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What is the value of the positive integer m?

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What is the value of the positive integer m?

by AAPL » Mon Mar 12, 2018 5:46 am
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.

The OA is B.

We can solve this DS question as follow,

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.

Option B is the correct answer.

Is there another strategic approach to this DS question? Can any experts help, please? Thanks!
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by Brent@GMATPrepNow » Mon Mar 12, 2018 6:05 am
AAPL wrote: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.
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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by GMATinsight » Mon Mar 12, 2018 6:09 am
AAPL wrote: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.

The OA is B.
Question: Value of Positive Integer m = ?

Statement 1: When m is divided by 6, the remainder is 3.

i.e. m may be 3, 9, 15, 21, 27... etc. Multiple values of m hence
NOT SUFFICIENT

Statement 2: When 15 is divided by m, the remainder is 6.

i.e. 1) 15-6 = 9 is divisible by m and
2) m must be greater than 6 because divisor must be greater than the remainder
3) m must be smaller than 15 otherwise the remainder will be 15 only

Hence, m may be only 9 (Only factor of 9 which is greater than 6)
SUFFICIENT

Answer: Option B

Hope this helps!!!
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