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24 Apr 2019, 01:21
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
63% (01:25) correct
37%
(01:23)
wrong
based on 76
sessions
History
Date
Time
Result
Not Attempted Yet
If n is a positive integer and the units' digit of 7^n is divisible by 3, which of the following must be true?
I. n is even.
II. n is odd.
III. n is divisible by 3.
(A) I only
(B) II only
(C) III only
(D) I and III
(E) None
I. n is even.
II. n is odd.
III. n is divisible by 3.
(A) I only
(B) II only
(C) III only
(D) I and III
(E) None
24 Apr 2019, 04:00
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\(7^1 = 7\)
\(7^2 = 49\). 9 divisible by 3.
\(7^3 = 343\). 3 divisible by itself
I: false, since n can be 3 too.
II: false, since n can be 2 too.
III: false, since n can be 2 and is not divisible by 3.
\(7^2 = 49\). 9 divisible by 3.
\(7^3 = 343\). 3 divisible by itself
I: false, since n can be 3 too.
II: false, since n can be 2 too.
III: false, since n can be 2 and is not divisible by 3.
25 Apr 2019, 18:51
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rohan2345
Since the pattern of units digits of 7^n is 7-9-3-1, we see that 7^2, 7^3, 7^6, 7^7, 7^10, 7^11, 7^14, 7^15, etc. all have units digits that is divisible by 3. We see that not all values of n are even, or odd, or divisible by 3. So none of the Roman numerals is true.
Answer: E
