Question

if x and y are the two digits of the number 585xy such that this number is divisible by 80,then x+y is equal to

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Answer 1

Answer:

x+y=6

Step-by-step Solution

Rule: For a number to be divisible by 10, its last digit should be 0 and for a number to be divisible by 8, its last 3-digits should be evenly divisible by 8.

The question and condition:

"585xy" is divisible by 80. Find 'x+y'.

As per the question:

585xy is divisible by 80, which means it is divisible by 10 and then 8. For the number to be divisible 10, the last digit should be 0. Therefore, y=0.

Now, we are left with 585x which should be divisible by 8. For this, the last 3 digits i.e., 85x should be divisible by 8.

x cannot be 2 because, after division, it would give a floating-point number. Therefore, not divisible.

p should be 6, as 85x or 856/8=107

Therefore,

x=6, y=0

hence, x+y=6

The number: 58560

After dividing by 80, 732 is the quotient.

Answer 2

Answer:

The sum of the two digits x and y that make the number 585xy divisible by 80 is 5.

Step-by-step explanation:

To determine the value of x + y, we need to find the values of x and y that make the number 585xy divisible by 80.

To be divisible by 80, the number must be divisible by both 8 and 10.

Since the number is divisible by 10, we know that y must be 0.

Now, we need to determine the value of x that makes the number divisible by 8.

If a number's final three digits can be divided by 8, it is considered to be divisible by 8.

So, we need to find a value of x such that the number 585x0 is divisible by 8.

The last three digits of 585x0 are x0, so we need to find a value of x such that x0 is divisible by 8.

We can list out all the possible two-digit values of x and their corresponding values of x0 that are divisible by 8:

x = 10, x0 = 80

x = 12, x0 = 96

x = 14, x0 = 40

x = 16, x0 = 16

x = 18, x0 = 24

Out of these values, only x = 14 results in a two-digit number. Therefore, x must be 14, which means that y must be 0.

So, the number is 58514, and x + y = 1 + 4 = 5.

Therefore, the sum of the two digits x and y that make the number 585xy divisible by 80 is 5.

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