Princeton GMAT Math Bible------- remainder question

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amyyoung999: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Mon Dec 08, 2008 4:39 pm

by amyyoung999 » Fri Dec 19, 2008 3:10 pm

Please help me to solve this question using easy way

I encountered a few similiar questions when I took the test last month

the question is:

N is an integer,the remainder is 1 when N is divided by 3;the remainer is 2 when N is divided by 4,what's the remainder when N is divided by 12?

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Source: Beat The GMAT — Problem Solving | Fri Dec 19, 2008 3:10 pm

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Fri Dec 19, 2008 3:48 pm

N/3 = Q+1 where Q->quotient 1->remainder
N= 3Q+1

N/4 = Q+2
N= 4Q+2

The first number that will fit the bill is 10

After that u can find the lcm of 3a and 4 which is 12 and then write an expression to derive all other numbers that will leave a remainder 1 when divided by 3 and remainder 2 when divided by 4 as

N = 12Q+10

Eg: 10,22,34

As u can see the remainder will always be 10 when these numbers are divided by 12

Hope this helps!

-Cramya

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