What's the remainder of (3^50)/ 4? A.0 B.1 C.2 D.3 : PS Archive
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# What's the remainder of (3^50)/ 4? A.0 B.1 C.2 D.3

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What's the remainder of (3^50)/ 4? A.0 B.1 C.2 D.3  [#permalink]

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16 Mar 2006, 09:49
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What's the remainder of (3^50)/ 4?

A.0
B.1
C.2
D.3
E.4
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16 Mar 2006, 10:00

Picking #s is what I did to test different scenarios:

3^2 = 9 ---> remainder is 1
3^3 = 27 ---> remainder is 3
3^4 = 81 ---> remainder is 1

The pattern seem to be that the remainder is 1 whenever 3 is raised to an even number. On the test, I would stop here because of time constraint and choose B = 1.

Let me know if I'm wrong!
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16 Mar 2006, 10:33
Should be 1.

Odd power of 3, remainder = 3
Even power of 3, remainder = 1
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16 Mar 2006, 21:12
3^0 = 1
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81

The cycle goes 1-3-9-7

3^50 will have 9 has the units digit

Remainder = 1
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16 Mar 2006, 22:01
For me its B too...

Concept -

Odd number - remainder 3
Even Number - remainder 1
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17 Mar 2006, 07:04
I also used Wilfred`s brute force method which takes the full 2 minutes. However, Matador and Vivek pinpointed the trick. Nice observation guys
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17 Mar 2006, 07:27
good job, everyone~ ^_^ ...OA is 1.
17 Mar 2006, 07:27
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