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# M04-27

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Math Expert
Joined: 02 Sep 2009
Posts: 53066

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15 Sep 2014, 23:23
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3
00:00

Difficulty:

25% (medium)

Question Stats:

70% (00:46) correct 30% (00:44) wrong based on 143 sessions

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If $$S$$ is the set of all fractions defined by the formula $$\frac{n}{n+1}$$, where $$n$$ is a positive integer less than 20, what is the product of all the fractions that are in $$S$$?

A. $$\frac{1}{20}$$
B. $$\frac{1}{21}$$
C. $$\frac{1}{2}$$
D. $$\frac{19}{40}$$
E. $$\frac{19}{20}$$

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Math Expert
Joined: 02 Sep 2009
Posts: 53066

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15 Sep 2014, 23:23
1
1
Official Solution:

If $$S$$ is the set of all fractions defined by the formula $$\frac{n}{n+1}$$, where $$n$$ is a positive integer less than 20, what is the product of all the fractions that are in $$S$$?

A. $$\frac{1}{20}$$
B. $$\frac{1}{21}$$
C. $$\frac{1}{2}$$
D. $$\frac{19}{40}$$
E. $$\frac{19}{20}$$

$$\frac{1}{1+1} * \frac{2}{1+2} * ... * \frac{19}{1+19} = \frac{1}{2} * \frac{2}{3} * \frac{3}{4} * ... * \frac{19}{20} = \frac{19!}{20!} = \frac{1}{20}$$

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Senior Manager
Joined: 15 Sep 2011
Posts: 321
Location: United States
WE: Corporate Finance (Manufacturing)

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28 Jul 2015, 15:31
Bunuel wrote:
Official Solution:

If $$S$$ is the set of all fractions defined by the formula $$\frac{n}{n+1}$$, where $$n$$ is a positive integer less than 20, what is the product of all the fractions that are in $$S$$?

A. $$\frac{1}{20}$$
B. $$\frac{1}{21}$$
C. $$\frac{1}{2}$$
D. $$\frac{19}{40}$$
E. $$\frac{19}{20}$$

$$\frac{1}{1+1} * \frac{2}{1+2} * ... * \frac{19}{1+19} = \frac{1}{2} * \frac{2}{3} * \frac{3}{4} * ... * \frac{19}{20} = \frac{19!}{20!} = \frac{1}{20}$$

How do I know whether set $$S$$ is exhaustive of all the fractions within the range of $$0<n<20$$? Had this been a DS question, more information about the contents of the set would have been necessary. I mean, all 20 of them could be there just as much as one or two of them could have been.
Intern
Joined: 14 Jul 2015
Posts: 4

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29 Jul 2015, 08:10
The question mentions that S defines all the set of fractions >20. Hence all the values for n from 1-19 are taken.
Intern
Status: in process
Joined: 18 Jun 2017
Posts: 30
Location: Uzbekistan
Schools: Babson '21
GMAT 1: 690 Q47 V37
GPA: 4
WE: Education (Education)

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16 Dec 2017, 13:03
1
dang this is a good question)
Re: M04-27   [#permalink] 16 Dec 2017, 13:03
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# M04-27

Moderators: chetan2u, Bunuel

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