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.