 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  1-2-3 Remainder Resolution (Posted on 2016-02-16) 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) Comments: ( Back to comment list | You must be logged in to post comments.) d3 answer | Comment 2 of 12 | 1) Statements 2 and 3 are contradictory, so 1 is true.  Therefore, N = 24x + 1

2) From statement 0, N = 100y + 9z + 3.

3) If statement 3 is true, then (100y + 9z +3) mod 11 = 3 = (100y + 9z + 3) mod 5
Then 9z = 0 mod 5 and y = 2z mod 11.
But 9z = 0 mod 5 implies z = 0 or 5, and this fails if y = 2z mod 11.
So statement 3 is false.

4) So statement 2 is true.  Then (100y + 9z +3) mod 5 = 2
So z = 1 mod 5.  z = 1 or 6.
If z = 1, then N is even, and cannot be 24x + 1
So z must be 6.
Then 100y + 57 = 1 mod 24.
4y = 16 mod 24
y = 4

So the final answer is 457.

Checking, 457 mod 7 = 2

Edited on February 16, 2016, 11:56 am
 Posted by Steve Herman on 2016-02-16 11:55:49 Please log in:

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