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Either / Or (Posted on 2006-05-13) Difficulty: 2 of 5
I am a three digit number.
I am either divisible by 3 or by 5.
I am either divisible by 4 or by 6.
I am either divisible by 5 or by 7.
I am either divisible by 6 or by 8.
I am either divisible by 7 or by 9.
I am either divisible by 9 or by 11.

What am I?

(Note: "divisible" means leaving no remainder.)

  Submitted by tomarken    
Rating: 3.2500 (4 votes)
Solution: (Hide)
Assume that the number is divisible by 9. This would mean:

It is NOT divisible by 11.
It is NOT divisible by 7.
It IS divisible by 5.
It is NOT divisible by 3.

Of course, it cannot be divisible by 9 but not by 3, so this is not the case. Therefore, the number is divisible by 3, 7, and 11, but not by 5 or 9.

Multiples of 3, 7, and 11 are 231, 462, 693, and 924. 693 is divisible by 9, so that cannot be correct.

The correct answer must be divisible by either 4 or 6; 231 is divisible by neither, and 924 is divisible by both. Therefore the only number that works is 462 (it is divisible by 6, but not by 4 or 8).

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Explanation for Puzzle AnswerK Sengupta2022-02-24 20:37:52
Puzzle AnswerK Sengupta2022-02-24 20:33:56
SolutionSolutionPraneeth2007-08-20 04:15:58
SolutionAnswerThomas2006-05-22 18:09:44
Some Thoughtsre: The answer -- not soFederico Kereki2006-05-15 21:12:20
re: The answerCharlie2006-05-15 16:07:43
QuestionNegative thinkingSteve Herman2006-05-15 11:25:45
The answerLincoln2006-05-15 10:58:02
answerLincoln2006-05-15 10:55:58
re: 462Robby Goetschalckx2006-05-15 07:12:23
SolutionLogicallye.g.2006-05-15 07:06:26
Solution462John2006-05-14 07:35:09
Solutionre: That depends on whatDej Mar2006-05-13 19:51:35
re: That depends on what "or" is -- the truth values (spoilers)Charlie2006-05-13 12:59:49
re: That depends on what "or" is -- the exclusive story (spoiler)Charlie2006-05-13 12:25:52
SolutionThat depends on what "or" is -- computer solutionCharlie2006-05-13 12:22:48
SolutionA but not B or is it when followed by CLeming2006-05-13 10:46:29
SolutionA solution, perhaps?Phil_Osopher2006-05-13 10:21:09
SolutionAnswerVernon Lewis2006-05-13 10:15:07
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