Factoring

[afvatcha]

Came accross this question...

Is the integer N a multiple of 15?

N is a Multiple of 20

N+6 is a multiple of 3.

The right answer is C. But how can you use the 3 from part B if it is refing to N + 6.

[nitin_prakash_khanna]

Question is asking whether N is a multiple of 15. i.e Does N has 3^1 * 5^1 , in its prime factor box.?

St1. -> N is multiple of 20. So N has 2^2*5^1 in its prime box, which doesnt give us any info whether N has a 3 in its prime box or not. INSUFFICIENT

St2. -> N+6 = Multiple of 3
N= Multiple of 3 - 6
if you realize 6 is also multiple of 3 , So if you subtract a mulitiple of 3 from other multiple of 3 , it will always be divisible by 3, such as 21-12=9 etc.

So all this tells us is that N has a 3 in its prime box. But doesnt confirm whether it has a 5 in its prime box.
SO INSUFFICIENT.

Combining both gives us the required info that N has 3 and 5 in its prime box and hence it's a multiple of 15 , So Ans C.

Other alternative:
St 1.
N = 20,40,60,80,100,120.....
So we can see 60 &120 are multiple of 15 but others are not. SO INSUFFICIENT

St2.
N+6 = 3,6,9,12,15,18....
N= -3,0,3,6,9,12,15......

So N is a multiple of 3 but cant conlcude whether it's multiple of 15 or not.
So INSUFFICIENT.

Comibing both , you need multiples of 20 which are divisible by 3...So 60,120 ,180....
All of them are multiple of 15.SUFFICIENT.
Ans C.

HTH.

[afvatcha]

Thanks so much.

[Ben Ku]

nitin_prakash_khanna,

Good explanation. Thanks!