What is the value of the positive integer m ?

Question

(1) When m is divided by 6, the remainder is 3. 
(2) When 15 is divided by m, the remainder is 6.

DesiGmat · Accepted Answer

Here we go -

St1: When m is divided by 6, the remainder is 3. 
 m = 6a + 3
 m can take multiple values..
Clearly insufficient

St2: When 15 is divided by m, the remainder is 6.

15 = mq + 6 ---> mq = 9

as m is a positive integer

(m,q) = (1,9)
(m,q) = (3,3)
(m,q) = (9,1)

Remainder = 6 (given)

0<= remainder < divisor(m)

Only 9 satisfies.

Clearly B is sufficient.

frenzla88 · Answer

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.

General rule for reminder: y=divisor*quotient+reminder=xq+r, where 0 <equal r < x

(1) m=6q+3 so m can be 3, 9, 15, etc. not sufficient.

(2) 15=mq+6. So mq=9. We have 3 possibilities:
1: m=1 and q=9
2: m=3 and q=3
3: m=9 and q=1
But as from the general rule (0 <equal r < x) m>6, m=9
Sufficient

Answer B.

Konstantin1983 · Answer

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.

Statement 1. M=6q+3 Hence m could be 3,9,12,15 and so on. Insufficient
Statement 2. (15)=mq+6. Insufficient since we don't know the values of m and q
Both statements together. mq=9 ==>q=(9/m) and hence m=(54/m)+3 ==> we can multiply both part by m and get an equation (m^2)-3m-54=0. This equation has two roots 9 and (-6). Since m is a positive integer (-6) is out and we are left with m=9. Hence sufficient and answer C. But i am sure that there is a faster way to find a solution

mvictor · Answer

15/m = q + 6

m thus has to be more than 6
15 = mq +6
mq = 9
m can be only 9, since m has to be an integer, and q too.
B.

stonecold · Answer

Excellent Question
Here the concept we need is => Remainder≥0 and Remainder<divisor
in statement 1 => M=3,9etc=> Not suff
in sattement 2 => M must be greater than 6 so M=7,8,9..... but 15/M must generate a remainder of 5 => hence M=9 only

Smash that B

law258 · Answer

Question: m=?

(1) m/6 --> R=3

Therefore m could be 3,9,15....

NOT SUFFICIENT

(2) 15/m --> R=6

There is only one number, 9, that would allow us to get a remainder of 6. We know m must be positive, therefore we are safe to say the number is 9.

SUFFICIENT

B.

BrentGMATPrepNow · Answer

When it comes to remainders, we have a nice rule that says: 
   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

RELATED VIDEO FROM OUR COURSE
 https://www.youtube.com/watch?v=XCxgIR042tE

Kinshook · Answer

Asked: What is the value of the positive integer m ?

(1) When m is divided by 6, the remainder is 3. 
m = 6k + 3; where k is an integer
m = {3,9,15,21,....}
There are mulitple values of m possible
NOT SUFFICIENT

(2) When 15 is divided by m, the remainder is 6.
15 = mn + 6
mn = 9
m = 9/n
m = {9,3,1}: But 15 is completely divisible by 3 & 1.
m = 9 is the only possibility
SUFFICIENT

IMO B

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

What is the value of the positive integer m ?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

What is the value of the positive integer m ?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards