If q is an integer, then q is divisible by how many positive

Question

If q is an integer, then q is divisible by how many positive integers?

(1) If m is a divisor of q, there is only one value of m that satisfies the relationship 1 < m < q.

(2) m=3

Chiranjeevee · Answer

1. m is a divisor of q satisfying 1<m<q. so m is the only factor of q between 1 and q. sufficient
2. m=3 cannot conclude anything. insufficient

Hence A.

for calculation purpose: 
from 1, we can find that q is divisible by 3 positive integers: 1, m,and q

chetan2u · Answer

We are interested in FACTORS of q.....

(1) If m is a divisor of q, there is only one value of m that satisfies the relationship 1 < m < q. 
since it gives that there is ONLY one value between 1 and the number that is also a factor of q, we cam easily say that there are ONLY 3 factors of q - 1, m and q...
SUff....
 although suff, WHAT is the type of number - IT is a PERFECT square

(2) m=3 
there is nothing about q and p given
Insuff

A

hsbinfy · Answer

A.

1)only one value b/w 1 and q . So q is perfect square of odd number.  Suff

2)m=3 . useless

rickyric395 · Answer

1st statement - since m is divisor of q and there is only one value of possible and 1<m<q this equality holds true. We know that prime numbers have only 2 factor i.e 1 and that number, so if we square any prime number then factor of that squared number will increase by 1 eg- 2*2 = 4 [1,2,4], 3*3 = 9[1,3,9]. 5*5 = 25[1,5,25] hence q must be square of any prime number and that make m as the prime number whose square q is. Eg- q as 25, m as 5 then m is only divisor of q between 1 and q. Total factor of q will always be 3.

2nd statement - m=3, there is no info on q, hence this can't help.

Hence answer is A

2nd statement - m=3, there is no info on q, hence this can't help.

Hence answer is A

SaquibHGMATWhiz · Answer

Solution:      
  Pre Analysis:  
  We are  asked the number of factors of integer q

Statement 1:   If m is a divisor of q, there is only one value of m that satisfies the relationship 1 < m < q
  We already know that 1 and q will be a factor of q 
 Now from this statement, we can infer that m is the only other factor 
 Which means  q has 3 factors i.e., 1, m, q  
 Thus,  statement 1 alone is sufficient and we can eliminate options B, C and E

Statement 2:   m=3
  Cannot find the factors of q with this 
 Thus,  statement 2 alone is not sufficient

Hence the right answer is    Option A

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If q is an integer, then q is divisible by how many positive

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