CAT 1996 — QA Question 47
If a number 774958A96B is to be divisible by 8 and 9, the respective values of A and B will be
Answer & solution
Correct answer: 8 and 0
- A
7 and 8
8 and 0
- C
5 and 8
- D
None of these
For the number to be divisible by 9, the sum of the digits should be a multiple of 9.
We find that the sum of all the digits (excluding A and B) = (7 + 7 + 4 + 9 + 5 + 8 + 9 + 6) = 55. The next higher multiple of 9 is 63 or 72.
Hence, the sum of A and B should either be 8 or 17. We find that (a) and (c) cannot be the answer.
For a number to be divisible by 8, the number formed by its last three digits should be divisible by 8. The last three digits are 96B. The multiples of 8 beginning with 96 are 960 and 968. Hence, B can either be 0 or 8. Both of which satisfy our requirement of the number being divisible by 9 as well.
Therefore, A and B could either be 0 and 8 or 8 and 0 respectively.