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

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Intern
Joined: 22 Sep 2004
Posts: 28
A cipher lock consists of 3 2-digits numbers. Any 2 numbers [#permalink]

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25 Feb 2005, 13:53
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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?
Manager
Joined: 24 Jan 2005
Posts: 217
Location: Boston

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25 Feb 2005, 14:03

27, 25 and 45

I am not sure if we have an unique set or not.
Intern
Joined: 22 Sep 2004
Posts: 28

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25 Feb 2005, 14:08
How do you get it? Please explain
Manager
Joined: 24 Jan 2005
Posts: 217
Location: Boston

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25 Feb 2005, 14:15
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
SVP
Joined: 03 Jan 2005
Posts: 2233

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25 Feb 2005, 15:49
Right approach. But there are definitely multiple sets.

3,5,7
2,5,7
2,5,11
3,5,11
...
Manager
Joined: 27 Jan 2005
Posts: 100
Location: San Jose,USA- India

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25 Feb 2005, 18:14
Good solution anirban16 and good point made HongHu.

Thanks,
Manager
Joined: 24 Jan 2005
Posts: 217
Location: Boston

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28 Feb 2005, 15:07
Yup the numbers have to be prime. No unique set.
Director
Joined: 05 Jan 2005
Posts: 557

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05 Mar 2005, 01:49
Isn't this a typical backsolve question?
Senior Manager
Joined: 19 Feb 2005
Posts: 486
Location: Milan Italy

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05 Mar 2005, 05:44
In that case the stem shud say:
Which of the following could be..........?
05 Mar 2005, 05:44
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