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A cipher lock consists of 3 2-digits numbers. Any 2 numbers

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Intern
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A cipher lock consists of 3 2-digits numbers. Any 2 numbers [#permalink] New post 25 Feb 2005, 12:53
334.A cipher lock consists of 3 2-digits numbers. Any 2 numbers of them have a common factor greater than 1 and the 3 numbers have no common factor. What is the 3 numbers?
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 [#permalink] New post 25 Feb 2005, 13:03
How about these numbers

27, 25 and 45

I am not sure if we have an unique set or not.
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 [#permalink] New post 25 Feb 2005, 13:08
How do you get it? Please explain
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15,21,35 [#permalink] New post 25 Feb 2005, 13:15
My previous answer was wrong I overlooked one thing

Ok I did not use any formula.

Explanation:

The numbers have to be odd (otherwise all three will have a common factor which is 2). Now all you need is to pick 3 prime numbers lets pick 3 , 5 , 7 these are the only prime numbers less than 10 Right?

Now form three triplets

15 = 3*5
21 = 3*7
35 = 5*7

Ok

The all three taken together have no common factor
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 [#permalink] New post 25 Feb 2005, 14:49
Right approach. But there are definitely multiple sets.

3,5,7
2,5,7
2,5,11
3,5,11
...
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 [#permalink] New post 25 Feb 2005, 17:14
Good solution anirban16 and good point made HongHu.

Thanks,
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 [#permalink] New post 28 Feb 2005, 14:07
Yup the numbers have to be prime. No unique set.
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 [#permalink] New post 05 Mar 2005, 00:49
Isn't this a typical backsolve question?
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 [#permalink] New post 05 Mar 2005, 04:44
In that case the stem shud say:
Which of the following could be..........?
  [#permalink] 05 Mar 2005, 04:44
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A cipher lock consists of 3 2-digits numbers. Any 2 numbers

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