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If x and y are prime numbers, and n is a positive integer, what is the

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If x and y are prime numbers, and n is a positive integer, what is the factors’ number of xy^n?

1) xy=21
2) n=2


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[Reveal] Spoiler: OA

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Re: If x and y are prime numbers, and n is a positive integer, what is the [#permalink]

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New post 29 Mar 2016, 23:09
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If x and y are prime numbers, and n is a positive integer, what is the factors’ number of xy^n?

1) xy=21
2) n=2


-> In the original condition, there are 3 variables(x,y,n), which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer. When 1) & 2), 3(7^2) or 7(3^2) is derived. Then, the number of factors is (1+1)(2+1)=6, which is sufficient. Thus, C is the answer.

Note: when different prime numbers are given, the answer is most likely to be B.

-> When a word “different” is given, in 2) n=2, the number of factors is (1+1)(2+1)=6 from x(y^2), which is sufficient.
Therefore, the answer is B.
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Re: If x and y are prime numbers, and n is a positive integer, what is the [#permalink]

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New post 13 Jul 2017, 22:21
MathRevolution wrote:
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If x and y are prime numbers, and n is a positive integer, what is the factors’ number of xy^n?

1) xy=21
2) n=2


-> In the original condition, there are 3 variables(x,y,n), which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer. When 1) & 2), 3(7^2) or 7(3^2) is derived. Then, the number of factors is (1+1)(2+1)=6, which is sufficient. Thus, C is the answer.

Note: when different prime numbers are given, the answer is most likely to be B.

-> When a word “different” is given, in 2) n=2, the number of factors is (1+1)(2+1)=6 from x(y^2), which is sufficient.
Therefore, the answer is B.


1. But the Answer is C.
2. What does "factors' number" even mean? Number of factors?

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Re: If x and y are prime numbers, and n is a positive integer, what is the [#permalink]

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New post 16 Nov 2017, 12:09
Answer has to be C, unless and until x, y are given two different prime numbers

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Re: If x and y are prime numbers, and n is a positive integer, what is the   [#permalink] 16 Nov 2017, 12:09
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