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# Pedro has a number cube with 24 faces and an integer between

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Retired Moderator
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Pedro has a number cube with 24 faces and an integer between [#permalink]  05 Aug 2018, 14:30
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Question Stats:

100% (00:46) correct 0% (00:00) wrong based on 21 sessions
Pedro has a number cube with 24 faces and an integer between 1 and 24 on each face. Every number is featured exactly once. When he rolls, what is the probability that the number showing is a factor of 24?

[Reveal] Spoiler: OA
$$\frac{1}{3}$$

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Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 173

Kudos [?]: 2977 [0], given: 394

Re: Pedro has a number cube with 24 faces and an integer between [#permalink]  07 Aug 2018, 16:55
Expert's post
Explanation

Probability equals the number of desired outcomes divided by the total number of possible outcomes. Among the integers 1 through 24, there are four factor pairs of 24: (1, 24), (2, 12), (3, 8), and (4, 6), for a total of 8 factors. The total number of possible outcomes when rolling the cube once is 24. The probability that the number chosen is a factor of 24 is $$\frac{8}{24}=\frac{1}{3}$$.
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Re: Pedro has a number cube with 24 faces and an integer between [#permalink]  25 Aug 2018, 00:18
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This question seems flawed to me. Note the word 'between' - that implies the numbers 1 and 24 should not be included. BUT there are 24 faces, so I'm assuming the word 'inclusive' was missed out.
Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 173

Kudos [?]: 2977 [0], given: 394

Re: Pedro has a number cube with 24 faces and an integer between [#permalink]  25 Aug 2018, 00:20
Expert's post
jezzsk8 wrote:
This question seems flawed to me. Note the word 'between' - that implies the numbers 1 and 24 should not be included. BUT there are 24 faces, so I'm assuming the word 'inclusive' was missed out.

I think you have a valid point it should have been 1 and 24 inclusive.
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Re: Pedro has a number cube with 24 faces and an integer between [#permalink]  25 Aug 2018, 04:44
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I think the systematic approach to find the number of factors of an integer is to first do prime factorization of the number, add 1 to each power of the prime numbers and compute their product (the number of factors is equal to the product). E.g. 24=2^3x3 => number of factors = (3+1)(1+1)=8.
Re: Pedro has a number cube with 24 faces and an integer between   [#permalink] 25 Aug 2018, 04:44
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