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When 284 is divided by a certain divisor the remainder obtained is 8. When 801 is divided by the same divisor the remainder obtained is 9. However, when the sum of the two numbers 284 and 801 is divided by the divisor, the remainder obtained is 5. What is the value of the divisor?
  • a)
    10
  • b)
    12
  • c)
    16
  • d)
    20
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
When 284 is divided by a certain divisor the remainder obtained is 8. ...
When 284 is divided by a certain divisor the remainder obtained is 8.
Let the divisor be d.
When 284 is divided by d, let the quotient be 'x'.
The remainder is 8.
Therefore, 284 = xd + 8
When 801 is divided by the same divisor the remainder obtained is 9.
Let y be the quotient when 801 is divided by d.
Then, 801 = yd + 9.
When the sum of the two numbers, 284 and 801, is divided by the divisor, the remainder obtained is 5.
284 + 801 = 1085 = xd + yd + 8 + 9
1085 = xd + yd + 17
As xd and yd are divisible by d, the remainder when 1085 is divided by d should have been 17.
However, because we know that the remainder is 5, it would be possible only when 17 divided by d leaves a remainder of 5.
Then, d = 12.
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When 284 is divided by a certain divisor the remainder obtained is 8. When 801 is divided by the same divisor the remainder obtained is 9. However, when the sum of the two numbers 284 and 801 is divided by the divisor, the remainder obtained is 5. What is the value of the divisor?a)10b)12c)16d)20Correct answer is option 'B'. Can you explain this answer?
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