Question

If 23XY59 is a number with all distinct digits and divisible by 11, then the two digit
number XY will be

Answer 1

Answer:

61 and 17

Explanation:

sum of alternating digit from left

9+y+3 and 5+x+2

=12+y and 7+x

for divisible by 11 the their difference will be 0 or whole sum( 12+y+7+x) will be divisible by 11

for difference 0

12+y=7+x

=>  x-y=5(choose from option)

for second case

19+x+y

=>next x,y possible digit will be 1 and 7 or vice-versa.

so, 17 or 71 (choose from option)

Answer 2

The correct answer to the given question is (6, 1) and (1, 7).

Given:

23XY59 is a number with all distinct digits and id divisible by 11.

To Find:

The values of X and Y.

Solution:

According to the question, 23XY59 is divisible by 11.

We know that, if a number is divisible by 11, either the difference of alternating digits would be 0 or the sum will be divisible by 11.

Therefore,

Sum of alternating digits = $(9+y+3)$ and $(5+x+2)$

Sum of alternating digits = $(12+y)$ and $(7+x)$

For their difference to be 0, both have to be equal.

Equating,

$12+y=7+x\\ x-y=5$

Now,

Various value pairs of (x, y) satisfying the above equation are,

(6, 1), (7, 2), (8, 3), and (9, 4)

As the digits 2, 3, and 9 are already present in the given number, the solution possible here is (6, 1).

Hence, the number is 236159.

For case 2,  

$Y + 12 - X - 7 = 11$

$Y - X = 6$

Various value pairs of (x, y) satisfying the above equation are,

(1, 7), (2, 8), and (3, 9)

As the digits 2 and 9 are already present in the given number, the solution possible here is (1, 7).

Hence, the number is 231759.

Therefore, There can be 2 different solutions for (x, y) for all the digits to be distinct,

$(x, y)=(6, 1)$ and $(1, 7)$.

Hence, The values of x and y which would satisfy the question are, (6, 1) or (1, 7).

#SPJ2