If a and b are positive integers, is 3a^2*b divisible by 60?

Question

(1) a is divisible by 10.

(2) b is divisible by 18.

BrainLab · Answer

Question:  \frac{3b*a^2}{60} 
(1)  \frac{3b*(10k)^2}{60}  =  \frac{b*(10k)^2}{20}  a is a multiple of 10 and >0 means even if it's only equal to 10 it's divisible by 20 in the last expression. Sufficient 
(2) Clearly not sufficient
Answer A

Simran145 · Answer

Some people may choose c because they forget to take into account that the question stem has a^2 in it.
So, if a is divisible by 10 = 5*2.
a^2 will have at least two 5s and two 2s.

Thats what the question stem is indirectly asking. Does a^2b have two 2s and one 5.

Thus, 1 is sufficient.

Hence, the answer is A.

stonecold · Answer

For a moment i was about to mark C
then realised that 10 *10 which is the least value of A^2 will be divisible by 20
hence choose A
nice question

septwibowo · Answer

Is  3a^2b  divisible by 60?
- We can change 60 into  2^2*3*5 .
- Because we already have 3 in the numerator, so our job is to make sure whether a or b has  2^2  and 5 as its factor.

#1
- a divisible by 10 or  2^5 . Since our numerator change a into  a^2 , so we MUST HAVE  2^2*5^2  in our numerator.
- Whatever value of b,  3a^2b  divisible by 60.
SUFFICIENT.

#2
- b divisible by 18 or  2*3^2 , Since we still need to have 5 as factor, we do not know whether a have this factor.
- Divisibility of  3a^2b  by 60 depends solely on the a value - which we don't know here.
INSUFFICIENT.

A.

If a and b are positive integers, is 3a^2*b divisible by 60?

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GMAT Data Sufficiency (DS) Questions

If a and b are positive integers, is 3a^2*b divisible by 60?

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