MasterGMAT12 wrote:
What should be the approach to do the below question?
How many positive integers less than 20 can be expressed
as the sum of a positive multiple of 2 and a positive multiple
of 3?
(A) 14
(B) 13
(C) 12
(D) 11
(E) 10
We are looking at the set {1,2,3,4,5,...,19}
So all numbers of the form 2+3k (where k>=1) can be considered {5,8,11,14,17} - set 1
Similarly 4+3k (k>=1) gets us {7,10,13,16,19} - set 2
6+3k (k>=1) gets us {9,12,15,18} - set 3
8+3k (k>=1) : already in set 1
10+3k (k>=1) : already in set 2
12+3k (k>=1) : already in set 3
14+3k (k>=1) : already in set 1
16+3k (k>=1) : already in set 2
18+3k (k>=1) : already in set 3
So the full list is {5,7,8,9,10,11,12,13,14,15,16,17,18,19} which is 14 numbers
Thanks for the Questions & Answer.
Number = 2n+3n [i.e. 5,10,15] so my answer was "3" which was not there in the options. So I realized I m doing st wrong but I could not figure out until I saw the solution above.
, above solution will take >2 min. Then I realized we can stop at
, because the # of numbers are already 14 ; the greatest answer option. Is there any other clue to look for?