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Sets A and B each consist of three terms selected from the 5

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Kudos [?]: 88 [0], given: 35

Sets A and B each consist of three terms selected from the 5 [#permalink] New post 25 Dec 2012, 23:33
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A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

45% (03:19) correct 55% (01:56) wrong based on 33 sessions
Sets A and B each consist of three terms selected from the first five prime integers. No term appears more than once within a set, but any integer may be a term in both sets. If the average of the terms in Set A is 4 and the product of the terms in Set B is divisible by 22, how many terms are shared by both sets?

(1) The product of the terms in Set B is not divisible by 5.
(2) The product of the terms in Set B is divisible by 14.
[Reveal] Spoiler: OA

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Re: Sets A and B each consist of three terms selected from the 5 [#permalink] New post 26 Dec 2012, 02:23
Expert's post
Sets A and B each consist of three terms selected from the first five prime integers. No term appears more than once within a set, but any integer may be a term in both sets. If the average of the terms in Set A is 4 and the product of the terms in Set B is divisible by 22, how many terms are shared by both sets?

The first five primes are: 2, 3, 5, 7, and 11.
The average of the terms in Set A is 4 --> the sum of the terms is Set A is 4*3=12 --> A={2, 3, 7};
The product of the terms in Set B is divisible by 22 --> B={2, 11, x}.

(1) The product of the terms in Set B is not divisible by 5. This implies that 5 is not in Set B, thus B={2, 11, 3} or B={2, 11, 7}. In both cases, A and B share two terms. Sufficient.

(2) The product of the terms in Set B is divisible by 14. This implies that 7 must be in Set B, thus B={2, 11, 7}. Therefore, A and B share two terms. Sufficient.

Answer: D.
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Re: Sets A and B each consist of three terms selected from the 5   [#permalink] 26 Dec 2012, 02:23
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Sets A and B each consist of three terms selected from the 5

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