Question
If a number 774958A96B is to be divisible by 8 and 9, the respective values of A and B will be :
(CAT 1996)
(CAT 1996)
Answer: Option B
:
B
Ans: (b)
The number 774958A96B is divisible by 8 if 96B is divisible by 8. And 96B is divisible by 8 if B is either 0 or 8. Now to make the same number divisible by 9 sum of all the digits should be divisible by 9. Hence (55 + A + B) is divisible by 9 if (A + B) is either 0 or 8 ⇒ either A = 0 or B = 8, or A = 8 or B = 0. Since the number is divisible by both A and B. Hence A and B may take either values, i.e., 8 or 0.
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:
B
Ans: (b)
The number 774958A96B is divisible by 8 if 96B is divisible by 8. And 96B is divisible by 8 if B is either 0 or 8. Now to make the same number divisible by 9 sum of all the digits should be divisible by 9. Hence (55 + A + B) is divisible by 9 if (A + B) is either 0 or 8 ⇒ either A = 0 or B = 8, or A = 8 or B = 0. Since the number is divisible by both A and B. Hence A and B may take either values, i.e., 8 or 0.
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