If a 10-digit number 643x1145y2 is divisible by 88, then the value of (2x - 3y) for the largest alue of y is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. -27.
Concept used:
Divisibility rule of 11: If the difference of the sum of alternative digits of a number is divisible by 11, then that number is divisible by 11 completely
Divisibility rule of 8: If the last three digits of a number are divisible by 8, then the number is completely divisible by 8
Calculations:
If number 643x1145y2 is divisible by 88 then it will be divisible by 8 and 11
For 8: 5y2, largest value of y will be 9
Now for 11: (6 + 3 + 1 + 4 + 9) - (4 + x + 1 + 5 + 2) = 0
= 23 - x - 12 = 0
= x = 0
Now, using x = 0 and y = 9 in (2x - 3y) we get
⇒ 2(0) - 3(9) = - 27