Question

what are the values of x and y in 72x 23y for it to be perfectly divisible by 88

Answer 1

here you should use divisibility concepts .

Question said 72x23y is divisible by 88. Means 72x23y is divisible by 8 as well as 11.
we know, divisibility rule of 8 :- any number is divisible by 8 only if last three digits of that number are divisible by 8 . example:- 123472 , this is divisible by 8 because last three '472' are divisible by 8 .

so, last three digits of number is 23y should be divisible by 8
it is possible only when y = 2 , [ check : 232/8 = 116/4 = 58/2 = 29 ]

now, divisible rule of 11 :- any number is divisible by 11 , when difference between sum of all digits placed in odd positions and sum of all digits placed in even positions is zero or multiple of 11 .example :- 3245682
Sum of all digits placed odd positions , S₁ = 3 + 4 + 6 + 2 = 15
sum of all digits placed even positions , S₂= 2 + 5 + 8 = 15
∵ S₁ - S₂ = 0 so, 3245682 is divisible by 11.

So, use this concept here,
The number is 72x232 [∵ y = 2 ]
S₁ = 7 + x + 3 = 10 + x
S₂ = 2 + 2 + 2 = 6
For divisible by 11 , when S₁ - S₂ = 0 or 11n , where n is positive integers
10 + x - 6 = 0 ⇒x = -4 , but negative digit can't possible
10 + x - 6 = 11⇒ x = 7

Hence, x = 7 and y = 2

Answer 2

Answer:

X = 7 ,Y= 2

Step-by-step explanation:

88 is factor of 2 ,4 ,8, 11 ,88

it cannot end with odd number so a and b is eliminated

the number x2 should be divisible by 8 so 72 is divisible by 8

answer is 727232