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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7367
GMAT 1: 760 Q51 V42 GPA: 3.82
If 10!/(10-r)!<1,000, what is the greatest possible value of r?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 81% (01:47) correct 19% (01:14) wrong based on 58 sessions

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If $$\frac{10!}{(10-r)!}<1,000$$, what is the greatest possible value of r?

A. 1
B. 2
C. 3
D. 4
E. 5

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Director  V
Joined: 04 Dec 2015
Posts: 750
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
If 10!/(10-r)!<1,000, what is the greatest possible value of r?  [#permalink]

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MathRevolution wrote:
If $$\frac{10!}{(10-r)!}<1,000$$, what is the greatest possible value of r?

A. 1
B. 2
C. 3
D. 4
E. 5

$$\frac{10!}{(10-r)!}<1,000$$

By Checking the options the Greatest possible value of $$r$$ is $$= 5$$

Lets check the value of $$r = 5$$

$$\frac{10!}{(10-5)!}$$ $$=> \frac{10!}{5!}$$

$$\frac{10*9*8*7*6 * 5!}{5!}$$ $$=> 10*9*8*7*6$$

$$(10*9 = 90)$$ and $$(8*7 = 56)$$ ------------ (i)

$$90*50 = 4500$$ ------- (This value is greater than $$1000$$)

Therefore (i) will have value greater than $$1000$$.

Hence $$5$$ cannot be the value of $$r$$.

If we have the value without $$7$$ in (i), we will get a value less than $$1000$$.

Lets check for value of $$r = 3$$

$$\frac{10!}{(10-3)!}$$ $$=> \frac{10!}{7!}$$

$$\frac{10*9*8*7!}{7!}$$

$$10*9*8 = 720$$ ------------- (Less than $$1000$$)

Therefore greatest possible value of $$r = 3$$

Answer (C)...

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Re: If 10!/(10-r)!<1,000, what is the greatest possible value of r?  [#permalink]

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==>If you substitute r=1, 2, 3, 4.., for r=4, you get 10!/(10-4)!=10*9*8*7=5,040>1,000, and for r=3, you get 10!/(10-3)!=10*9*8=720<1,00.

Thus, the greatest possible value of r is r=3. The answer is C.
Answer: C
_________________ Re: If 10!/(10-r)!<1,000, what is the greatest possible value of r?   [#permalink] 12 Jul 2017, 01:10
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# If 10!/(10-r)!<1,000, what is the greatest possible value of r?

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