Problem Solving

If k is divisible by 2, 3, and 15, which of the following is also divisible by these numbers?
(A) k + 5
(B) k + 15
(C) k + 20
(D) k + 30
(E) k + 45

sanju09 wrote:If k is divisible by 2, 3, and 15, which of the following is also divisible by these numbers?
(A) k + 5
(B) k + 15
(C) k + 20
(D) k + 30
(E) k + 45

k is divisible by 2, 3, and 15, so for k + x to be divisible by these numbers x should also be divisible by all these numbers.From the options, only 20 and 30 are divisible by 2, and only 30 is divisible by 3(between 20 and 30), so Option D - k+30

I'm sure there's an "algebraic" way of doing this, but its much simpler to test it with k = 30 (which is the lowest k divisible by 2,3 and 15)

Plugging k = 30, (D) is the only option which is still divisible by 2,3 and 15

sanju09 wrote:If k is divisible by 2, 3, and 15, which of the following is also divisible by these numbers?
(A) k + 5
(B) k + 15
(C) k + 20
(D) k + 30
(E) k + 45

2 , 3 and 15 are co prime numbers...

Now to find the least common no which is divisible by 2, 3 and 15 we take the LCM of the numbers which is 30....

Hence k = 30

Again we need to find the number , divisible by the no's will be by checking the options individually -

A. 30 +5 which is not divisible by 2 and 3

B. 30+15 which is not divisible by 2 and 3

C. 30+20 which is not divisible by 2 and 3

D. 30 + 30 which is divisible by 2 and 3 and 15...

Hence answer will be D..