Question

when 1000 is added to 459x251 and the resulting number is divided by 11 the remainder is 8 find x​

Answer 1

Answer:

x= 10563 .727

Step-by-step explanation:

459×251 = 115209

now we need to add 1000 to 115209 =116209

let the quotient be X

(11 ×X) +8 = 116209

11X + 8= 116209

11X =116201

X= 10563.727

Answer 2

Answer:

The correct answer is 8.

Step-by-step explanation:

Here x is digit of the number and not the multiplication symbol. We use the property of modulo here.

We use (a + b)%n = a%n + b%n

Let a = 459x251 and b = 1000.

According to data in the question, (a + b) % 11 = 8

b%11 = 10.

So, according to relation (a+b)%n = a%n + b%n, we get

8 = a%n + 11

Therefore, a%n = -2%11 = 9%11.

So, we conclude that a = 459x251 produces reminder 9 when divided by 11.

This implies that a - 9 should be divisible by 11.

Which means 459x242 should be divisible by 11.

Now if any number is divisible by 11 then difference between sum of digits at odd positions and sum of digits at even position should be multiple of 11.

In our case :

Sum of odd positions = 4 + 9 + 2 + 2 = 17

Sum of even positions = 5 + x + 5 = 9 + x

Now the difference should be multiple of 11.

Here the difference is 17 - 9 - x = 8 - x.

Now $0 \leq x \leq 9$, so, only possible value of 8 - x is 0. So, x = 8.

You can check the answer by adding 1000 to 4598251 and then taking reminder when you divide the resulting number by 11.