\(X\) 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
Target Test Prep is 20% off right now!
Use code FLASH20
Available with Beat the GMAT members only code
MORE DETAILS
\(X\) is a number that on squaring produces \(Y.\) If \(Y\) has \(3\) factors, how many such \(X\) are present in the
This topic has expert replies
-
Gmat_mission
- Legendary Member
- Posts: 1622
- Joined: Thu Mar 01, 2018 7:22 am
- Followed by:2 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
-
Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7254
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Solution:Gmat_mission wrote: ↑Sun Jan 17, 2021 11:22 am\(X\) 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
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
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
