Problem Solving

Please check your source.
I think the original question is as follows...

Both 5^2 and 3^3 are factors of n × 2^5 × 6^2 × 7^3 where n is a positive integer. What is the smallest possible positive value of n?

Say, N = n × 2^5 × 6^2 × 7^3

If 5^2 and 3^3 are factors of N, then N must contain two 5s and three 3s.

Now, 2^5 × 6^2 × 7^3 does not contain any 5. But it does contain two 3s in 6^2 = (2*3)^2

Hence, the missing two 5s and one 3 must be a factor of n.
Hence, minimum possible value of n is (5^2)*3 = 3*25 = 75

The correct answer is D.

PS : According to the question you have posted, following the similar logic the minimum possible value of n should be 33*(52/2) = 33*26

aman88 wrote:What if the question asked the largest possible value of n?

There is no definite answer to this question. As our requirement is n must have two 5s and one 3, we can find the minimum positive value for n. But the maximum value of n can be the largest possible positive multiple of 75 which we cannot definitely determine.