cramya wrote:An integer when divided by 6 has remainder 2 and when divided by 8 gives remainder 4. What is the remainder when the integer is divided by 48?
1. 0
2. between 1 and 6
3. between 7 and 12
4. between 13 and 19
5. <= 20
[spoiler]OA: E[/spoiler]
Beautiful question Cramya.
Lets go back to our fundemantals, before we solve this problem:
LCM, Lowest Common Multiple:
In arithmetic and number theory, the least common multiple or lowest common multiple (lcm) or smallest common multiple of two integers a and b is the smallest positive integer that is a multiple of both a and b.
Let's say the remainder was zero when the integer was divided by 6 and 8.
Then, LCM(6,8 ) = 24 will be the lowest number that can satisfy this question and obviously diving by 48 would give us either 24 or 0 as a remainder.
But this is Alice's wonderland. In GMAT we will have 2 as a remainder when divided by 6, and 4 as a remainder when divided by 8. We need to find this NUMBER and find it its multiples or series and test it with 48.
Integer, I , can be defined as:
I = 6a+2 , if we use the remainder equation
I = 8b+4 if we use the remainder equation
If we insert the first equation into the second
6a+2-4 = 8b
6a-2 =8b ( which means that 6a-2 is divisible by 8 )
b=0,1,2,3,4,...etc
for b=0, a=not integer
b=1, a=not integer
b=2, a=3 BINGO
So I=6a+2 =20
you can actually find the same number by sorting the numbers like:
2,8,14,
20,26,...etc ( 6a+2)
4,12,
20,28,...etc (8b+4)
Now we have to find out when this pattern will repeat itself:
Our star point is 20, and our LCM is 24
just like y=ax+b
Integer = 24X+20
So integer set will lookl like as below:
20, 44, 68, 92, ...
if we divide these numbers by 48 the remainder set will be:
20, 44, 20, 44, 20, 44
Hence the answer is:
F) 20 or 44 
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