Bunuel wrote:
A positive integer, when divided by 6 gives the remainder 2, and when divided by 8 gives the remainder 4. What is the remainder when the integer is divided by 48?
A. 0
B. Between 1 and 6, inclusive
C. Between 7 and 12, inclusive
D. Between 13 and 19, inclusive
E. Greater than or equal to 20
Kudos for a correct solution.
Let the positive integer be N.
N/6 has remainder 2 or equivalently -4
N/8 has remainder 4 or equivalently -4
Therefore, LCM of 6 and 8 = 24 will have a reminder -4 or equivalently 24 - 4 = 20.
so, N = 24K + 20
When you divide this by 48, you will get reminder either 20 or 44.
That is if N = 44 then reminder is 44, this will hold true for odd values of K.
and if N = 20 then reminder is 20, this will hold true for even values of K.
Hence reminder has to be greater than or equal to 20.
The solution provided by Karishma is more easy to follow, but while solving the problem I recognized that that both divisions have same negative reminders so 6*8 = 48 should have also -4 remainder or 48-4 = 44 reminder. I was stuck there till I realized that LCM of 6 and 8 is 24 not 48.