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.
The OA is the option E.
How can I show that the correct option is E? I don't know what should I do.
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What is the units digit of 3^n?
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Vincen
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Hello M7MBA.M7MBA wrote: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.
The OA is the option E.
How can I show that the correct option is E? I don't know what should I do.
Let's take a look here.
(1) n = 2x + 1, where x is a positive integer.
- If x=1 then n=3, therefore $$3^n=3^3=27\ \Rightarrow\ \ units\ digit\ is\ 7.$$
- If x=2 then n=5, therefore $$3^n=3^5=243\ \Rightarrow\ \ units\ digit\ is\ 3.$$
Since we get two different values, this statement is NOT SUFFICIENT.
(2) n = 2k - 1, where k is a positive integer.
- If k=1 then n=1, therefore $$3^n=3^1=3\ \Rightarrow\ \ units\ digit\ is\ 3.$$
- If k=2 then n=3, therefore $$3^n=3^3=27\ \Rightarrow\ \ units\ digit\ is\ 7.$$
Since we get two different values, this statement is NOT SUFFICIENT.
Now, using both statements together we get: $$n=n\ \Rightarrow\ \ \ 2x+1=2k-1\ \Rightarrow\ \ k=x+1.$$
- If x=1 then k=2 and n=3, therefore $$3^n=3^3=27\ \Rightarrow\ \ units\ digit\ is\ 7.$$
- If x=2 then k=3 and n=5, therefore $$3^n=3^5=243\ \Rightarrow\ \ units\ digit\ is\ 3.$$
Since we get two different values, this case is NOT SUFFICIENT.
Therefore, the correct answer is the option E.
I hope it helps you.
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Jay@ManhattanReview
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We have to determine the units digit of 3^n.M7MBA wrote: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.
The OA is the option E.
How can I show that the correct option is E? I don't know what should I do.
Let's take each statement one by one.
(1) n = 2x + 1, where x is a positive integer.
=> n is an odd number. Let's see how. Say x = 1, then n = 3; say x = 2, then n = 5
Case 1: n = 3, then the units digit of 3^3 (= 27) = 7.
Case 2: n = 5, then the units digit of 3^5 (= 243) = 3.
No unique answer. Insufficient.
(2) n = 2k - 1, where k is a positive integer.
=> n is an odd number. Let's see how. Say k = 1, then n = 1; say k = 2, then n = 3
Case 1: n = 1, then the units digit of 3^1 (= 3) = 3.
Case 2: n = 3, then the units digit of 3^5 (= 27) = 7.
No unique answer. Insufficient.
(1) and (2) together:
Even combining the two statements will not help since n is still an odd number, rendering the unit digit of 3^n = 3 or 7.
No unique answer. Insufficient.
The correct answer: E
Hope this helps!
-Jay
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