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Value of m

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Value of m

by manik11 » Mon Feb 29, 2016 6:16 am
What is the value of positive integer m?

(1) The remainder when any integer is divided by m is less than 5.
(2) The remainder when any integer is divided by m is an even number.

OA : B
Source Bell Curves

Hi Experts...I eliminated option B based on the following two cases:

Statement 2) The remainder when any integer is divided by m is an even number
Case 1 : any integer = 5 ; m = 3 Remainder = 2 (Even)
Case 2 : any integer = 5 ; m = 1 Remainder = 0 (Even)
=> Two different values of m

Could you guys please tell me where did I made the mistake?

Thanks!
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by ceilidh.erickson » Mon Feb 29, 2016 6:51 am
Statement 2) The remainder when any integer is divided by m is an even number
Case 1 : any integer = 5 ; m = 3 Remainder = 2 (Even)
Case 2 : any integer = 5 ; m = 1 Remainder = 0 (Even)
=> Two different values of m

Could you guys please tell me where did I made the mistake?
You tested 2 different values for m, but not 2 different values for ANY integer. You should ask, "with this particular value for m, will I ALWAYS get an even remainder?"

If m = 3 and "any integer" = 5, then the remainder is 2 (even).
If m = 3 and "any integer" = 4, then the remainder is 1 (odd).

Thus, m = 3 does not keep our statement true. It's an invalid value.

So, rather than continuing to test numbers, just think: if m is a positive integer, what integer would ALWAYS result in an even remainder, whether divided into an even or an odd integer? The only option --> 1. 1 is a factor of every positive integer, so it will yield a remainder of 0 (even) when divided into any integer.

This is sufficient to tell us that m = 1.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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by Brent@GMATPrepNow » Mon Feb 29, 2016 2:52 pm
manik11 wrote:What is the value of positive integer m?

(1) The remainder when any integer is divided by m is less than 5.
(2) The remainder when any integer is divided by m is an even number.
Target question: What is the value of positive integer m?

Statement 1: The remainder when any integer is divided by m is less than 5.

Useful rule concerning remainders: When positive integer N is divided by positive integer D, the remainder R is such that 0 < R < D
For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0

Given the above rule, statement 1 basically tells us that m is less than or equal to 6.
So, m could equal 6, 5, 4, 3, 2 or 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The remainder when any integer is divided by m is an even number.
How is this possible?
If we're not sure, let's IGNORE statement 2 and see what happens with different values of m.
m = 5. If we divide some positive integer by 5, the remainder will be 4, 3, 2, 1, or 0 (some odd and some even)
m = 4. If we divide some positive integer by 4, the remainder will be 3, 2, 1, or 0 (some odd and some even)
m = 3. Here, the remainder will be 2, 1, or 0 (some odd and some even)
m = 2. Here, the remainder will be 1, or 0 (one odd and one even)
m = 1. The remainder will be 0 (EVEN) AHA!!!
This is the only case where the remainder MUST BE EVEN.
So, it must be true that m = 1

Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent
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by Matt@VeritasPrep » Fri Mar 04, 2016 4:08 pm
You got off to a good start, but remember that you have to consider ALL integers. So 5 gives you two options, but 7 / 3 gives you an odd, so m can't be 3.

A nice approach when working with "any integer" is to choose the most convenient one. (Thinking that number up is the hard part, of course!) Since we can use any integer, why not use 1?

1 divided by ANYTHING greater than 1 leaves an odd remainder. So we must be dividing by 1, otherwise we can't use 1 as our "any integer", contradicting the premise.

So m = 1, and we're set!
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