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There are two decks of 10 cards each. The cards in each deck

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There are two decks of 10 cards each. The cards in each deck [#permalink]

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New post 01 Dec 2013, 16:35
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Difficulty:

  95% (hard)

Question Stats:

46% (02:00) correct 54% (02:36) wrong based on 104 sessions

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There are two decks of 10 cards each. The cards in each deck are labeled with integers from 11 to 20 inclusive. If we pick a card from each deck at random, what is the probability that the product of the numbers on the picked cards is a multiple of 6?

A. 0.23
B. 0.36
C. 0.40
D. 0.42
E. 0.46
[Reveal] Spoiler: OA

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Re: There are two decks of 10 cards each. The cards in each deck [#permalink]

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New post 01 Dec 2013, 23:06
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If 6 is a multiple, we need 2 and 3 as a factor of the number. If we factor the numbers 11 through 20 we have:

11 = 11
12 = 2*2*3
13 = 13
14 = 7*2
15 = 5*3
16 = 2*2*2
17 = 17
18 = 3*2*3
19 = 19
20 = 5*2*2

Combos that have a 2 and a 3 as factors (first + second card):

12 + anything - 19 of these possibilities (we count 12 + 12 only once)
14 + 15 - 2 of these possibilities
15 + 16 - 2 of these possibilities
15 + 20 - 2 of these possibilities
18 + anything (except 12, since that is counted in our first option) - 17 of these possibilities

Total possibilities that will be a multiple of 6: 42
Total possibilites: 10*10=100

Probability = 42/100 = 0.42

Answer: D

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Re: There are two decks of 10 cards each. The cards in each deck [#permalink]

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New post 03 Nov 2014, 09:00
James, I did it basically the same way but still took me 2:26 to get the answer. What would be the quickest way to figure this problem out?

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Re: There are two decks of 10 cards each. The cards in each deck [#permalink]

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New post 10 Oct 2017, 05:08
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Re: There are two decks of 10 cards each. The cards in each deck   [#permalink] 10 Oct 2017, 05:08
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There are two decks of 10 cards each. The cards in each deck

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