Question

If the 7digit number 134x58y is divisible by 72, then the value of (2x+y) is

Answer 1

Answer:

The value of 2x + y is 8.

Step-by-step explanation:

Consider the provided number 134x58y

If a number divisible by 72 that means it should be divisible by 9 and 8.

If the number is divisible by 9 then the sum of digits should be divisible by 9.

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

If the number is divisible by 8 then the last three digits should be divisible by 8.

Thus, 54y should be divisible by 8.

Therefore, the possibilities for y is 0, 2, 4, 6, 8. As 8 is even number so the end digit should be even.

By try and error we can find that 580, 582, 586, 588 are not divisible by 8 but 584 is divisible by 8.

Therefore, the value of y must be 4.

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

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

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

Now, we need to find the number next to 25 which is divisible by 9. Remember 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.

Note, 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.

Now we have the value of x = 2 and y = 4

Substitute the value of x and y in 2x+y we get,

2x + y= 2(2) + 4

         = 4 + 4

         = 8

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