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What is the units digit of 3^n?

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Bunuel
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What is the units digit of 3^n? [#permalink] New post   22 Apr 2016, 04:41
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E

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25% (medium)

Question Stats:

75% (01:53) correct 25% (01:32) wrong based on 65 sessions
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What is the units digit of 3^n?

(1) n = 2x + 1, where x is a positive integer.
(2) n = 2k – 1, where k is a positive integer.
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E
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Re: What is the units digit of 3^n? [#permalink] New post   22 Apr 2016, 06:50
3^n has a cyclicity of 4 with units digit as 3,9,7,1 depending on the value of n

Stmnt 1
when x=1 n=3 units digit of 3^n is 7
when x=2 n=5 units digit of 3^n is 3

Different answers so Insufficient

Stmnt 2
when k=1 n=1 units digit of 3^n is 3
when k=2 n=2 units digit of 3^n is 9

Different answers so insufficient

Stmnt 1 + 2
2x+1= 2k-1 > x+1=k
when x=1 k=2
so n= 3 > units digit of 3^n is 7
or
n=2 > units digit of 3^n is 9
Different answers again so insufficient

Ans E
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Re: What is the units digit of 3^n? [#permalink] New post   26 Apr 2016, 05:02
3 has a cyclicity of 4, so the question asks to find the remainder when n is divided by 4

(1) n = 2x + 1, where x is a positive integer.

\(\frac{2x+1}{4}\)
when x = 1 remainder is 3
when x = 2 remainder is 1
insuf

(2) n = 2k – 1, where k is a positive integer

\(\frac{2k-1}{4}\)
when k = 1 remainder is 1
when k = 2 remainder is 3
insuf

together:
\(2x + 1 = 2k – 1\)
we get x + 1 = k

replacing k by (x+1) in statement 2 we find that statement 1 equals statement 2: hence insufficient
Answer E
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gmatclubot
Re: What is the units digit of 3^n? [#permalink]
26 Apr 2016, 05:02
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Bunuel
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