\(X\) is a number that on squaring produces \(Y.\) If \(Y\) has \(3\) factors, how many such \(X\) are present in the

[Gmat_mission]

\(X\) is a number that on squaring produces \(Y.\) If \(Y\) has \(3\) factors, how many such \(X\) are present in the first \(20\) natural numbers?

A) 2
B) 4
C) 5
D) 7
E) 8

Answer: E

Source: e-GMAT

[Scott@TargetTestPrep]

\(X\) is a number that on squaring produces \(Y.\) If \(Y\) has \(3\) factors, how many such \(X\) are present in the first \(20\) natural numbers?

A) 2
B) 4
C) 5
D) 7
E) 8

Answer: E

Source: e-GMAT

Solution:

We are given that Y = X^2. Recall that the only perfect squares that have exactly 3 factors are the squares of prime numbers. Since Y has only 3 factors, X must be a prime such that X^2 will have 2 + 1 = 3 factors. Since there are 8 primes in the first 20 natural numbers (they are 2, 3, 5, 7, 11, 13, 17, and 19), there are 8 values of X.

Answer: E