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kiran120680
Moderator - Masters Forum
Joined: 18 Feb 2019
Last visit: 27 Jul 2022
Posts: 706
Given Kudos: 276
Location: India
Schools: AGSM '20 EDHEC Sept 2019 Intake Great Lakes '21 IE
GMAT 1: 460 Q42 V13
GPA: 3.6
09 Jun 2019, 10:04
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
64% (01:55) correct
36%
(02:03)
wrong
based on 250
sessions
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If m is a positive integer, is √m a prime number?
I. √m leaves a remainder of 1 when divided by 6
II. m has 3 factors
I. √m leaves a remainder of 1 when divided by 6
II. m has 3 factors
09 Jun 2019, 11:44
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Using Statement 1, √m could be 7, and could be prime, or √m could be 25, and could be non-prime.
The only numbers with precisely 3 divisors are the squares of primes: if p is prime, the number p^2 has the divisors 1, p and p^2 (any number with two distinct prime divisors p and q will always have at least the four divisors 1, p, q and pq, so our number here can only have one prime factor p, and if it has exactly 3 divisors, it must be equal to p^2). So Statement 2 is sufficient.
The only numbers with precisely 3 divisors are the squares of primes: if p is prime, the number p^2 has the divisors 1, p and p^2 (any number with two distinct prime divisors p and q will always have at least the four divisors 1, p, q and pq, so our number here can only have one prime factor p, and if it has exactly 3 divisors, it must be equal to p^2). So Statement 2 is sufficient.
01 Dec 2020, 03:34
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IanStewart,buneul
i found that answer should be D
I was not able to prove statement 1 false i only got three numbers that are prime
25,49,121 and square root of them is prime numbers
statement 2 is sufficient
because a perfect square prime has three factors
for me the answer is D, please help
i found that answer should be D
I was not able to prove statement 1 false i only got three numbers that are prime
25,49,121 and square root of them is prime numbers
statement 2 is sufficient
because a perfect square prime has three factors
for me the answer is D, please help
Thanks IanStewart got it 
