What Remains of M and N

[prerak.bathia]

Hi,

I think I found a different way to solve a remainders problem, but I just want to make sure that it is a valid way to think about the problem and that my logic is correct. The question from the MGMAT CAT is:

If m and n are positive integers such that m/n = 13.24, which of the following could NOT be the remainder when m is divided by n?

A 12
B 16
C 30
D 48
E 120


While I think I understand the explanation that is given, I did something different which led me to the correct answer. I simply divided each answer choice by .24 (or multiplied by 25/6 as that is easier for me) and the one that did not divide evenly was my answer (Answer choice B). Is that an okay way to solve the problem or will I eventually get burned on a question like that? Also, are there any similar questions that people can find in the OG books for some practice on remainder questions? I tend to spend a lot of time on them.

Thanks for the help!

[RonPurewal]

Hi,

I think I found a different way to solve a remainders problem, but I just want to make sure that it is a valid way to think about the problem and that my logic is correct. The question from the MGMAT CAT is:

If m and n are positive integers such that m/n = 13.24, which of the following could NOT be the remainder when m is divided by n?

A 12
B 16
C 30
D 48
E 120


While I think I understand the explanation that is given, I did something different which led me to the correct answer. I simply divided each answer choice by .24 (or multiplied by 25/6 as that is easier for me) and the one that did not divide evenly was my answer (Answer choice B). Is that an okay way to solve the problem or will I eventually get burned on a question like that? Also, are there any similar questions that people can find in the OG books for some practice on remainder questions? I tend to spend a lot of time on them.

Thanks for the help!

hi -

actually, yes, this method will work.

if you care to know why, i can write the reasons. it would be a rather long and detailed post, full of theory and rather unapplicable to the gmat, but i could write it if you so desire.

--

this problem is modeled on, and is almost exactly identical to, problem 13 in the OG diagnostic test (the test that's in the front of the book). this diagnostic test is the same in the 11th and 12th edition OG books.

there actually aren't that many remainder problems in the OG books, but there are a fair number of them in these forums.
the best way to find them is to perform a search in the forum.

you can use the in-forum search box (which i don't find particularly convenient), or you can search on google and just restrict your search to manhattangmat.com (or even to the forums).
if you don't know how to do this, here's how:
google
site:manhattangmat.com remainder
or
site:manhattangmat.com/forums remainder

[mayanknitc]

That was a good approach. Thanks!

[abysince1984]

[quote="RonPurewal
If m and n are positive integers such that m/n = 13.24, which of the following could NOT be the remainder when m is divided by n?

A 12
B 16
C 30
D 48
E 120



actually, yes, this method will work.

if you care to know why, i can write the reasons. it would be a rather long and detailed post, full of theory and rather unapplicable to the gmat, but i could write it if you so desire.
[/quote]

Ron

Could you please write the reasons why this method will work ? Thanks in advance.

[Ben Ku]

[quote="RonPurewal
If m and n are positive integers such that m/n = 13.24, which of the following could NOT be the remainder when m is divided by n?

A 12
B 16
C 30
D 48
E 120



actually, yes, this method will work.

if you care to know why, i can write the reasons. it would be a rather long and detailed post, full of theory and rather unapplicable to the gmat, but i could write it if you so desire.

Ron

Could you please write the reasons why this method will work ? Thanks in advance.[/quote]

You can rephrase the problem m / n = 13.24 as m / n = 13 + R / n, where R is the remainder. So here, R / n = 0.24, so R = 0.24 n. If n is a whole number, then R / 0.24 must also be a whole number. The answer choices where 0.24 divides evenly into R are possible remainders.

Hope that makes sense.