MathRevolution wrote:

[GMAT math practice question]

If r is an integer, and \(700 < \frac{10!}{(10-r)!}<1,000\), then r=

A. 1

B. 2

C. 3

D. 4

E. 5

An easy way to solve this question is to plug in the answers given, calculate the value of \(\frac{10!}{(10-r)!}\) and see whether it satisfies or violates the inequality in the problem prompt.

A/\(r = 1\)

This gives us: \(\frac{10!}{(10-r)!} = \frac{10!}{9!} = 10\). This violates the inequality given in the problem prompt.

B/ \(r = 2\)

This gives us: \(\frac{10!}{(10-r)!} = \frac{10!}{8!} = 10*9 = 90\). This also violates the inequality given in the problem prompt.

C/ \(r = 3\)

This gives us: \(\frac{10!}{(10-r)!} = \frac{10!}{7!} = 10*9*8 = 720\). This satisfies the inequality given in the problem prompt, therefore, this is our answer

(we can afford to stop here since this is not a DS question nor is the unknown a polynomial/non-integer with multiple potential values).Thus, the answer is C.