# 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 functionG(n) is defined as the product of the squares of all the consecutive positive integers between 1 andn, inclusive. The exponent on 2 in the prime factorization ofF(3)/G(3) isA. 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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