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N is a positive integer and N=XYZ , where X,Y and Z are unique prime

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N is a positive integer and N=XYZ , where X,Y and Z are unique prime  [#permalink]

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New post Updated on: 03 Jul 2017, 21:42
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N is a positive integer and N=XYZ , where X,Y and Z are unique prime numbers. Which of the following CANNOT be true?

A. N is a multiple of 14
B. N is a multiple of 15
C. N is a multiple of 21
D. N is a multiple of 27
E. N is a multiple of 35

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Originally posted by Skywalker18 on 03 Jul 2017, 20:36.
Last edited by Bunuel on 03 Jul 2017, 21:42, edited 1 time in total.
Renamed the topic and edited the question.
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Re: N is a positive integer and N=XYZ , where X,Y and Z are unique prime  [#permalink]

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New post 03 Jul 2017, 20:54
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Skywalker18 wrote:
N is a positive integer and N=XYZ , where X,Y and Z are unique prime numbers . Which of the following CANNOT be true?
A. N is a multiple of 14
B. N is a multiple of 15
C. N is a multiple of 21
D. N is a multiple of 27
E. N is a multiple of 35


N = XYZ
So XYZ is the prime factorisation of N. None of them has an exponent other than 1. So each each prime factor appears only once in N.

27 = 3^3 is not possible since the exponent of 3 is 3.

Answer (D)
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Re: N is a positive integer and N=XYZ , where X,Y and Z are unique prime  [#permalink]

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New post 03 Jul 2017, 23:30
Of the answer options,
14 can be formed using the product of 2 unique prime numbers(2*7)
15 can be formed using the product of 2 unique prime numbers(3*5)
21 can be formed using the product of 2 unique prime numbers(3*7)
35 can be formed using the product of 2 unique prime numbers(5*7)

Only \(27(3^3)\) (Option D) cannot be formed using the product of 2 unique prime numbers)
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Re: N is a positive integer and N=XYZ , where X,Y and Z are unique prime  [#permalink]

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New post 03 Jul 2017, 23:49
Skywalker18 wrote:
N is a positive integer and N=XYZ , where X,Y and Z are unique prime numbers. Which of the following CANNOT be true?

A. N is a multiple of 14
B. N is a multiple of 15
C. N is a multiple of 21
D. N is a multiple of 27
E. N is a multiple of 35


Answer : D, Since X,Y, Z should be unique, only 27 violates the uniqueness criteria.
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Re: N is a positive integer and N=XYZ , where X,Y and Z are unique prime   [#permalink] 03 Jul 2017, 23:49
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