Question

if the number 1358*16 is exactly divisible by 11 then *

Answer 1

The digit at * is 0

Given :

The number 1358*16 is exactly divisible by 11

To find :

The digit at *

Concept :

Divisibility by 11 rule :

A number is divisible by 11 if the difference between the sum of the digits at odd places and the sum of the digits at even places of the number is 0 or divisible by 11

Solution :

Step 1 of 2 :

Write down the given number

Here the given number is 1358*16

Step 2 of 2 :

Find the digit at *

Let the digit at * is n

Then the number becomes 1358n16

Sum of the digits at even places

= 3 + 8 + 1

= 12

Sum of the digits at odd places

= 1 + 5 + n + 6

= n + 12

Difference between the sum of the digits at odd places and the sum of the digits at even places

= (n + 12) - 12

= n

Since the number 1358n16 is divisible by 11

∴ Either n is 0 or divisible by 11

Since n is one digit

∴ n = 0

Hence digit at * is 0

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Answer 2

Answer:

$*=0$

Step-by-step explanation:

We know the divisibility rule of 11.

$Sum\ of\ odd\ digits - Sum\ of\ even\ digits = 0\ or\ multiple\ of\ 11$

The given number is 1358*16

Sum of odd digits = $12 + *$

Sum of even digits = $12$

Put this values in the above formula, we get.

$12+*-12=0$

$\therefore *=0$

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