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

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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

OA C

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AAPL wrote:
Tue May 04, 2021 4:41 pm
GMAT Paper Tests

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

OA C
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

Cheers,
Brent
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