B = 4150 – A When B is divided by 7, 14 and 21 the remainder is 5 in each case. What is the value of A?
Show answer & explanation
Correct answer: C
Explanation
Given:
B = 4150 − A
The remainder when B is divided by 7, 14, and 21 is 5.
According to the formula:
If a number yields the same remainder when divided by 7, 14, and 21, then
B − 5 will be divisible by LCM(7, 14, 21).
LCM(7, 14, 21) = 42
B − 5 = 42k
⇒ B = 42k + 5
Now, B = 4150 − A
4150 − A = 42k + 5
A = 4150 − (42k + 5)
A = 4145 − 42k
Now, B ≤ 4150 ⇒ 42k + 5 ≤ 4150
42k ≤ 4145
k ≤ 98
Substituting k = 98:
A = 4145 − (42 × 98)
= 4145 − 4116
= 29