Question

If 23xy59 is a number with all distinct digits and divisible by 11, then two-digit number xy will be

Answer 1

Solution:

It is given that number 2 3 x y 59 is divisible by 11.

So, if a number is divisible by 11,

Then ,⇒ (sum of digits at even places) - (Sum of digits at odd places)=11 × k

or,

⇒ (sum of digits at odd places) - (Sum of digits at even places)=11 × k

sum of number at odd places= 2+x+5= 7 +x

Sum of number at even places= 3 +y+9=12 +y

Difference of two = 12 +y -7-x =5-x+y

If (5-x+y) is divisible by 11, then 5-x+y=0 or Multiple of 11.

Means, x-y=5

So, different possibilities of x and y , when both of them are even integers such that ,0≤x≤9,0≤y≤9,and x-y=5,  than  x y are (9,4),(8,3),(6,1),(5,0).