GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
If $n$ is an integer, and $n>0$, which of the following could be the u
[#permalink]
20 Nov 2025, 09:21
20 Nov 2025, 09:21
Expert Reply
00:00
Question Stats:
40% (00:37) correct
60% (00:48) wrong based on 5 sessions
Hide Show timer Statistics
If $n$ is an integer, and $\(n>0\)$, which of the following could be the units digit of \(1,572^n\)?
Indicate all such numbers.
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
(F) 5
(G) 6
(H) 7
(I) 8
(J) 9
Indicate all such numbers.
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
(F) 5
(G) 6
(H) 7
(I) 8
(J) 9
- Part of the project: GRE Daily Quant Challenge - Topic-Wise 2025!!!
- Also replying to the unanswered questions
ShowHide Answer
Official Answer
C,E,G,I
Re: If $n$ is an integer, and $n>0$, which of the following could be the u
[#permalink]
11 Dec 2025, 02:25
11 Dec 2025, 02:25
Expert Reply
The units digit of a power $A^n$ is determined entirely by the units digit of the base $A$.
1. Identify the Units Digit of the Base
The base is 1,572 . The units digit of the base is 2 .
We only need to look at the units digit of $2^n$ for $n=1,2,3, \ldots$.
2. Determine the Pattern of the Units Digits for Powers of 2
\(\begin{tabular}{lll}
Exponent $(n)$ & Calculation $\left(2^n\right)$ & Units Digit \\
1 & $2^1=2$ & 2 \\
2 & $2^2=4$ & 4 \\
3 & $2^3=8$ & 8 \\
4 & $2^4=16$ & 6 \\
5 & $2^5=32$ & 2 \\
6 & $2^6=64$ & 4
\end{tabular}\)
Export to Sheets
The pattern of the units digits repeats every 4 powers: $\(\mathbf{2 , 4 , 8 , 6 , 2 , 4 , 8 , 6 , \ldots}\)$
3. Identify All Possible Units Digits
The possible units digits are the numbers that appear in this repeating cycle: $\mathbf{2 , 4 , 6 , a n d} 8$.
4. Select the Corresponding Options
The options that match the possible units digits are: (C) 2 (E) 4 (G) 6 (I) 8
The correct choices are (C), (E), (G), and (I).
1. Identify the Units Digit of the Base
The base is 1,572 . The units digit of the base is 2 .
We only need to look at the units digit of $2^n$ for $n=1,2,3, \ldots$.
2. Determine the Pattern of the Units Digits for Powers of 2
\(\begin{tabular}{lll}
Exponent $(n)$ & Calculation $\left(2^n\right)$ & Units Digit \\
1 & $2^1=2$ & 2 \\
2 & $2^2=4$ & 4 \\
3 & $2^3=8$ & 8 \\
4 & $2^4=16$ & 6 \\
5 & $2^5=32$ & 2 \\
6 & $2^6=64$ & 4
\end{tabular}\)
Export to Sheets
The pattern of the units digits repeats every 4 powers: $\(\mathbf{2 , 4 , 8 , 6 , 2 , 4 , 8 , 6 , \ldots}\)$
3. Identify All Possible Units Digits
The possible units digits are the numbers that appear in this repeating cycle: $\mathbf{2 , 4 , 6 , a n d} 8$.
4. Select the Corresponding Options
The options that match the possible units digits are: (C) 2 (E) 4 (G) 6 (I) 8
The correct choices are (C), (E), (G), and (I).
gmatclubot
Re: If $n$ is an integer, and $n>0$, which of the following could be the u [#permalink]
11 Dec 2025, 02:25
Moderators:
