It’s time again for another Veritas Prep Challenge Question. Once again you’ll find that exponents will play a fairly significant role in this question. Stay tuned to the GMAT Tip of the Week post tomorrow for an explanation of this question and a quick checklist for everything you need to know about GMAT exponents.

For integers x, y, and z, if (3^x) (4^y) (5^z) = 3,276,800,000 and x + y + z = 15, what is the value of xy/z?

(A) undefined
(B) 0
(C) 3
(D) 5
(E) 15

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3 Responses

1. smith a says:

32768, 00000 is a multiple of 4 and 5, but not a multiple of 3.
Therefore, (3^x) in the above would be yielding a value of 1 implying x = 0, which leads to the answer choice of xyz = 0* yz = 0.

2. Giovanni Gastone says:

3,276,800,000 is split into 32,768 and 100,000.

32,768 is comprised of only factors of 2, and no factors of 3.

100,000 is comprised of factors of 2 and 5, and no factors of 3.

Recognizing that there isn’t any factor of 3 in 3,276,800,000, we know the “x” in “(3^x) (4^y) (5^z) = 3,276,800,000” must be 0 because anything to the power of 0 results in 1. In this case, 3^0 results in 1.

The question asks for the value of xy/z. It doesn’t matter what y or z is, because x is zero, xy must be zero, and xy/z must also be zero.

Giovanni

3. Shrivast says:

Answer should be zero as the number is not a multiple of 3.