Hi, I came across this problem in GregMat’s 2 month plan [ Week 1 Day 6 - Mega Quant Practice ]

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How many positive integers less than 20 are equal to

the sum of a positive multiple of 3 and a positive

multiple of 4 ?

(A) Two

(B) Five

(C) Seven

(D) Ten

(E) Nineteen

On the session, it was solved as -

Factors of 3 - 3, 6, 9, 12, 15, 18

Factors of 4 - 4, 8, 12, 16

And option selected was (D) 10.

However, since 0 is also a positive integer less than 20, and a multiple of 3 and 4 (0 is a multiple of every integer), can we also include 0 as factors of 3 and 4?

So now, the possible sums are -

3, 4, 7, 10, 11, 13, 14, 15, 16, 17, 18, 19?

But, I don’t see 12 as an option. Am I missing something here?