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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?

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