If the 5 digit number 688xy is divisible by 3, 7 and 11, then what is the value of (5x + 3y)?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 39.
Here it is given that 688xy is divisible by 3, 7 and 11.
The divisibility of 3 says that if the sum of the digits of a number is divisible by 3 then the number will be divisible by 3.
= 6 + 8 + 8 + x + y = 21 + x + y + 1 ( 21 is already a multiple of 3 so one can ignore this)
possible value of x + y = 2, 5, 8, 11, 14,17.
The divisibility rule of 11 says that the sum of the digits at an odd place - the sum of the digits at even place = 0 or 11.
= 6 + 8 + y - 8 - x
= 6 + y - x
at y = 8 and x = 3 we get,
= 6 + 8 - 3 = 11(satisfy)
⇒ (5x + 3y) = 5 × 3 + 3 × 8 = 39.