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# Doubt

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Intern
Joined: 01 Feb 2018
Posts: 30

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17 Nov 2018, 07:01
Is Odd to any power always odd?

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Manager
Joined: 10 Oct 2018
Posts: 177
Location: United States
GPA: 4
WE: Human Resources (Human Resources)

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17 Nov 2018, 07:38
1
Yes. Any odd number raised to any number will be odd.

Let's find what is 3^20.
3^1=3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243
Now you can't calculate this manually all by yourself.Yes, you can but it is going to be a tedious job! We need shortcuts for GMAT. Imagine you are doing long multiplication but only keeping track of the last digit. You can notice a trend-3,9,7,1,3,9,7,1........ The next number in the sequence has to end in 3 no matter what the other digits are, and the cycle will continue. So 3^20 will end by 1.
All powers of integers have these cycles. That's a useful thing to know. In this case we can learn that no even number occurs in the cycle, so 3^anything is odd.

Every number, whether it is even or odd, negative or positive, when raised to any number will give you a trend of last digit. The last digits of odd numbers are as follows:

3^any number= 3,9,7,1.....
5^any number= 5,5,5,5.....
7^any number= 7,9,3,1....
9^any number= 9,1,9,1....

Notice that every ending or last digit of odd number raised to any number is odd.

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Intern
Joined: 01 Feb 2018
Posts: 30

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17 Nov 2018, 07:45
Thabks

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Intern
Status: Working
Affiliations: IT
Joined: 18 Nov 2017
Posts: 18
Location: India
GPA: 3.9
WE: Information Technology (Computer Software)

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27 Nov 2018, 19:28
yes
Re: Doubt   [#permalink] 27 Nov 2018, 19:28
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