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06 Sep 2019, 10:56
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Does the integer m have at least 4 positive prime factors?
(1) m/14 is a positive integer.
(2) m/15 is a positive integer.
(1) m/14 is a positive integer.
(2) m/15 is a positive integer.
06 Sep 2019, 11:38
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Statement 1 on its own is not sufficient. This is because it says m/14=k, where k is a positive integer.
The minimum value of m that satisfy this condition is 14 and it has 2 and 7 as prime factors. When m=14 the answer is No.
However when m=210, the prime factors of m are 2,3,5, and 7. The answer in this case however is Yes. Hence not sufficient.
Statement also states that m/15=x, where x is a positive integer.
And the least possible value of m=15. 15 has 3 and 5 as prime factors. The answer to the question when m=15 is No.
However when m=210, which also satisfy the condition in statement 1, there are four prime factors of m, which are 2,3,5, and 7 and the answer to the question posed in the question stem in this case is yes. Hence statement 2 is also not sufficient on its own.
Taking both statements together, we need a value of m which satisfy both conditions, i.e. m/14=k and m/15=x, where k and x are positive integers. We get the minimum value of m to be 14*15=210.
And 210 has four prime factors i.e. 2,3,5, and 7.
Considering 210 is the least possible value of m that satisfy the two conditions, we can answer Yes to the question, does m have at least 4 prime factors.
The answer is therefore C.
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The minimum value of m that satisfy this condition is 14 and it has 2 and 7 as prime factors. When m=14 the answer is No.
However when m=210, the prime factors of m are 2,3,5, and 7. The answer in this case however is Yes. Hence not sufficient.
Statement also states that m/15=x, where x is a positive integer.
And the least possible value of m=15. 15 has 3 and 5 as prime factors. The answer to the question when m=15 is No.
However when m=210, which also satisfy the condition in statement 1, there are four prime factors of m, which are 2,3,5, and 7 and the answer to the question posed in the question stem in this case is yes. Hence statement 2 is also not sufficient on its own.
Taking both statements together, we need a value of m which satisfy both conditions, i.e. m/14=k and m/15=x, where k and x are positive integers. We get the minimum value of m to be 14*15=210.
And 210 has four prime factors i.e. 2,3,5, and 7.
Considering 210 is the least possible value of m that satisfy the two conditions, we can answer Yes to the question, does m have at least 4 prime factors.
The answer is therefore C.
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06 Sep 2019, 17:17
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Bunuel
Does the integer m have at least 4 positive prime factors?
(1) m/14 is a positive integer.
(2) m/15 is a positive integer.
(1) m/14 is a positive integer.
(2) m/15 is a positive integer.
Statement 1 or statement 2:
Individually they might have 4 prime factors or more, but we can only confirm two per each statement so individually they are insufficient.
Combining the statements:
(1) means m contains factors of 2 and 7, (2) says m contains 3 and 5. Therefore combining we know m contains 2, 3, 5, 7 as factors, which is sufficient.
Answer: C
