Question

if the 8-dights number 179x091y is divisible by 88 then what is the value of (x-y)?​

Answer 1

Answer:

Here is the answer to ur question.

Answer 2

Answer:

x - y = 2

Step-by-step explanation:

Now at first glance its might be impossible to solve, but thinking further all Questions eventually gets an Answer.

Lets take the Divisor first.

Divisor = 88

Now,

88 = 8 × 11

And if a number is divisible by 88, then logically it should be divisible by 8 and 11 right?

Yes.

So,

179x091y should be divisible by 8 and 11.

So, now what.

Now, here is when divisibility rule of numbers becomes crucial.

Divisibility rule of 8 tells us that, A number is divisible by 8 only if its last 3 digits are divisible by 8.

Hence,

179x091y is divisible by 8, only if 91y is divisible by 8, and since we know that 179x091y is divisible by 8, again logically, 91y should also be divisible by 8.

Now, let's divide 91y with 8,

11□

________

8 | 91y

- 8

——

11

- 8

——

3y

So, now we are left with 3y as the remainder.

Here,

3y is a two digit number starting with 3.

Thus, we know that, in 8's table only 32 is divisible by 8.

Hence,

3y = 32

y = 2

Thus,

The number becomes 179x0912.

Again, this number is also divisible by 11.

The divisibility rule of 11 says that, a number is divisible by 11, if its alternate sum of digits are a multiple of 11.

Thus,

1 - 7 + 9 - x + 0 - 9 + 1 - 2 = 11k

where k is an integer.

-7 - x = 11k

x = -7 - 11k

Let k = 0,

x = -7 - 11(0)

x = (-7)

x = (-7)

Since the digit of a number can't be negative, x ≠ (-7).

Let k = (-1)

x = -7 - 11(-1)

x = -7 + 11

x = 4

Thus,

x = 4 is the smallest and the only solution for x,

So, The original number is 17940912.

Hence,

x = 4 and y = 2

Now, we must find what (x - y) is,

So,

x - y = 4 - 2

= 2

Hence,

x - y = 2

Hope it helped and believing you understood it. All the best.