Problem solving - 1

Problem Solving - Numbers

If (3^4)(5^6)(7^3)=(35^n)(x), where x and n are both positive integers, how many different positive values of n are there?

A) 1

B) 2

C) 3

D) 4

E) 6

Answer - C

(3^4)(5^6)(7^3)=(35^n)(x)

Now 35 = 5 * 7

=> 35^n = 5^n * 7^n

3^4 * 5^3 * (5^3 * 7^3) = (35^n) * x

So x is a multiple of 3^4 * 5^3 n => 3 n is a positive integer So n=1, 2, 3