It is given that the 10-digit number 55y1725x00 is exactly divisible by 88. What is the value of (y - x)?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 2.
Given, the number is divisible by 88, i.e. the number is divisible by both 8 and 11.
Divisibility rule of 8: When the last three digits of a number is divisible by 8, the number is divisible by 8.
⇒ 5x00 should be divisible by 8
Possible values of x = 2; 6
Divisibility rule of 11: Difference between the sum of the digits at odd places and at even places is either 0 or 11.
Now, difference in the alternate digits = 0 - 0 + x - 5 + 2 - 7 + 1 - y + 5 - 5
⇒ x - y - 9 = 0
⇒ x - y = 9
Also, x - y - 9 = -11
⇒ x - y = -2
Now checking the possibility of values of x,
For x = 2, 2 - y = 9
⇒ y = -7 (Not possible)
Also, 2 - y = -2
⇒ y = 4
For, x = 6, 6 - y = 9
⇒ y = -3 (Not possible)
Also, 6 - y = -11
⇒ y = 17 (Not possible, single digit)
Now, x = 2 and y = 4
⇒ y-x = 4 - 2 = 2