What is the value of the positive integer \(m?\)
(1) When \(m\) is divided by \(6,\) the remainder is \(3.\)
(2) When \(15\) is divided by \(m,\) the remainder is \(6.\)
Answer: B
Source: GMAT Prep
What is the value of the positive integer \(m?\)
This topic has expert replies

 Legendary Member
 Posts: 1622
 Joined: 01 Mar 2018
 Followed by:2 members
GMAT/MBA Expert
 [email protected]
 GMAT Instructor
 Posts: 16118
 Joined: 08 Dec 2008
 Location: Vancouver, BC
 Thanked: 5254 times
 Followed by:1268 members
 GMAT Score:770
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
When it comes to remainders, we have a nice rule that says:Gmat_mission wrote: ↑Sun Jan 23, 2022 1:22 amWhat is the value of the positive integer \(m?\)
(1) When \(m\) is divided by \(6,\) the remainder is \(3.\)
(2) When \(15\) is divided by \(m,\) the remainder is \(6.\)
Answer: B
Source: GMAT Prep
If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
Target question: What is the value of positive integer m?
Statement 1: When m is divided by 6, the remainder is 3
According to the above rule, we can write the following:
The possible values of m are: 3, 3+6, 3+(2)(6), 3+(3)(6)...
Evaluate to get: the possible values of m = 3, 9, 15, 21, etc.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: When 15 is divided by m, the remainder is 6
According to the above rule, we can conclude that....
Possible values of 15 are: 6, 6 + m, 6 + 2m, 6 + 3m, ...
Aside: Yes, it seems weird to say "possible values of 15," but it fits with the language of the above rule]
Now, let's test some possibilities:
15 = 6...nope
15 = 6 + m. Solve to get m = 9. So, this is one possible value of m.
15 = 6 + 2m. Solve to get m = 4.5
STOP. There are 2 reasons why m cannot equal 4.5. First, we're told that m is a positive INTEGER. Second, the remainder (6 in this case) CANNOT be greater than the divisor (4.5)
If we keep going, we get: 15 = 6 + 3m. Solve to get m = 3. Here, m cannot equal 3 because the remainder (6) CANNOT be greater than the divisor (3).
If we keep checking possible values (e.g., 15 = 6 + 3m, 15 = 6 + 4m, etc), we'll find that all possible values of m will be less than the remainder (6).
So, the ONLY possible scenario here is that m must equal 9
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B