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PROVE THAT THE TENS DIGIT 3 X IS AN EVEN NUMBER ?

PROVE THAT THE TENS DIGIT 3X IS AN EVEN NUMBER ? 

Grade:Upto college level

1 Answers

mycroft holmes
272 Points
11 years ago

Use induction.

 

It is true for n =1,2,3 etc.

 

Suppose it is true for n = k i.e. 3k has its tens digit even. 3k+1 = 3. 3k. The last digit of 3k is 1 or 3 or 7 or 9. If the last digit is 1 or 3, there is no carry over from multiplying by 3, so that the tens digit remains even. If the last digit is 7 or 3, the carry is 2, so again the tens digit is still even.

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