Manhattan GMAT Challenge Problem of the Week – 22 October 2012

by on October 22nd, 2012

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Question

The function F(n) is defined as the product of all the consecutive positive integers between 1 and n^2, inclusive, whereas the function G(n) is defined as the product of the squares of all the consecutive positive integers between 1 and n, inclusive. The exponent on 2 in the prime factorization of F(3)/G(3) is

A. 1
B. 2
C. 3
D. 4
E. 5

Answer

Apply the definitions of the functions to F(3) and to G(3).

F(3) = “the product of all the consecutive positive integers between 1 and n^2, inclusive”
= 1×2×3×4×5×6×7×8×9 (since 3^2 = 9)
= 9!

G(3) = “the product of the squares of all the consecutive positive integers between 1 and n, inclusive”
= 1^2×2^2×3^2
= 1×4×9

F(3)/G(3) = 1×2×3×4×5×6×7×8×9 / (1×4×9) = 2×3×5×6×7×8 = 2×3×5×(2×3) ×7×(2^3) = 2^5×3^2×5×7

The exponent on the 2 is 5.

The correct answer is E.

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