eGmat question (600 level)
If Q is a perfect square of an odd positive integer and if 8Q^8 has four prime factors, then how many prime factors does √Q have?
A) 1
B) 2
C) 3
D) 4
E) cannot be determined
Plz explain the solution.
Hi Shashank,
Answer should be C.
Given, Q is a perfect square and also its an odd number.
So, Q can be 9, 25 , 49 etc.
But also given 8*Q^8 has four prime factors.
Since, 8 is nothing but 2^3, So 2 is a prime and Q is an odd number. So Q don’t have a “2” as a prime factor, so it should have three other odd prime factors.
Like, Q could be 3^2 * 5^2 * 7^2
So, sqrt of Q will have the same number of prime factors as Q.
So, the answer is C.
Hope this helps.
