Let d + 2(2b + c) = 19. What will be the remainder when the 4-digit number abcd is divided by 8?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 3.
abcd = 1000a + 100b + 10c + d
For abcd to be divisible by 8, 100b + 10c + d must be divisible by 8
(100b + 10c + d)/8
= [100b + 10c + 19 - 2(2b + c)]/8 [d = 19 - 2(2b + c)]
= (100b + 10c - 4b - 2c + 19)/8
= (96b + 8c + 19)/8
= (96b + 8c)/8 + 19/8
96b + 8c is divisible by 8, and only 19 will give a remainder of 3