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1-2-3 Remainder Resolution (Posted on 2016-02-16) Difficulty: 3 of 5
Abe challenges Bee to determine a 3-digit positive integer N.
It is known that the number formed by the last two digits of N when divided by 9, yields a remainder of 3.

Abe makes the following statements, precisely one of which is false:
  1. N divided separately by each of 2, 4, 6, and 8 yields a remainder of 1.
  2. N divided separately by each of 5 and 7 yields a remainder of 2.
  3. N divided separately by each of 5 and 11 yields a remainder of 3.
Determine the value of N from the above statements and given clues.

No Solution Yet Submitted by K Sengupta    
Rating: 4.5000 (2 votes)

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Solution Solution Comment 12 of 12 |
The first clue yields a set of 90 numbers - half even, half odd.  Looking at the clues, there is a conflict between clues 2 and three (i.e. division by 5 leaves different remainders), so the false statement must be one of these.

From clue 1, all even number can be eliminated.  Dividing the odd ones by both 6 and 8 reduces the set to these five numbers:

121, 193, 457, 721, 793

After dividing these numbers by 5, 7, and 11, the only one with matching remainders is 457.

  Posted by hoodat on 2016-06-28 05:15:07
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