If a 10-digit number 2094x843y2 is divisible by 88, then the value of (5x - 7y) for the largest possible value of x, is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 5.
For the number to be divisible by 88, the number should be divisible by 11 and 8 both
A number is divisible by 8 if the number formed by the last three digits is divisible by 8
3y2 should be divisible by 8
So, y =1 or 5 or 9
A number is divisible by 11 if the difference between the sum of its digits at odd places and the sum of its digits at even places is divisible by 11
If divisible by 11:
⇒ (2 + 9 + x + 4 + y) - (0 + 4 + 8 + 3 + 2) = 0 or multiple of 11
⇒ x + y - 2 = 0 or multiple of 11
Now, for y = 1
⇒ x + 1 - 2 = 0 or multiple of 11
⇒ x - 1 = 0 = x = 1
for y = 5
⇒ x + 5 - 2 = 0 or multiple of 11
⇒ x + 3 = 11 = x = 8
for y = 9
⇒ x + 9 - 2 = 0 or multiple of 11
⇒ x + 7 = 11 = x = 4
Since the largest possible value of x is 8 which is at y = 5
So,
⇒ (5x - 7y) = 5 × 8 - 7 × 5 = 40 - 35 = 5