Find the greatest number 234a5b, which is divisible by 22 but not divisible by 5.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 234652
Concept used:
If a number is divisible by 22, it will be divisible by 2 and 11
For a number to be divisible by 2, the unit place should be even number or 0(with ten place).
For a number to be divisible by 11, if the sum of the digits in the odd places and the sum of the digits in the even places difference is a multiple of 11 or zero.
Calculations:
For a number not divisible by 5, value of b can not be 0.
To get the greatest number a > b
⇒ (2 + 4 + 5) - (3 + a + b) = 0 or multiple of 11
⇒ a + b = 8
Possible value of a and b are (8, 0) (7, 1) (6, 2) (5, 3) (4, 4) and so on
When b = 2, a = 6 and
when b = 4, a = 4
So we know that for the greatest value a > b,
So the required number is 234652.