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On being divided by a three digit number, the numbers 95336 and 91545 leave the same remainder. Find the number and the remainder.
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- 234 and 109
- 233 and 105
- 223 and 115
- None of these
Correct Option: C
Let the remainder in each case be t.
Then, the numbers (95336 – t) and (91545 – t) will be exactly divisible by that three digit number. As discussed earlier, the difference of the two numbers, i.e.,
[(95336 – t) – (91545 – t)] or, 3791 is exactly divisible by the three digit number. In other words, that three digit number will be a factor of 3791.
Now, 3791= 17 × 223
Since, the factors of 3791 have only 223 as three digit factor.
So, Required number = 223
Now, we divide 95336 by 223 to get remainder.
