Question

If 23XY70 is a number with all distinct digits and divisible by 11, find XY.

• A. 50
• B. 72
• C. 61
• D. 83

Answer 1

Answer:

C. 61

We know that, for a number to be divisible by 11, the difference between the sum of digits in odd places and the sum of digits in even places should be either 0 or a number divisible by 11. (2+X+5) – (3+Y+9) = 0 or multiple of 11 X – Y – 5 = 0 or multiple of 11 If X=6 and Y=1, X – Y – 5 = 0 and hence divisible by 11. If X=1 and Y=7, X – Y – 5 = -11, which is a multiple of 11 and hence divisible by 11. XY=17 cannot be the answer, because 23XY70 is a number with all distinct digits and 7 is already present in the number. Therefore, XY is 61.