If n = 8^11 8, what is the units digit of n?

Question

If n = 8^11 – 8, what is the units digit of n?

A. 0
B. 1
C. 4
D. 6
E. 8

yezz · Answer

8(8^10 - 1)
8^1 = 8
8^2 = 16
8^3 = 32
8^4 = 64
8^5 = 128

thus 8^10 ends in 4, 4-1 = 3 , 3*8 = 24 units didgit is 4...c

scthakur · Answer

C.

8^11-8 = 8(8^10 - 1).

Now, 8^1 ends with 8
8^2 ends with 4
8^3 ends with 2
8^4 ends with 6..after this last digit will repeat.

Hence, 8^8 will end with 6 and 8^10 will end with 4.
4 - 1 = 3 and 3*8 ends with 4.

spriya · Answer

n = 8^11 – 8= 8((2^10)^3 -1)=8((1024^3 -1))=> ####3*8 => 4 is the digit !!!

IMO C

LiveStronger · Answer

E :8

n = 8^10(8-1) = 7 * 8^10 = 2^30 *7

2^1 - units digit is 2
2^2 - units digit is 4
2^3 - units digit is 8
2^4 - units digit is 16
2^5 - units digit is 2
.......

Basically, units digit cycle repeats every 4 times
So, 2^30 - units digit 4
units digit of 4 * 7 = 8

mrsmarthi · Answer

Well more or less similar explanation of what LiveStronger, but getting a different ans.

8 ^ 11 - 8 = 8 (8 ^ 10 - 1)

==> 8 (2 ^ 30 - 1)

Last digit of 2 ^ 30 is 4 based on what explanation LiveStronger is saying. 2 ^ 30 - 1 yields 4 - 1 = 3 as the unit digit. Now on multiply this with 8, we get unit digit as 4.

My Ans will be C.

I see some confusion in this line of explanation.

GMAT TIGER · Answer

n = 8^11 – 8

8^1 has unit digit 8
8^2 has unit digit 4
8^3 has unit digit 2
8^4 has unit digit 6

8^5 has unit digit 8
this is the pattern.

so 8^8 has 6 in unit digit
so 8^12 als has 6 in unit digit
so 8^11 als has 2 in unit digit

so if we deduct 8 from xxxxxxx2, the unit digit will be 4.

x2suresh · Answer

8^1 = unit digit 8
8^2 = unit digti 4
8^3= unit digit 2
8^4 = unit digt 6
8^5 = unit digit 8
..
repeats for every 4 times.

8^11 .. unit digit is 2

8^11 – 8 uniit digit is 4

C

jchae90 · Answer

If n = 8^11-8, what is the unit digit of n?

A. 0
B. 1
C. 4
D. 6
E. 8

***
First time posting - if anyone know how I can upload the answer without spoiling it please let me know!

abhinav008 · Answer

unit digit of 8^11 -8 is 
8 ( 8^10 -1 ) so basically we have to find unit digit of 8^10

Now unit digit of 8^1 = 8
8^2 = 4 
8^3 = 2
8^4 = 6
8^5 = 8 so cyclicity is 4 => 8^10 will have unit digit same as 8^2 which is 4

So unit digit of 8 ( 8^10 -1 ) = 8 ( 4-1) = 4 so C

Bunuel · Answer

Merging topics. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Thank you!

sagarsir · Answer

Always divide the power (incase 11) by 4 and use the remainder as the new power. The question now becomes 8^3 - 8. Now 8^3 has last digit 2. Since 8^11 (or for that matter 8^3) is greater than 8, we subtract 8 from 12 ( the 10+2 --> 10 has come from carry over from the tenth place). thus 12 - 8 = 4 is the answer. Option C Kudos if you like

Dabhishek · Answer

pheww.. a close shave got 3 by mistake n then upon seeing no 3 in options, recalculate... n then got 4 :lol:

ScottTargetTestPrep · Answer

Observe that n = 8^11 - 8 = 8(8^10 - 1). Let’s first find the pattern of units digits of powers of 8:

8^1 = 8

8^2 = 4

8^3 = 2

8^4 = 6

8^5 = 8

We see that the pattern of units digits of powers of 8 is 8-4-2-6. Furthermore, the units digit of powers of 8 that are multiples of 4 is 6 and the units digit of powers of 8 that are 2 more than multiples of 4 is 4. That is, the units digit of 8^10 is 4. Replace 8^10 with 4 and we have 8(4 - 1) = 8(3) = 24. Since 24 has a units digit of 4, n also has units digit of 4.

Answer: C

pkshankar · Answer

Unit's digit of  8^{n}  where 'n' is positive integer repeats after every 4 powers i.e.
 8^{1}  =  8 
 8^{2}  = 6 4 
 8^{3}  = 51 2 
 8^{4}  = 409 6 
 8^{5}  = 3276 8 
likewise 8^{11} = unit's digit is 2
hence the units digit of  8^{11} -11 = 4

AnupamKT · Answer

Unit digit of 8^11 can be found as below:
Unit digit of 8^(4n+3) will be 2. Hence 8^11 will be 2 in it's unit digit.
Hence 8^11-8 will have 4 in it's unit digit. Hence option C will be correct.

Posted from my mobile device

MHIKER · Answer

The unit digit cyclicity for 2,3, 7, and 8 is 4
So, we have to divide the 11 by 4 the remainder is 3
now get result 8^3 which is 512
now 512-8= 504
The unit digit is 4
Ans. C

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If n = 8^11 8, what is the units digit of n?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If n = 8^11 8, what is the units digit of n?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards