Last visit was: 24 Apr 2026, 04:16 It is currently 24 Apr 2026, 04:16
Home
Messages
Tests
Schools
Events
Close
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

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 GMAT 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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
aiming4mba
User avatar
Joined: 20 Nov 2009
Last visit: 22 May 2012
Posts: 97
Own Kudos:
1,088
Given Kudos: 64
Posts: 97
Kudos: 1,088
Another remainder question 21 Mar 2011, 12:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
What is the remainder when 7^84/342

A. 1
B. 2
C. 3
D. 4
E. 5



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 23 Apr 2026
Posts: 16,442
Own Kudos:
79,400
 [2]
Given Kudos: 485
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,442
Kudos: 79,400
 [2]
Another remainder question 22 Mar 2011, 18:32
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
aiming4mba
What is the remainder when 7^84/342

A. 1
B. 2
C. 3
D. 4
E. 5
Show more

First up, GMAT questions don't involve painful calculations. So there has to be some obvious link between 7 and 342. It helps one to know the squares of first 20 numbers and cubes of first 10 numbers.
What immediately comes to mind is that 7^3 = 343

So \(\frac{7^{84}}{342} = \frac{(7^3)^{28}}{342} = \frac{343^{28}}{342} = \frac{(342 + 1)^{28}}{342}\)

Now, when you open \((a + b)^n\), every term will be divisible by a except the last term i.e. \(b^n\) (using binomial theorem)
So every term of \((342 + 1)^{28}\) will be divisible by 342 except the last term 1^{28} = 1. Hence remainder is 1.

If you are not comfortable with binomial theorem, don't worry about it. Just remember that when you write down all the terms of \((a + b)^n\), each term is divisible by a except the last term b^n. To see an example, let's take a small value of n
\((a+b)^2 = a^2 + 2ab + b^2\)
\((a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\)
All terms are divisible by a except the last term.
There are other ways to get to the answer but they are a little cumbersome...

Is this question from some GMAT specific source?
User avatar
aiming4mba
User avatar
Joined: 20 Nov 2009
Last visit: 22 May 2012
Posts: 97
Own Kudos:
1,088
Given Kudos: 64
Posts: 97
Kudos: 1,088
Another remainder question 22 Mar 2011, 23:31
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thanks Karishma, its clear now. yes, this question is from a prep material by a coaching centre for GMAT
User avatar
ashkanator
User avatar
Joined: 16 Mar 2011
Last visit: 29 May 2012
Posts: 135
Own Kudos:
22
Given Kudos: 1
Posts: 135
Kudos: 22
Another remainder question 23 Mar 2011, 17:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasPrepKarishma
aiming4mba
What is the remainder when 7^84/342

A. 1
B. 2
C. 3
D. 4
E. 5

First up, GMAT questions don't involve painful calculations. So there has to be some obvious link between 7 and 342. It helps one to know the squares of first 20 numbers and cubes of first 10 numbers.
What immediately comes to mind is that 7^3 = 343

So \(\frac{7^{84}}{342} = \frac{(7^3)^{28}}{342} = \frac{343^{28}}{342} = \frac{(342 + 1)^{28}}{342}\)

Now, when you open \((a + b)^n\), every term will be divisible by a except the last term i.e. \(b^n\) (using binomial theorem)
So every term of \((342 + 1)^{28}\) will be divisible by 342 except the last term 1^{28} = 1. Hence remainder is 1.

If you are not comfortable with binomial theorem, don't worry about it. Just remember that when you write down all the terms of \((a + b)^n\), each term is divisible by a except the last term b^n. To see an example, let's take a small value of n
\((a+b)^2 = a^2 + 2ab + b^2\)
\((a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\)
All terms are divisible by a except the last term.
There are other ways to get to the answer but they are a little cumbersome...

Is this question from some GMAT specific source?
Show more
like the way you do these hard remainder problems...
User avatar
Banterninja
User avatar
Joined: 27 Feb 2011
Last visit: 05 Sep 2011
Posts: 14
Status:Targeting 750+
Location: Chennai, India
Concentration: Consulting, Marketing
GPA: 3.86
Posts: 14
Kudos: 0
Another remainder question 25 Mar 2011, 21:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasPrepKarishma
aiming4mba
What is the remainder when 7^84/342

A. 1
B. 2
C. 3
D. 4
E. 5

First up, GMAT questions don't involve painful calculations. So there has to be some obvious link between 7 and 342. It helps one to know the squares of first 20 numbers and cubes of first 10 numbers.
What immediately comes to mind is that 7^3 = 343

So \(\frac{7^{84}}{342} = \frac{(7^3)^{28}}{342} = \frac{343^{28}}{342} = \frac{(342 + 1)^{28}}{342}\)

Now, when you open \((a + b)^n\), every term will be divisible by a except the last term i.e. \(b^n\) (using binomial theorem)
So every term of \((342 + 1)^{28}\) will be divisible by 342 except the last term 1^{28} = 1. Hence remainder is 1.
Show more

Really good explanation! I followed your explanation on 2^92/7. There were possible alternatives then. But this one, your logic will work way more faster than what was also suggested there.
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 23 Apr 2026
Posts: 16,442
Own Kudos:
79,400
 [1]
Given Kudos: 485
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,442
Kudos: 79,400
 [1]
Another remainder question 26 Mar 2011, 19:52
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Banterninja


Really good explanation! I followed your explanation on 2^92/7. There were possible alternatives then. But this one, your logic will work way more faster than what was also suggested there.
Show more

Yes, once you get used to these ideas, you can solve these questions orally.
User avatar
gmat1220
User avatar
Joined: 03 Feb 2011
Last visit: 17 Feb 2020
Posts: 461
Own Kudos:
1,015
Given Kudos: 123
Status:Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Products:
My Reviews
Posts: 461
Kudos: 1,015
Another remainder question 27 Mar 2011, 01:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
A is alright. But another answer can be 7.

7^84 = (7^4) ^21. i.e 4*21 = 84
7^4 = 2401 will leave remainder 7 when divided by 342.
2401= 7 * 342 + 7

Unit digit of 7^21 is same as the unit digit of 7^1.

aiming4mba
What is the remainder when 7^84/342

A. 1
B. 2
C. 3
D. 4
E. 5
Show more
User avatar
gmat1220
User avatar
Joined: 03 Feb 2011
Last visit: 17 Feb 2020
Posts: 461
Own Kudos:
1,015
Given Kudos: 123
Status:Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Products:
My Reviews
Posts: 461
Kudos: 1,015
Another remainder question 27 Mar 2011, 02:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thanks fluke !!!!!. Yeah I realized this when I in the gym :-D Kudos......
User avatar
subhashghosh
User avatar
Retired Moderator
Joined: 16 Nov 2010
Last visit: 25 Jun 2024
Posts: 894
Own Kudos:
1,302
Given Kudos: 43
Location: United States (IN)
Concentration: Strategy, Technology
Products:
My Reviews
Posts: 894
Kudos: 1,302
Another remainder question 27 Mar 2011, 03:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Brilliant explanation Karishma. +1 to you.
User avatar
qweert
User avatar
Joined: 27 May 2010
Last visit: 02 May 2014
Posts: 140
Own Kudos:
214
Given Kudos: 3
Posts: 140
Kudos: 214
Another remainder question 04 Apr 2011, 05:02
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Very helpful explanation. I would definitely keep this in mind.

Thank you Karishma...



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!