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!
What is the value of the positive integer m?
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- Brent@GMATPrepNow
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When it comes to remainders, we have a nice rule that says: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.
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
- GMATinsight
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Question: Value of Positive Integer m = ?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.
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!!!
"GMATinsight"Bhoopendra Singh & Sushma Jha
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