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# If x and y are both odd prime numbers and x < y, how many distinct

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Math Expert
Joined: 02 Sep 2009
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If x and y are both odd prime numbers and x < y, how many distinct  [#permalink]

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12 Feb 2016, 11:07
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60% (01:02) correct 40% (01:08) wrong based on 359 sessions

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If x and y are both odd prime numbers and x < y, how many distinct positive integer factors does 2xy have?

A) 3
B) 4
C) 6
D) 8
E) 12

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Joined: 14 Jan 2016
Posts: 6
Re: If x and y are both odd prime numbers and x < y, how many distinct  [#permalink]

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12 Feb 2016, 14:40
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My take on this:

The solution should be the same for all numbers that fulfill the condition above. As x and y are odd prime numbers, they must be > 2. Also, they must be distinct as x<y.

I choose x=3 and y=5:

How many factors does 2x3x5=30 have:

1, 2, 3, 5, 6, 10, 15, 30 = 8 distinct positive integer factors.

Hence, the correct answer is D.
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If x and y are both odd prime numbers and x < y, how many distinct  [#permalink]

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12 Feb 2016, 16:12
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Since 2xy prime factors are x^1*y^1*2^1, its total number or factors must be (1+1)(1+1)(1+1)=2^3=8. Thus, I think D would be the correct answer.
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Re: If x and y are both odd prime numbers and x < y, how many distinct  [#permalink]

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16 Feb 2016, 13:58
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2xy can be divide by 1, 2, x, y, 2xy, 2x, 2y, and xy which are 8 in number.
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Re: If x and y are both odd prime numbers and x < y, how many distinct  [#permalink]

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18 Jun 2017, 02:36
N = a^p * b^q * c^r

a,b,c are primes

Number of factors = (p+1)(q+1)(r+1)
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Re: If x and y are both odd prime numbers and x < y, how many distinct  [#permalink]

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04 Feb 2020, 04:37
Lets say x = 5 , y = 7 Thus 2xy = 70 = 2^1 X 5^1 X 7^1

Number of factors = (1+1)*(1+1)*(1+1) = 8

THus correct answer should be D
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Re: If x and y are both odd prime numbers and x < y, how many distinct  [#permalink]

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09 Feb 2020, 04:24
Bunuel wrote:
If x and y are both odd prime numbers and x < y, how many distinct positive integer factors does 2xy have?

A) 3
B) 4
C) 6
D) 8
E) 12

Solution:

We can let x = 3 and y = 5 Thus:

2 * 3 * 5 = 30

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. We see that 30 has 8 factors.

Alternate Solution:

Since 2xy = 2^1 * x^1 * y^1 and 2, x and y are all distinct prime numbers, the number of factors 2xy has is (1 + 1)(1 + 1)(1 + 1) = (2)(2)(2) = 8.

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Re: If x and y are both odd prime numbers and x < y, how many distinct   [#permalink] 09 Feb 2020, 04:24