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daviesj
Joined: 23 Aug 2012
Last visit: 09 May 2025
Posts: 115
Given Kudos: 35
Status:Never ever give up on yourself.Period.
Location: India
Concentration: Finance, Human Resources
Schools: MBS '17 (A$) Smurfit FT'16 (A)
GMAT 1: 570 Q47 V21
GMAT 2: 690 Q50 V33
GPA: 3.5
WE:Information Technology (Finance: Investment Banking)
26 Dec 2012, 00:33
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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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.
(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.
26 Dec 2012, 03:23
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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.
Answer: D.
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.
JusTLucK04
19 Dec 2014, 18:25
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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.
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.
