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# If r is an integer, and 700 < 10!/(10-r)!<1,000, then r=

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4481

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If r is an integer, and 700 < 10!/(10-r)!<1,000, then r= [#permalink]

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21 Nov 2017, 17:23
00:00

Difficulty:

35% (medium)

Question Stats:

75% (00:45) correct 25% (01:25) wrong based on 28 sessions

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[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
[Reveal] Spoiler: OA

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Re: If r is an integer, and 700 < 10!/(10-r)!<1,000, then r= [#permalink]

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21 Nov 2017, 18:37
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

Hi....

$$\frac{10!}{(10-r)!}=10*9*8..*(10-(r-1)$$
Now it is given this value is more than 700 and less than 1000
10*9*8=720
So 10-(r-1)=8.....r-1=10-8=2....r=2+1=3
C
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Re: If r is an integer, and 700 < 10!/(10-r)!<1,000, then r= [#permalink]

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22 Nov 2017, 04:27
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).

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Kudos [?]: 3168 [0], given: 0

GPA: 3.82
If r is an integer, and 700 < 10!/(10-r)!<1,000, then r= [#permalink]

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22 Nov 2017, 18:54
=>

Note that
$$\frac{10!}{(10-r)!} = 10 * (10-1) * … * (10-r+1)$$.

Test different values of $$r$$:
$$r=1 : 10$$
$$r=2 : 10 * 9 = 90$$
$$r=3 : 10 * 9 * 8 = 720$$
$$r=4 : 10 * 9 * 8 * 7 = 5040$$

Therefore,$$r = 3$$.

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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If r is an integer, and 700 < 10!/(10-r)!<1,000, then r=   [#permalink] 22 Nov 2017, 18:54
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