B = 3560 – A. When B is divided by 8, 12 and 16 the remainder is 4 in each case. What is the value of A?
Show answer & explanation
Correct answer: A
Explanation
Given:
B = 3560 − A
B divided by 8, 12, 16, remainder = 4
If B divided by 8, 12, 16, remainder is 4, then (B − 4) is divisible by their LCM.
LCM(8, 12, 16) = 48
Therefore, B − 4 = 48k ⇒ B = 48k + 4
3560 − A = 48k + 4
A = 3560 − (48k + 4)
A = 3556 − 48k
Taking k = 74:
A = 3556 − 48 × 74
= 3556 − 3552
= 4