Which is the least number that must be subtracted from 1856 so that the remainder when divided by 7, 12, and 16 is 4?

(CAT 1994)

The correct option is D 172
Ans: (d)

LCM of (7, 12, 16) = 336. If we divide 1856 by 336 then remainder is 176. Since it is given that remainder in this condition is 4. Hence the least number to be subtracted = (176 - 4) = 172.

Alternate Approach:

In case you don't remember this method: go from answer options by subtracting the answer option from 1856 and divide by each of 7,12, and 16 to get a reminder of 4.