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

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Bunuel
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If x and y are both odd prime numbers and x < y, how many distinct [#permalink] New post  12 Feb 2016, 12:07
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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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livio04
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If x and y are both odd prime numbers and x < y, how many distinct [#permalink] New post  12 Feb 2016, 17:12
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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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Nova12
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Re: If x and y are both odd prime numbers and x < y, how many distinct [#permalink] New post  12 Feb 2016, 15:40
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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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Re: If x and y are both odd prime numbers and x < y, how many distinct [#permalink] New post  16 Feb 2016, 14:58
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2xy can be divide by 1, 2, x, y, 2xy, 2x, 2y, and xy which are 8 in number.
answer D
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Re: If x and y are both odd prime numbers and x < y, how many distinct [#permalink] New post  18 Jun 2017, 03:36
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] New post  04 Feb 2020, 05:37
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] New post  09 Feb 2020, 05:24
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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.

Answer: D
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Re: If x and y are both odd prime numbers and x < y, how many distinct [#permalink] New post  17 Oct 2022, 19:07
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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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