x=3 and y=-4. Then |xy|=12. So, why is not sufficient the statement (1)?

Experts, could you give me some help? Thanks.

(1) (y+4)(x - 3) = 0

Case 1: Say y = 4, then x may have any value. If x = ±3, then |xy| = 12; however, if x ≠ ±3, then |xy| ≠ 12. The answer is No. Insufficient.

(2) y = 4

We do not have any information about the value of x. Insufficient.

(1) and (2) combined

From (2), we have y = 4 and from (1), we have (y+4)(x - 3) = 0, thus for (y+4)(x - 3) = 0, x must be 3.

So |xy| = |3*4| = 12. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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VJesus12 wrote: I don't understand. From the statement (1) we can get that x=3 and y=-4. Then |xy|=12. So, why is not sufficient the statement (1)?

If (y+4)(x-3) = 0, then we can conclude that EITHER x = 3 OR y = -4 (or both).
So, for example, x = 3 and y = 2 satisfies the equation (y+4)(x-3) = 0, even though y does not equal -4 in this solution.

Cheers,
Brent