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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: 30
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A cipher lock consists of 3 2-digits numbers. Any 2 numbers [#permalink]  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?
Manager
Joined: 24 Jan 2005
Posts: 217
Location: Boston
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Kudos [?]: 5 [0], given: 0

27, 25 and 45

I am not sure if we have an unique set or not.
Intern
Joined: 22 Sep 2004
Posts: 30
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Kudos [?]: 3 [0], given: 0

How do you get it? Please explain
Manager
Joined: 24 Jan 2005
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Kudos [?]: 5 [0], given: 0

15,21,35 [#permalink]  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
SVP
Joined: 03 Jan 2005
Posts: 2251
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Kudos [?]: 213 [0], given: 0

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
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Location: San Jose,USA- India
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Good solution anirban16 and good point made HongHu.

Thanks,
Manager
Joined: 24 Jan 2005
Posts: 217
Location: Boston
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Kudos [?]: 5 [0], given: 0

Yup the numbers have to be prime. No unique set.
Director
Joined: 05 Jan 2005
Posts: 561
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Kudos [?]: 12 [0], given: 0

Isn't this a typical backsolve question?
Senior Manager
Joined: 19 Feb 2005
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Location: Milan Italy
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Kudos [?]: 10 [0], given: 0

In that case the stem shud say:
Which of the following could be..........?
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