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# Two fair dice are thrown together. what is the probability that the nu

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Intern
Joined: 02 Sep 2015
Posts: 4
Two fair dice are thrown together. what is the probability that the nu  [#permalink]

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22 Sep 2015, 18:18
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Difficulty:

65% (hard)

Question Stats:

56% (02:15) correct 44% (02:46) wrong based on 73 sessions

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Two fair dice are thrown together. what is the probability that the number obtained on one of the dice is a multiple of the number obtained on the other die?

A) 11/18
B) 5/18
C) 5/9
D) 8/9
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Re: Two fair dice are thrown together. what is the probability that the nu  [#permalink]

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22 Sep 2015, 20:36
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Hi rverma007,

What is the source of this question? I ask because you've listed just 4 answer choices, which is not realistic. If you're studying from material that is not proper GMAT material, then you could very well be hurting your chances at scoring at a high level on the Official GMAT.

Regardless, here's how to answer this question. Each of the two dice has 6 possible outcomes (1 - 6, inclusive), so there are (6)(6) = 36 possible pairs of dice rolls.

We have to figure out how many of those pairs include a number that is a multiple of the other number. We can list them out:

1,6 and 6,1
1,5 and 5,1
1,4 and 4,1
1,3 and 3,1
1,2 and 2,1
1,1

2,6 and 6,2
2,4 and 4,2
2,2

3,6 and 6,3
3,3

4,4
5,5
6,6

22 of the 36 options fit the description of what we're looking for. 22/36 = 11/18

Final Answer:

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Re: Two fair dice are thrown together. what is the probability that the nu  [#permalink]

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23 Sep 2015, 09:48
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rverma007 wrote:
Two fair dice are thrown together. what is the probability that the number obtained on one of the dice is a multiple of the number obtained on the other die?

A) 11/18
B) 5/18
C) 5/9
D) 8/9

You can go the other way around:
Find the pairs in which neither is a multiple of the other.
Ignore all pairs with 1 since the other number will be a multiple of 1.

If one number is 2, the other can be 3 or 5. So two possible options. We could have 2 on the other die so total 4 options (2, 3) (2, 5), (3, 2), (5, 2).

If one number is 3, the other can be 4 or 5. Again, there will be 4 total options.

If one number is 4, the other can be 5 or 6. Again, there will be 4 total options.

If one number is 5, the other can be 6. There will be total 2 options.

There are total 4 + 4 + 4 + 2 = 14

Probability that neither is a multiple of the other = 14/36 = 7/18

Probability that one number is a multiple of the other = 1 - 7/18 = 11/18

Answer (A)
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Re: Two fair dice are thrown together. what is the probability that the nu  [#permalink]

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08 Apr 2019, 19:38
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Re: Two fair dice are thrown together. what is the probability that the nu   [#permalink] 08 Apr 2019, 19:38
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# Two fair dice are thrown together. what is the probability that the nu

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