Question

950*2* in these no .at the place of * there is te same digit and that no.is completely divisible by 11..then which is that digit
*
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Answer 1

The missing digit in the number is 3.

• To check whether a number is divisible by 11 we apply the divisibility test of 11
• The divisibility test of 11  says that the difference of the sum of digits in the even place and the sum of the digits in the odss place must be divisible by 11.
• Let us assume the unknown digit as x and evaluate
• Calculating the sum of digits in the evens place= 2+0+9 = 11
• Calculating the sum of digits in the odds place = x + x + 5 = 2x + 5
• Difference between both the sums = 11 - 5 -2x
• Difference must be divisible by 11.
• Therefore , 6 -2x = 11a (where a is any integer)
• Let us assume a to be 0 and evaluate

6 - 2x =0, x = 3

x = 3 is an acceptable solution.

• Now we assume a to be 1 and evaluate

6 - 2x = 11 , 2x = -4 , x=-2

We cannot accept this solution as x cannot be negative(Digit cannot be negative).