Problem Solving

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

Source: Q42, pg. 12, GMAT Hacks Challenge Problem Set

OA: A

Easiest way is just to write down the numbers from 1-20 and check them
smallest possible number will be 5 = 3+2
Lets take the next number 6. can it be expressed as sum of multiples of 2 and 3? NO
7 = 4+3
8 = 2+6
9 = 6+3
10 = 4+6
11 = 8+3
12 = 6+6
13 = 4+9
14 = 8+6
15 = 6+9
16 = 4+12
17 = 2+15
18 = 6+12
19 = 4+15

So all numbers except 1,2,3,4 and 6 can be expressed as sum of multiples of 2 and 3.
Ans = 19 - 5 = 14 nos
Hence E

Troika wrote: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

Source: Q42, pg. 12, GMAT Hacks Challenge Problem Set

OA: A

N = 2x + 3y
N = 5 + 2x' + 3y' where x' and y' are whole numbers
Since with a combination of 2x' and 3y' we can get any number greater than 1,
N = 5,7,...,19

So total = 14