Question

an odd three digit number is divisible by 5 and 11 and sum of its digits is 16.find the number.
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Answer 1

Answer: The number is 385.

Step-by-step explanation:

Let the number is xyz.

The last digit has to options z = 0,5

But it is give that number is odd,so Z can be equal to 5

z = 5

Divisibility rule of 11 says:

Sum of odd places of number -sum of even places numbers= 11n

where n is any integer

As well as

$x + y + z = 16 \\ \\ x + y + 5 = 16 \\ \\ x + y = 11...eq1 \\ \\ x + z - y = 11n \\ \\ x + 5 - y = 11n \\ \\ x - y = 11n - 5...eq2 \\ \\ from \: eq1 \: and \: eq2 \\ \\ 2x = 11n + 6 \\ \\ x = \frac{11n + 6}{2}$

n can not be 1,because 17/2 can not be x,x can be a positive integer

for x there can be four options,

2,4,6,8 but for that case x+y=11 condition not satisfied

For n= 0

$x = \frac{11(0) + 6}{2} \\ \\x=3\\\\y=11-3\\\\y=8$

So,that number is 385.

Hope it helps you.

Answer 2

Answer:

Your answer 385

I hope your help