Last visit was: 20 Jul 2024, 07:37 |
It is currently 20 Jul 2024, 07:37 |

Customized

for You

Track

Your Progress

Practice

Pays

- Jul
**21**### GRE Practice Quiz (July 21st) - Quant, Data Analysis, Text Completion, Sentence Equivalence

06:30 AM PDT

-07:25 AM PDT

Solve GRE practice problems covering Quant (One answer choice and multiple answer choice), Data Interpretation, Text Completion, Sentence Equivalence, and Reading Comprehension Problems. - Jul
**23**### Free GRE Prep Hour

07:00 PM EDT

-08:00 PM EDT

Strategies and techniques for approaching featured GRE topics. One hour of live, online instruction

Which of the following could be the units digit 98^x
[#permalink]
30 Jul 2017, 08:50

1

Expert Reply

Question Stats:

Which of the following could be the units digit \(9^{8^x}\), where x is an integer greater than 1?

Indicate all such digits:

❑ zero

❑ 1

❑ 2

❑ 3

❑ 4

❑ 5

❑ 6

❑ 7

❑ 8

❑ 9

ShowHide Answer

Official Answer

C,E,G,I

Retired Moderator

Joined: **10 Apr 2015 **

Posts: **6218**

Given Kudos: **136 **

Re: Which of the following could be the units digit 98^x
[#permalink]
03 Aug 2017, 15:43

2

1

Bookmarks

Carcass wrote:

Which of the following could be the units digit \(98^x\), where x is an integer greater than 1?

Indicate all such digits:

❑ zero

❑ 1

❑ 2

❑ 3

❑ 4

❑ 5

❑ 6

❑ 7

❑ 8

❑ 9

Indicate all such digits:

❑ zero

❑ 1

❑ 2

❑ 3

❑ 4

❑ 5

❑ 6

❑ 7

❑ 8

❑ 9

Show: ::

C,E,G,I

98^1 = 98

98^2 = (98)(98) = ---4 [note: we need only recognize that the units digit of 98^2 will be equal to the units digit of (8)(8), which is 4]

98^3 = (98)(98)(98) = (---4)(98) = ----2 [note: we need only recognize that the units digit of (---4)(98) will be equal to the units digit of (4)(8), which is 2]

98^4 = (98)(98)(98)(98) = (----2)(98) = ----6

98^5 = (98)(98)(98)(98)(98) = (----6)(98) = ----8

At this point, we are repeating the pattern. So, there's no need to continue.

The pattern of units digits will be 8, 4, 2, 6, 8, 4, 2, 6, 8, etc

Answer: 2, 4, 6, 8 (C, E, G, I)

Cheers,

Brent

Re: Which of the following could be the units digit 98^x
[#permalink]
04 Aug 2017, 06:41

Expert Reply

Honestly,

I do not think such question adhere to the standards..........

I do not think such question adhere to the standards..........

Re: Which of the following could be the units digit 98^x
[#permalink]
10 Dec 2019, 07:25

Carcass wrote:

Honestly,

I do not think such question adhere to the standards..........

I do not think such question adhere to the standards..........

YES, But it is the better one for clarifying the unit digit conception.

Retired Moderator

Joined: **16 Apr 2020 **

Status:**Founder & Quant Trainer**

Affiliations: **Prepster Education**

Posts: **1546**

Given Kudos: **172 **

Location: **India**

WE:**Education (Education)**

Re: Which of the following could be the units digit 98^x
[#permalink]
11 Mar 2021, 23:48

Carcass wrote:

Which of the following could be the units digit \(98^x\), where x is an integer greater than 1?

Indicate all such digits:

❑ zero

❑ 1

❑ 2

❑ 3

❑ 4

❑ 5

❑ 6

❑ 7

❑ 8

❑ 9

\(8\) has a repeating pattern of \(4\)

\(8^1 = 8\)

\(8^2 = 64\)

\(8^3 = 512\)

\(8^4 = 4,096\)

\(8^5 = 32,768\)

i.e. 8, 4, 2, and 6 repeat at the units place every 4 powers

Hence, C, E, G, and I

Re: Which of the following could be the units digit 98^x
[#permalink]
18 Dec 2022, 11:17

Expert Reply

Fixed typo in the question. it was NOT \(98^x\) but

\(9^{8^x}\)

Thank you

\(9^{8^x}\)

Thank you

Re: Which of the following could be the units digit 98^x
[#permalink]
19 Dec 2022, 18:48

Carcass wrote:

Fixed typo in the question. it was NOT \(98^x\) but

\(9^{8^x}\)

Thank you

\(9^{8^x}\)

Thank you

Does this change to the answer to the question? Shouldn't it only be 1 as the only possible units digit since nine will always be raised to an even exponent?

Re: Which of the following could be the units digit 98^x
[#permalink]
19 Dec 2022, 23:47

Expert Reply

Not really, because we do have just a double step to perform but essentially the way to solve is the same

8^x if you to assess the pattern of 8

Turns out, you have to asses the pattern of nine based on the pattern of 8

Regards

8^x if you to assess the pattern of 8

Turns out, you have to asses the pattern of nine based on the pattern of 8

Regards

Re: Which of the following could be the units digit 98^x
[#permalink]
05 Jan 2023, 10:27

1

I tried to solve the question as it is considered 9^8^x

1) 9^0=1

9^1=9

9^2=81 so in every two steps units digit repeats as "1"

2)8^x is the exponent of the question so

For the x>1, 8^x/2 such as 64/2, 512/2, 4096/2.... remainder would be "0"

Note: I diveded numbers every time to 2 because in the first explanation it repeats in every 2 steps.

3)For every circumustance remainder is "0" so 9^0=1 means for 9^8^x units digit is 1

İs it correct?

Thank You

1) 9^0=1

9^1=9

9^2=81 so in every two steps units digit repeats as "1"

2)8^x is the exponent of the question so

For the x>1, 8^x/2 such as 64/2, 512/2, 4096/2.... remainder would be "0"

Note: I diveded numbers every time to 2 because in the first explanation it repeats in every 2 steps.

3)For every circumustance remainder is "0" so 9^0=1 means for 9^8^x units digit is 1

İs it correct?

Thank You

Re: Which of the following could be the units digit 98^x
[#permalink]
05 Jan 2023, 10:49

1

Expert Reply

Essentially yes

Re: Which of the following could be the units digit 98^x
[#permalink]
28 Dec 2023, 19:41

Carcass wrote:

Essentially yes

Could you change the answer on the problem? It's still showing up as the answer to the question (98)^x

Re: Which of the following could be the units digit 98^x
[#permalink]
19 Feb 2024, 11:55

The answer here should be B

Re: Which of the following could be the units digit 98^x
[#permalink]
19 Feb 2024, 12:58

Expert Reply

Why ?

gmatclubot

Re: Which of the following could be the units digit 98^x [#permalink]

19 Feb 2024, 12:58
Moderators:

Multiple-choice Questions — Select One or More Answer Choices |
||

## Hi Generic [Bot],Here are updates for you: |