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The smallest number subtracted from 8112 to make it exactly divisible by 99 is:
- a)95
- b)93
- c)96
- d)45
Correct answer is option 'B'. Can you explain this answer?
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The smallest number subtracted from 8112 to make it exactly divisible ...
To find the smallest number that needs to be subtracted from 8112 to make it exactly divisible by 99, we need to understand the concept of divisibility by 99.
Divisibility Rule for 99:
A number is divisible by 99 if the sum of its digits is divisible by 9 and the number formed by the last two digits is divisible by 11.
Step 1: Check if 8112 is divisible by 99.
Sum of the digits of 8112 = 8 + 1 + 1 + 2 = 12
Last two digits of 8112 = 12
Since the sum of the digits is divisible by 9 and the number formed by the last two digits is divisible by 11, we can conclude that 8112 is divisible by 99.
Step 2: Find the remainder when 8112 is divided by 99.
To find the remainder, we divide 8112 by 99:
8112 ÷ 99 = 82 remainder 30
Step 3: Determine the smallest number to subtract from 8112 to make it divisible by 99.
Since the remainder is 30, we need to subtract the remainder from 99 to get the smallest number to be subtracted.
99 - 30 = 69
Therefore, the smallest number that needs to be subtracted from 8112 to make it exactly divisible by 99 is 69.
Thus, the correct answer is option 'B' (93).
Divisibility Rule for 99:
A number is divisible by 99 if the sum of its digits is divisible by 9 and the number formed by the last two digits is divisible by 11.
Step 1: Check if 8112 is divisible by 99.
Sum of the digits of 8112 = 8 + 1 + 1 + 2 = 12
Last two digits of 8112 = 12
Since the sum of the digits is divisible by 9 and the number formed by the last two digits is divisible by 11, we can conclude that 8112 is divisible by 99.
Step 2: Find the remainder when 8112 is divided by 99.
To find the remainder, we divide 8112 by 99:
8112 ÷ 99 = 82 remainder 30
Step 3: Determine the smallest number to subtract from 8112 to make it divisible by 99.
Since the remainder is 30, we need to subtract the remainder from 99 to get the smallest number to be subtracted.
99 - 30 = 69
Therefore, the smallest number that needs to be subtracted from 8112 to make it exactly divisible by 99 is 69.
Thus, the correct answer is option 'B' (93).
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The smallest number subtracted from 8112 to make it exactly divisible by 99 is:a)95b)93c)96d)45Correct answer is option 'B'. Can you explain this answer?
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