The fraction \(\dfrac{11!}{77}\) is equivalent to which of the following?

[BTGmoderatorLU]

Source: Princeton Review

The fraction \(\dfrac{11!}{77}\) is equivalent to which of the following?

A. \(2^7 3^3 5^2\)
B. \(2^9 3^4 5^2\)
C. \(2^8 3^4 5^2\)
D. \(2^8 3^4 5^2 7^2\)
E. \(2^8 3^4 5^2 11\)

The OA is C

[gentvenus]

Wow this is a tough one

[Scott@TargetTestPrep]

Source: Princeton Review

The fraction \(\dfrac{11!}{77}\) is equivalent to which of the following?

A. \(2^7 3^3 5^2\)
B. \(2^9 3^4 5^2\)
C. \(2^8 3^4 5^2\)
D. \(2^8 3^4 5^2 7^2\)
E. \(2^8 3^4 5^2 11\)

The OA is C

Solution:

Since 11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 and 77 = 11 x 7, when the former is divided by the latter, the quotient is:

10 x 9 x 8 x 6 x 5 x 4 x 3 x 2 = 2 x 5 x 3^2 x 2^3 x 2 x 3 x 5 x 2^2 x 3 x 2 = 2^8 x 3^4 x 5^2

Answer: C