BTGmoderatorLU wrote: ↑Sun Jan 19, 2020 3:34 pm
Source: Economist GMAT
If a is an even integer and a/18 is an odd integer, which of the following is NOT an even integer?
A. \(\frac{a^2}{54}\)
B. \(\frac{a^2}{12}\)
C. \(\frac{a^2}{9}\)
D. \(\frac{a^2}{6}\)
E. \(\frac{a^2}{2}\)
The OA is
B
Let's take each option one by one.
A. \(\frac{a^2}{54}\) = (a/18)*(a/3) = Odd *a/3; if a = 54, then a /3 = 54/3 = 18, even; thus, Odd*Even = Even. This is not the correct answer.
B. \(\frac{a^2}{12}\): a*(a/12) = (3a/2)*(a/18) = 3a/2* Odd. Since a/18 is odd and 18 has only 2 as its prime even factor, a cannot be a multiple of 4 or greater even numbers. Thus, a/2 = odd, and 3a/2 = Odd*Odd = Odd. Thus, (3a/2)*Odd = Odd*Odd = Odd. Thus is the correct answer.
C. \(\frac{a^2}{9}\) = (a/18)*(2a) = Odd*Even = Even. This is not the correct answer.
D. \(\frac{a^2}{6}\) = (a/18)*(3a) = Odd*Odd*Even = Even. This is not the correct answer.
E. \(\frac{a^2}{2}\) = (a/18)*(9a) = Odd*Odd*Even = Even. This is not the correct answer.
The correct answer:
B
Hope this helps!
-Jay
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