|
|
GMAT 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.
11 Nov 2022, 13:49
Kudos
Bookmarks
C
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:
81% (00:44) correct
19%
(00:57)
wrong
based on 141
sessions
History
Date
Time
Result
Not Attempted Yet
GMATCoachBen
Expert
Tutor
Joined: 21 Mar 2017
Last visit: 29 Apr 2026
Posts: 463
Given Kudos: 215
Status:Professional GMAT Trainer
Affiliations: GMAT Coach
Location: United States (WA)
GMAT Focus 1: 775 Q87 V90 DI88 (Online) 
GMAT 1: 760 Q50 V44
GMAT 2: 770 Q51 V44
GMAT 3: 770 Q50 V44
GMAT 4: 770 Q50 V45 (Online)
GMAT 5: 780 Q51 V48
Expert reply
11 Nov 2022, 14:23
Kudos
Bookmarks
Bunuel
First, find the units digit pattern for powers of 2:
2^1 = 2 (1st step in our pattern)
2^2 = 4 (2nd step)
2^3 = 8 (3rd step)
2^4 = 16 (4th step)
Note that if we continue writing out the pattern, we only need to multiply the units digit of 16 by 2 (we only care about the "6", not the "1")
2^5 --> 6*2 = 12 --> ends in 2
We can see that the pattern repeats for every 4 numbers: 2, 4, 8, 6...
Therefore, if the power is a multiple of 4, the units digit will be a 6.
For example:
2^40 ends in a 6
2^41 ends in a 2
2^42 ends in a 4
2^43 ends in an 8
2^44 ends in a 6
So, the next step is to find where the power of 2222 lands in the pattern.
The quickest way is to notice that 2220 is a multiple of 4, because the last 2 digits are a multiple of 4. Therefore, 2^2220 would end in a 6.
So, 2222 is 2 steps farther in our pattern, which goes "2,4,8,6", and therefore ends in a 4, so the answer is C.
To become very quick and accurate on these, flashcards are helpful, such as the ones below:
Attachments
2022-11-11 13_32_14-Brainscape_ What would you like to learn today_.png [ 44.94 KiB | Viewed 6328 times ]
2022-11-11 13_32_39-Brainscape_ What would you like to learn today_.png [ 67.85 KiB | Viewed 6316 times ]
12 Dec 2023, 06:26
Kudos
Bookmarks
↧↧↧ Detailed Video Explanation to the Problem ↧↧↧
We need to find the units digit of \(2^{2222}\)
Lets start by finding the cyclicity of units' digit in powers of 2
\(2^1\) units’ digit is 2
\(2^2\) units’ digit is 4
\(2^3\) units’ digit is 8
\(2^4\) units’ digit is 6
\(2^5\) units’ digit is 2
That means that units digit of power of have a cycle of 4
=> We need to divide the power (2222) by 4 and check what is the remainder
2222 divided by 4 gives 2 remainder
=> Units digit of \(2^{2222}\) = Units digit of \(2^2\) = 4
So, Answer will be C
Hope it helps!
MASTER how to find Units digit of Power of 2
We need to find the units digit of \(2^{2222}\)
Lets start by finding the cyclicity of units' digit in powers of 2
\(2^1\) units’ digit is 2
\(2^2\) units’ digit is 4
\(2^3\) units’ digit is 8
\(2^4\) units’ digit is 6
\(2^5\) units’ digit is 2
That means that units digit of power of have a cycle of 4
=> We need to divide the power (2222) by 4 and check what is the remainder
2222 divided by 4 gives 2 remainder
=> Units digit of \(2^{2222}\) = Units digit of \(2^2\) = 4
So, Answer will be C
Hope it helps!
MASTER how to find Units digit of Power of 2
