Last visit was: 09 Nov 2024, 17:22 It is currently 09 Nov 2024, 17:22

Close

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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Verbal Expert
Joined: 18 Apr 2015
Posts: 29922
Own Kudos [?]: 36162 [1]
Given Kudos: 25899
Send PM
Intern
Intern
Joined: 15 Jun 2023
Posts: 17
Own Kudos [?]: 16 [1]
Given Kudos: 29
Send PM
Verbal Expert
Joined: 18 Apr 2015
Posts: 29922
Own Kudos [?]: 36162 [1]
Given Kudos: 25899
Send PM
Verbal Expert
Joined: 18 Apr 2015
Posts: 29922
Own Kudos [?]: 36162 [0]
Given Kudos: 25899
Send PM
Re: While shifting his departmental store, Mr. Johnson found the number of [#permalink]
Expert Reply
OE


The number of articles in the store was 7^{20} which were stored in 8 rooms of equal capacity. As 𝑛 articles were left with no space in the room, hence the minimum value of 𝑛 will be the remainder we get when 7^{20} is divided by 8

n= the remainder of \(\frac{7^{20}}{8}\)

dividing \(7^1\) by 8 the remainder is 7

\(7^2\) by 8 we have a remainder of 1

So we do have a ciclicity

Dividing the odd powers of 7 by 8 gives us a remainder 7 whereas dividing even powers of 7 by 8 gives us a remainder 1.

Now, we need to find the remainder when \(7^{20}\) is divided by 8.

Since, the power is even, the remainder will be 1.
Hence, the answer is B.
Ans.(B)
Prep Club for GRE Bot
Re: While shifting his departmental store, Mr. Johnson found the number of [#permalink]
Moderators:
GRE Instructor
78 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne