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

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notrandom
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If q is an integer, then q is divisible by how many positive [#permalink] New post   04 Nov 2013, 23:05
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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
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Re: If q is an integer, then q is divisible by how many positive [#permalink] New post   05 Nov 2013, 00:12
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notrandom wrote:
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


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
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Re: If q is an integer, then q is divisible by how many positive [#permalink] New post   12 Jun 2016, 04:49
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notrandom wrote:
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


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
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Re: If q is an integer, then q is divisible by how many positive [#permalink] New post   12 Jun 2016, 07:59
A.

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

2)m=3 . useless
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If q is an integer, then q is divisible by how many positive [#permalink] New post   20 Sep 2022, 23:53
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
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Re: If q is an integer, then q is divisible by how many positive [#permalink] New post   22 Sep 2023, 08:02
Expert Reply
notrandom wrote:
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


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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Re: If q is an integer, then q is divisible by how many positive [#permalink]
22 Sep 2023, 08:02
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