Sets A and B each consist of three terms selected from the 5 : GMAT Data Sufficiency (DS)
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# Sets A and B each consist of three terms selected from the 5

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Sets A and B each consist of three terms selected from the 5 [#permalink]

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25 Dec 2012, 23:33
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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]

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26 Dec 2012, 02:23
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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.

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Re: Sets A and B each consist of three terms selected from the 5 [#permalink]

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19 Dec 2014, 17:25
Nice Question..
The first five prime integers are 2, 3, 5, 7, and 11.
Set A: The average of the terms in Set A is 4, so the sum of the terms is (4)(3) = 12. There is only one
way for three of the first five primes to sum to 12: 2 + 3 + 7. Set A is {2, 3, 7}.
Set B: The product of the terms in Set B is divisible by 22, so 2 and 11 are terms in Set B. Set B is
{2, 11, x}, where x can be 3, 5, or 7.
We know that Sets A and B share one term: the 2. If x is either 3 or 7, the sets will share two terms. If
x is 5, the sets will only share one term.

Thus, we can rephrase the question as “Is x = 5?” A definite Yes or No answer leads to a definite
value answer for the number of shared terms (that is, Yes = 1, No = 2).

(1) SUFFICIENT: If the product of the terms in Set B is not divisible by 5, x ≠ 5 and the answer to
our rephrased question is a definite No.

(2) SUFFICIENT: If the product of the terms in Set B is divisible by 14, then 2 and 7 are terms in B.
Therefore, x = 7 and the answer to our rephrased question is a definite No.
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Re: Sets A and B each consist of three terms selected from the 5 [#permalink]

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20 Dec 2014, 22:12
Set B product divisible by 22 i.e should have 2 and 11.
Set A average =4 i.e sum =12 i.e should have 2,3 ,7
a/c to statement 1 set B product not divisible by 5 so set be does not contain 5 so what are the options either 3 or 7. So in Set be could be either of the following 2,3,11 or 2,7, 11. In both the cases it shares two integers with set b i.e 2,3 or 2,7. Hence sufficient.

A/c to statement 2 product of the terms in Set b divisible by 14 so must have 2 and 7 set B has 2,7 and 11 as the integers.Now Set be has two integers common with set A i.e 2 and 7. hence sufficient. Hope this explanation helps.
Re: Sets A and B each consist of three terms selected from the 5   [#permalink] 20 Dec 2014, 22:12
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