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.
We have to determine the units digit of 3^n.
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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