If the five-digit number 235xy is divisible by 3, 7 and 11, then what is the value of (3x - 4y)?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 10
235xy is divisible by three, it means sum of the digits of 235xy is also divisible by 3.
2 + 3 + 5 + x + y = 10 + x + y.
one can say that, x + y can be 2 , 5, 8 and 11.........(1)
235xy is divisible by 11 it means,
(7 + y) - (3 + x) = 0, 11
4 + y - x = 0, 11...............(2)
If y - x = -4 and x + y = 8 then we get y = 2 and x = 6.
Required number 23562 must be divisible by 7.
562 - 023 = 539.
539 is divisible by 7.
So x = 6 and y = 2 satisfied.
3x - 4y = 3 × 6 - 4 × 2
= 18 - 8 = 10.