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When 242 is divided by a certain divisor the remainder obtained is 8. When 698 is divided by the same divisor the remainder obtained is 9.

However, when the sum of the two numbers 242 and 698 divided by the divisor, the remainder obtained is 4.

The value of the divisor?

  • A.11
  • B.17
  • C.13
  • D.23

Answer: C

Let the divisor be dd. 

When 242 is divided by the divisor, let the quotient be 'xx' and we know that the remainder is 8.
Therefore, 242=xd+8242=xd+8

Similarly, let yy be the quotient when 698 is divided by dd.
Then, 698=yd+9698=yd+9.

242+698=940=xd+yd+8+9242+698=940=xd+yd+8+9
940=xd+yd+17940=xd+yd+17

As xd and ydxd and yd are divisible by dd, the remainder when 940 is divided by dd should have been 17.

However, as the question states that the remainder is 4, it would be possible only when 17/d leaves a remainder of 4.

If the remainder obtained is 4 when 17 is divided by dd, then dd has to be 13

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