kevincan wrote:

If k is a two digit positive integer, what is the value of k?

(1) There is exactly 1 three digit integer that is a multiple of both 140 and 21k.

I like A.

Strategy-wise, this is a tough question, therefore, answers C and E are doubtful.

If 140 and 21k has exactly one 3 digit common multiple, then K is solvable.

Find all 3 digit multiples of 140

140, 280, 420, 560, 700, 840, 980

The only ones divisible by 21 are 420 and 840.

If k=20, then there are TWO 3 digit multiples of 140 and 21k (420 and 840).

If k=40, then there is only ONE 3 digit multiple of 140 and 21k (840)

Therefore K=40.

SUFF

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kevincan wrote:

(2) Each prime factor of k is a factor of 140.

The prime factors of 140 = 2, 2, 5, 7

Therefore, the prime factors of K=any combination of above prime factors.

K=10, 20, 28, 35, 70 etc etc. Too many options,

INSUFF