CAT 1996 — QA Question 47
Answer the questions based on the following information.
A series S1 of five positive integers is such that the third term is half the first term and the fifth term is 20 more than the first term. In series S2, the nth term defined as the difference between the (n + 1)th term and the nth term of series S1, is an arithmetic progression with a common difference of 30.
If a number 774958A96B is to be divisible by 8 and 9, the respective values of A and B will be
Answer & solution
- 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.