If m/12 has a remainder of 9 what is the remainder if m is

Question

If m/12 has a remainder of 9 what is the remainder if m is divided by 24? I don't remember all the answers this was from the GMAT.

Amit05 · Answer

What are the Answer choices.. ?? The outcome is 9 and 21.
What is OA ?

nfa1rhp · Answer

This was on the GMAT test I can't remember the answer. Can someone explain why the answer is 9 and 21? I don't understand how to approach this question, thanks.

anonymousegmat · Answer

the question is not silly, so don't worry. get comfortable with these problems as they are very frequent on the gmat... a very basic understanding of number theory/properties is important... and unfortunately not many of us have this skill. people generally don't need to think intuitively about numbers and patterns etc in there day to day lives... 


i thought of it this way:

m is some multiple of 12 + 9. i don't know if the GMAT ever asks about negative multiples (???-- can someone confirm this as I think my methodd falls apart for negative multiples) 

21... 33... 45... 57etc

when they talk about remainders etc... think of the gmat formula y=xq+r where y is the dividend, x is the divisor, q is the quotient and r is the remaineder. these are all integers, and because r is a remainder, it has to be lower than x (or else you'd be able to divide by x one more time)
0=24*0+9
21=24*0+21 <--- 21 is not divisable by 24 so the remainder is 21
33=24*1+9
45=24*1+21
57=24*2+9

the pattern repeats forever

jimmyjamesdonkey · Answer

Not understanding the explanation. Can someone take another stab, especially since this has been logged as a official GMAT question being used.

Thanks.

Mishari · Answer

Did this question show up in a GMATprep practice test or an actual GMAT test ?

jimmyjamesdonkey · Answer

I think he was saying the actual GMAT, hence why he does not know the OA or choices.

ywilfred · Answer

m = 12q1 + 9

if q1 = 0, m = 9 -----> m/24, r = 9
if q1 = 1, m = 21 ----> m/24, r = 21
if q1 = 2, m = 33 ----> m/24, r = 9
if q1 = 3, m = 45 ----> m/24, r = 21
etc

Depending on the answer choices, it's either 9 or 21.

jimmyjamesdonkey · Answer

Can anyone explain the remainder formula in more depth. This is the first I am seeing of this formula, and I have studied from Manhattan, PR, and Kaplan materials.

r019h · Answer

this topic is touched upon in OG 11 but here's an explanation

say you divide 9/7, you get 7*1 + 2, where remainder = 2

now, m/12 leaves a remainder of 9 which can be denoted as:
m = 12x + 9

x=0, m=9
m/24 = 9/24 where R= 9

x=1, m= 21
m/24 = 21/24 where R= 21

x= 2, m= 33
m/24 = 33/24 where R= 9

x= 3, m=45
m/24= 45/24 where R = 21

x=4, m= 57
m/24 = 57/24 where R= 9

hence remainder is either 9 or 21.

jimmyjamesdonkey · Answer

What is x in this equation?

anonymousegmat · Answer

you should buy the official guide and review their math section. they give some rules that we have to follow for the gmat which are very important and some are counterintuitive to what you have learned throughout your whole life (like square root(X^2) =|x|) 

x is the quotient in r019h's explanation. the quotient is "the end result" how many times x qoes into y. they are not interested in fractions or decimals in these types of problems... strictly integers here.

9 divided by 24 = 0 + 9. 24 'goes into' 9 zero times, with a remainder of 9.

although r019h made some mistakes when he got to x=2; he uses y=xq+r.

definately buy the OG. Kaplan, Manhattan etc... are good for some tricks and are helpful but you absolutely need the OG. I read Manhattan's Word Translations. They didn't even mention nCk. they wanted me to draw freaking anagrams.

jimmyjamesdonkey · Answer

I have the OG - I only saw one question in the guide regarding remainders, and I do not recall the explanation breaking out this formula.

If m/12 has a remainder of 9 what is the remainder if m is

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