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.
OA is B
Why this cannot be E ? In both statements m can be 3 and 9. Am i missing anything ?
Thanks & Regards
Sachin
What is the value of the positive integer m ?
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- sachin_yadav
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Ok, you got it right regarding Statement 1. With the information Statement 1 we can only tell that m = 6k + 3, with k being unknown, and therefore we cannot determine the value of m from this information.sachin_yadav 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.
OA is B
Why this cannot be E ? In both statements m can be 3 and 9. Am i missing anything ?
So Statement 1 is insufficient.
However, Statement 2 gives us a key piece of information, because there is only one number such that dividing 15 by that number gives a remainder of 6, and that number is 9. If we divide 15 by 3, as you suggested, the remainder is 0.
So Statement 2 gives information sufficient to answer the question.
Choose B.
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When it comes to remainders, we have a nice rule that says:sachin_yadav 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
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I think the mistake that you made here was simply to subtract 6 from 15, from which you got 9, and to think of the factors of 9: 3 and 9. The problem is that 3 goes evenly into 15, so there would be no remainder. (Incidentally, this would also be true for the other factor of 9: 1).sachin_yadav wrote:Why this cannot be E ? In both statements m can be 3 and 9. Am i missing anything ?
Remember with remainder problems:
- if a number is a multiple of the divisor, the remainder is 0.
- the remainder can never be larger than the divisor.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education