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09 Dec 2025, 23:17
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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:
15%
(low)
Question Stats:
80% (00:55) correct
20%
(01:16)
wrong
based on 165
sessions
History
Date
Time
Result
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What is the digit at the units place in the expanded form of 27^38 ?
A. 1
B. 3
C. 6
D. 7
E. 9
A. 1
B. 3
C. 6
D. 7
E. 9
10 Dec 2025, 00:59
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To find the units digit of, focus on the units digit of 27, which is 7, since only this affects the final units place
The units digits of powers of 7 follow a cyclicity of 4: 7, 9, 3, 1
Then the pattern repeats
For the exponent 38, divide by the cycle length: 38/4, which will give a remainder of 2
A remainder of 2 corresponds to the units digit of 9.
Hence, E
The units digits of powers of 7 follow a cyclicity of 4: 7, 9, 3, 1
Then the pattern repeats
For the exponent 38, divide by the cycle length: 38/4, which will give a remainder of 2
A remainder of 2 corresponds to the units digit of 9.
Hence, E
10 Dec 2025, 02:15
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We only need the unit digit pattern of powers of 7 (because 27 ends in 7).
Pattern of 7’s powers (unit digit only):
* 71 → 7
* 72 → 9
* 73 → 3
* 74 → 1
Then it repeats every 4 powers: 7, 9, 3, 1 ...
We need 27(38) → unit digit same as 738.
Find position in cycle:
38 mod 4 = 2
So take the 2nd number in the pattern → 9
Answer: 9 (Option E)
Pattern of 7’s powers (unit digit only):
* 71 → 7
* 72 → 9
* 73 → 3
* 74 → 1
Then it repeats every 4 powers: 7, 9, 3, 1 ...
We need 27(38) → unit digit same as 738.
Find position in cycle:
38 mod 4 = 2
So take the 2nd number in the pattern → 9
Answer: 9 (Option E)
