If j is a multiple of 12, and k is a multiple of 21, then jk must be a multiple...

[BTGmoderatorLU]

Source: Princeton Review

If j is a multiple of 12, and k is a multiple of 21, then jk must be a multiple of which of the following?

A. 8
B. 15
C. 22
D. 28
E. 35

The OA is D

[Brent@GMATPrepNow]

Source: Princeton Review

If j is a multiple of 12, and k is a multiple of 21, then jk must be a multiple of which of the following?

A. 8
B. 15
C. 22
D. 28
E. 35

The OA is D

j is a multiple of 12
This means we can write j = 12n (for some integer n)

k is a multiple of 21
This means we can write k = 21m (for some integer m)

jk must be a multiple of which of the following?
jk = (12n)(21m)
= (4)(3)(n)(7)(3)(m)
= (28)(3)(n)(3)(m)

Clearly, jk is a multiple of 28

Answer: D

[Scott@TargetTestPrep]

Source: Princeton Review

If j is a multiple of 12, and k is a multiple of 21, then jk must be a multiple of which of the following?

A. 8
B. 15
C. 22
D. 28
E. 35

The OA is D

Solution:

Since j is a multiple of 12 and k is a multiple of 21, jk must be a multiple of the LCM of 12 and 21 and all its factors. Since the LCM of 12 and 21 is 3 x 4 x 7 = 84 and one of its factors is 28, jk is a multiple of 28.

Answer: D