Question

if 7 digit no is 134x58y is divisible by 72 then find (2x+y)​

Answer 1

Answer:

The value of (2x + y) is 8.

Step-by-step explanation:

Consider the provided number 134x58y

It is given that the number divisible by 72 that means it should be divisible by 9 and 8.

1) The number is divisible by 9 if the sum of digit is divisible by 9.

$1+3+4+x+5+8+y=\frac{(21+x+y)}{9}$

2) The number is divisible by 8 if the last three digits is divisible by 8.

So, 54y should be divisible by 8.

Thus, the choices for y is 0, 2, 4, 6, 8.

The number 580, 582, 586, 588 are not divisible by 8 but 584 is divisible by 8.

Thus, the value of y is 4.

Substitute y = 4 in $\frac{(21+x+y)}{9}$.

$\frac{(21+x+4)}{9}$

$\frac{(25+x)}{9}$

Now, find the number next to 25 which is divisible by 9. Note, x should be a single digit number. So, the possible choices for x are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

The number next to 25 which is divisible by 9 is 27. Therefore by adding 2 in 25 we can get the number 27.

Remember, we can take 36 as to make 36 we need to add 11 in 25 and 11 is not a 1 digit number.

Therefore, the value of x must be 2.

We have the value of x = 2 and y = 4

Substitute the value of x and y in 2x+y:

2x + y= 2(2) + 4

         = 4 + 4

         = 8

Hence, the value of 2x + y is 8.