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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 How to solve it | Comment 10 of 12 |
2 and 3 cannot both be true. Therefore, 1 must be true. That means that N=1 mod 24. If 2 is true, then N=2 mod 35. Therefore, N=457 mod 840. Since N is a 3-digit number, N=457. If 3 is true, then N=3 mod 55. Therefore, N=553 mod 840. Since N is a 3-digit number, N=553.

We know that N=457 or 553. Now, 57=3 mod 9 and 53=8 mod 9. Therefore, N=457.

  Posted by Math Man on 2016-02-16 17:46:06
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