Manhattan GMAT Challenge Problem of the Week – 22 October 2012
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Question
The function F(n) is defined as the product of all the consecutive positive integers between 1 and
, 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 , inclusive”
= 1×2×3×4×5×6×7×8×9 (since 
= 9)
= 9!
G(3) = “the product of the squares of all the consecutive positive integers between 1 and n, inclusive”
= 
×
×
= 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×(
) = 
××5×7
The exponent on the 2 is 5.
The correct answer is E.
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