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The numbers in which of the following pairs do NOT have

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boomtangboy
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The numbers in which of the following pairs do NOT have [#permalink] New post   28 Apr 2012, 21:43
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The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common ?

A. 10 and 20
B. 12 and 18
C. 24 and 32
D. 21 and 63
E. 22 and 88
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C
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Bunuel
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Re: The numbers in which of the following pairs do NOT have [#permalink] New post   29 Apr 2012, 04:12
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boomtangboy wrote:
The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common ?

A. 10 and 20
B. 12 and 18
C. 24 and 32
D. 21 and 63
E. 22 and 88


There is no need to make prime factorization of all numbers and to check whether they have a pair of distinct prime divisors in common.

32 has only one prime 2 (32=2^5) in its prime factorization, so it can not have a PAIR of distinct prime divisors in common with ANY of the numbers.

Answer: C.
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Re: The numbers in which of the following pairs do NOT have [#permalink] New post   23 Jul 2012, 22:03
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I worked down from A, but Bunuel solution is ingenious.

The problem states...."The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common ?"

32 only has 2 as a prime factor so clearly not a distinct pair, thus it's automagically
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BrentGMATPrepNow
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Re: The numbers in which of the following pairs do NOT have [#permalink] New post   02 Dec 2020, 10:06
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boomtangboy wrote:
The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common ?

A. 10 and 20
B. 12 and 18
C. 24 and 32
D. 21 and 63
E. 22 and 88


A. 10 and 20
10 = (2)(5)
20 = (2)(2)(5)
So, 10 and 20 both have 2 as a prime divisor, and they both have 5 has a prime divisor.
In other words, they have a PAIR a prime divisors in common
Eliminate A

B. 12 and 18
12 = (2)(2)(3)
18 = (2)(3)(3)
So, 12 and 18 both have 2 as a prime divisor, and they both have 3 has a prime divisor.
In other words, they have a PAIR a prime divisors in common
Eliminate B

C. 24 and 32
32 = (2)(2)(2)(2)(2)
So, 32 has only ONE distinct prime divisor
As such, it's impossible for 24 and 32 to have a PAIR a prime divisors in common

Answer: C

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Brent
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Re: The numbers in which of the following pairs do NOT have [#permalink] New post   05 Jun 2023, 18:59
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Re: The numbers in which of the following pairs do NOT have [#permalink]
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