n = 475AB is a positive integer whose tens and units digits are A and B, respectively. If n is divisible by 5,8 and 9, then what is (10A + B)?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 20
Given:
n = 475AB
Concept USed:
Divisibility rule of 5: A number with unit digit 0 or 5 is divisible by 5
Divisibility of 8: If the sum of the last three digits of the number is divisible by 8, the number is divisible by 8.
Divisibility of 9: If the sum of the digits ofa number is divisible by 9, the number is divisible by 9.
Explanation:
According to the given question,
The number is divisible by 5, then B can be either 0 or 5
If the number is divisible by 8, the unit digit has to be even, so B = 0
Now, 5A0 is divisible by 8, A = 2
Now, 4 + 7 + 5 + 2 + 0 = 18 which is divisible by 9
Now, required value = 10(2) + 0 = 20
Hence the required answer is 20.