Thursday, August 31, 2006

I am a number

I am a number with the following properties:

1. If I am not a multiple of 4, then I am between 60 and 69.
2. If I am a multiple of 3, I am between 50 and 59.
3. If I am not a multiple of 6, I am between 70 and 79.

What number am I?

3 comments:

  1. 76 -

    Is a multiple of 4
    Is not a multiple of 3
    Is not a multiple of 6

    ReplyDelete
  2. consider possible multiples of 3: 51, 54, 57. But none of these are multiples of 4, so they must be between 60 and 69. Since they are not, we were wrong to consider multiples of 3. I am not a multiple of 3.

    Since I am not a multiple of 3, I am not a multiple of 6 (right?).

    Since I am not a multiple of 6, I must be between 70 and 79.

    Since I am not between 60 and 69, I must be a mulitple of 4.

    Multiples of 4 between 70 and 79 are 72 and 76, but 72 is a multiple of 3.

    I am 76.

    ReplyDelete
  3. Very nicely explained Jonathan. 76 is the answer.

    ReplyDelete

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