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 units digit of
[#permalink]
28 Jan 2021, 03:10
28 Jan 2021, 03:10
Expert Reply
1
Bookmarks
00:00
Question Stats:
88% (00:45) correct
11% (04:21) wrong based on 9 sessions
Hide Show timer Statistics
What is the units digit of \(13^{2003}\)?
(A) 1
(B) 3
(C) 7
(D) 8
(E) 9
Kudos for the right answer and explanation
(A) 1
(B) 3
(C) 7
(D) 8
(E) 9
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
What is the units digit of
[#permalink]
28 Jan 2021, 05:45
28 Jan 2021, 05:45
1
Carcass wrote:
What is the units digit of \(13^{2003}\)?
(A) 1
(B) 3
(C) 7
(D) 8
(E) 9
Kudos for the right answer and explanation
(A) 1
(B) 3
(C) 7
(D) 8
(E) 9
Kudos for the right answer and explanation
Look for a pattern
13^1 = 13
13^2 = (13)(13) = ---9 [aside: we need not determine the other digits. All we care about is the units digit]
13^3 = (13)(13^2) = (13)(---9) = ----7
13^4 = (13)(13^3) = (13)(---7) = ----1
13^5 = (13)(13^4) = (13)(---1) = ----3
NOTICE that we're back to where we started.
13^5 has units digit 3, and 13^1 has units digit 3
So, at this point, our pattern of units digits keep repeating 3, 9, 7, 1, 3, 9, 7, 2, . . .
We say that we have a "cycle" of 4, which means the digits repeat every 4 powers.
So, we get:
13^1 = --3
13^2 = ---9
13^3 = ----7
13^4 = ----1
13^5 = ----3
13^6 = ---9
13^7 = ----7
13^8 = ----1
13^9 = ----3
13^10 = ----9
etc.
Notice that when the exponent is a MULTIPLE of 4 (4, 8, 12, 16, ...), the units digit will be 1
Since 2000 is a MULTIPLE of 4, we know that the units digit of 13^2000 will be 1
Continuing with the pattern:
13^2001 = --3
13^2002 = ---9
13^2003 = ----7
Answer: C
Here's an article I wrote on this topic (with additional practice questions): https://www.greenlighttestprep.com/arti ... big-powers
Cheers,
Brent
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
What is the units digit of
[#permalink]
13 Dec 2023, 08:20
13 Dec 2023, 08:20
1
We need to find the units digit of \(13^{2003}\)
Units digit of \(13^{2003}\) will be same as units digit of \(3^{2003}\)
Lets start by finding the cyclicity of units' digit in powers of 3
\(3^1\) units’ digit is 3
\(3^2\) units’ digit is 9
\(3^3\) units’ digit is 7
\(3^4\) units’ digit is 1
\(3^5\) units’ digit is 3
That means that units digit of power of 3 has a cycle of 4
=> We need to divide the power (2003) by 4 and check what is the remainder
2003 divided by 4 gives 3 remainder
=> Units digit of \(13^{2003}\) = Units digit of \(3^3\) = 7
So, Answer will be C
Hope it helps!
MASTER how to find Units digit of Power of 3
Units digit of \(13^{2003}\) will be same as units digit of \(3^{2003}\)
Lets start by finding the cyclicity of units' digit in powers of 3
\(3^1\) units’ digit is 3
\(3^2\) units’ digit is 9
\(3^3\) units’ digit is 7
\(3^4\) units’ digit is 1
\(3^5\) units’ digit is 3
That means that units digit of power of 3 has a cycle of 4
=> We need to divide the power (2003) by 4 and check what is the remainder
2003 divided by 4 gives 3 remainder
=> Units digit of \(13^{2003}\) = Units digit of \(3^3\) = 7
So, Answer will be C
Hope it helps!
MASTER how to find Units digit of Power of 3
