Question

if the 7 digit number 134x58y is divisible by 72 , then the value of (2x+y) is
(1) 8
(2) 9
(3) 6
(4) 7​

Answer 1

Answer:1) 8

2x+y=8

Step-by-step explanation:

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

I) divisible by 9:

Sum of digits should be divisible by 9

So 1+3+4+x+5+8+y=(x+y+21)%9=0...(1)

II) divisible by 8:

Last three digits should be divisible by 8

Here, 54y should be divisible by 8

So possibilities of y is 0,2,4,6,8 because end number should be even.

By calculating, 584 is the number divisible by 8

So y=4

Sub in equation (1),

(x+4+21)%9=(x+25) %9=0

So x should be positive and single digit no

So x must be 2 satisfying above equation

x=2, y=4

So 2x+y=4+4=8

Answer 2

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

Step-by-step explanation:

We have,

The seven-digit number is:

134x58y

To find, x and y =?

If the number is divisible by 72 and is divisible by 9 and 8.

If the number is divisible by 8, the last three digits are also divisible by 8.

54y is divisible by 8

584 is divisible by 8.

∴ The value of y = 4

1 + 3 + 4 + x + 5 + 8 +4 = 25 + x,  the sum of digits is divisible by 9.

∴ x = 2

∴ (2x + Y) = 2 × 2 + 4 = 8

Hence, the value of (2x+y) is "8"