The largest four-digit number which when divided by 4, 7, or 13 leaves a remainder of 3 in each case is:
Show answer & explanation
Correct answer: B
Explanation
Given:
The remainder when dividing a number by 4, 7, and 13 = 3
Requires the largest 4-digit number
Formula:
If the number is N, then N is exactly divisible by 3, 4, 7, and 13.
LCM(4, 7, 13) = 364
Largest 4-digit number = 9999
9999 − 3 = 9996
Now divide 9996 by 364.
364 × 27 = 9828
N − 3 = 9828
N = 9828 + 3
N = 9831