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Re: What is the value of the positive integer m ?
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14 Jan 2015, 06:45

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
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Re: What is the value of the positive integer m ?
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14 Jan 2015, 16:06

1

2

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

What is the value of the positive integer m ?
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21 Aug 2016, 05:12

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

Re: What is the value of the positive integer m ?
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12 Mar 2018, 07:09

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Bunuel 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.

Kudos for a correct solution.

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