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

[amyyoung999]

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?

[cramya]

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