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.
What is the ones digit of 3^23 - 2^18?
[#permalink]
27 Jul 2017, 10:05
27 Jul 2017, 10:05
1
Expert Reply
2
Bookmarks
00:00
Question Stats:
80% (01:11) correct
20% (01:17) wrong based on 90 sessions
Hide Show timer Statistics
Re: What is the ones digit of 3^23 - 2^18?
[#permalink]
25 Sep 2017, 06:11
25 Sep 2017, 06:11
1
Let's use the fact that unit digits are recurrent in powers so that
\(3^1=3\)
\(3^2=9\)
\(3^3=..7\)
\(3^4=..1\)
\(3^5=..3\)
...
And
\(2^1=2\)
\(2^2=4\)
\(2^3=8\)
\(2^4=..6\)
\(2^5=..2\)
....
Thus, \(3^21=...7\) and \(2^18=...4\). Then, their difference will terminate with a 7-4=3!
\(3^1=3\)
\(3^2=9\)
\(3^3=..7\)
\(3^4=..1\)
\(3^5=..3\)
...
And
\(2^1=2\)
\(2^2=4\)
\(2^3=8\)
\(2^4=..6\)
\(2^5=..2\)
....
Thus, \(3^21=...7\) and \(2^18=...4\). Then, their difference will terminate with a 7-4=3!
Re: What is the ones digit of 3^23 - 2^18?
[#permalink]
25 Sep 2017, 06:30
25 Sep 2017, 06:30
3
Carcass wrote:
Now we know
Ones digit of\(2 ^ {any power}\) = 2,4,8,6 i.e it keeps repeating after every 4 cycle
Ones digit of \(3 ^ {any power}\) = 3,9,7,1 i.e it keeps repeating after every 4 cycle
Now ones digit of \(3^{23}\) = 7 (divide 23/4 , since it repeats after every 4 cycle and the remainder is 3, so we have to consider the third term i.e 7 (3,9,7,1))
Similarly ones digit of \(2^{18}\) = 4 (divide 18/4 , since it repeats after every 4 cycle and the remainder is 2,
so we have to consider the second term i.e 4(2,4,8,6))
Now
the ones digit of \(3^{23} - 2^{18}\) = 7-4 = 3
