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What is 1/X + 2/Y ?

(1) X + Y = 16
(2) XY = 48

VERITAS PREP OFFICIAL SOLUTION:

Correct Answer: E

From statement 1, we can derive various pairs of values for X and Y that will give us 16, but we don't know which pair is correct. Thus, we can eliminate A and D. From statement 2, we can again came up with possible pairs of values for X and Y that will give us 48, but we have the same problem that we did with statement 1: we don't know which pair we need. We can eliminate B. With 1 and 2 combined, we realize that X and Y have to be 12 and 4. At this point, it might be tempting to say that we can solve for a value, but we can't. We don't know which is which. If we make X=12 and Y=4, our equation becomes 1/12 + 2/4, or 1/12 + 6/12, giving us a solution of 7/12. If X=4 and Y=12, our equation is 1/4 + 2/12, or 3/12 + 2/12, giving us 5/12. Since we can't arrive at one answer, we must answer E.
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