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M04-27

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M04-27  [#permalink]

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New post 16 Sep 2014, 00:23
1
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A
B
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E

Difficulty:

  25% (medium)

Question Stats:

71% (00:46) correct 29% (00:43) wrong based on 140 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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Re M04-27  [#permalink]

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New post 16 Sep 2014, 00:23
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. \(\frac{19}{20}\)

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


Answer: A
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: M04-27  [#permalink]

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New post 28 Jul 2015, 16:31
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. \(\frac{19}{20}\)

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

Answer: A



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.
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Re: M04-27  [#permalink]

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New post 29 Jul 2015, 09:10
The question mentions that S defines all the set of fractions >20. Hence all the values for n from 1-19 are taken.
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Re: M04-27  [#permalink]

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New post 16 Dec 2017, 14:03
1
dang this is a good question)
Re: M04-27 &nbs [#permalink] 16 Dec 2017, 14:03
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