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.
Dec 03Action Plan to Score 760 on the GMAT
07:00 AM PST
-09:00 AM PST
Attend the upcoming GMAT Strategy masterclass to get your personalized study plan that defines the exact metrics you need to hit to score GMAT 760 ‘effectively’.- Dec 04
Master 700-level Inequalities and Absolute Value Questions
07:00 AM PST
-09:00 AM PST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Dec 04How Mantavya Got a 770 on GMAT (In Just 2 Months) with GMATWhiz
11:30 AM EST
-12:30 PM EST
770 on the GMAT? It's a goal that many students aspire to achieve, but only 1% of all test takers receive it. Watch this interview to learn how Mantavya scored a remarkable 770 GMAT with just 2 months of preparation in first attempt.
Dec 04Free GMAT Prep Hour
08:00 PM EST
-09:00 PM EST
Strategies and techniques for approaching featured GMAT topics. One hour of live, online instruction
Dec 08Prep smart with Magoosh GMAT
07:00 PM PST
-08:00 PM PST
Magoosh students get into top business schools like MIT Sloan, HBS, Stanford GSB, Wharton and more. See why over 6 million students trust us for exam prep.
What is the remainder when 7^9 - 4 is divided by 7?
[#permalink]
14 Apr 2017, 03:32
14 Apr 2017, 03:32
2
Kudos
16
Bookmarks
00:00
A
B
C
D
E
Difficulty:
15%
(low)
Question Stats:
72%
(00:56)
correct
28%
(00:59)
wrong
based on 266
sessions
Hide Show timer Statistics
What is the remainder when 7^9 - 4 is divided by 7?
[#permalink]
Updated on: 12 Jul 2021, 08:37
Updated on: 12 Jul 2021, 08:37
4
Kudos
2
Bookmarks
Expert Reply
Top Contributor
amathews wrote:
What is the remainder when 7^9 - 4 is divided by 7?
A)1
B)2
C)3
D)4
E)5
A)1
B)2
C)3
D)4
E)5
KEY STRATEGY: If we take 7^9 - 4 and add zero to it, the value doesn't change.
We're going to add zero by subtracting 3 and adding 3 at the same time.
So, 7^9 - 4 = 7^9 - 4 - 3 + 3
= 7^9 - 7 + 3
= 7(7^8 - 1) + 3
= 7(some integer) + 3
As we can see, our initial number can be rewritten as 3 more than some multiple of 7.
So, if we divide that number by 7, the remainder will be 3
Answer: C
RELATED VIDEO
_________________
Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing - Learn more
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing - Learn more
Originally posted by BrentGMATPrepNow on 14 Apr 2017, 05:27.
Last edited by BrentGMATPrepNow on 12 Jul 2021, 08:37, edited 1 time in total.
Last edited by BrentGMATPrepNow on 12 Jul 2021, 08:37, edited 1 time in total.
Re: What is the remainder when 7^9 - 4 is divided by 7?
[#permalink]
14 Apr 2017, 03:36
14 Apr 2017, 03:36
4
Kudos
1
Bookmarks
Expert Reply
amathews wrote:
What is the remainder when 7^9 - 4 is divided by 7?
A)1
B)2
C)3
D)4
E)5
A)1
B)2
C)3
D)4
E)5
7^9 - 4 = {a multiple of 7} - 4, so it's 4 less than a multiple of 7 (3, 10, 17, ...), so the remainder is 3.
Answer: C.
_________________
New to the GMAT CLUB Forum?
My Signature Questions' Collection:
What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
- Posting Rules: QUANTITATIVE | VERBAL.
Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant
Questions' Bank By Tags and Difficulty: GMAT Club's Complete Questions' Bank
My Signature Questions' Collection:
What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
General Discussion
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 5650
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Re: What is the remainder when 7^9 - 4 is divided by 7?
[#permalink]
14 Apr 2017, 06:00
14 Apr 2017, 06:00
1
Kudos
2
Bookmarks
amathews wrote:
What is the remainder when 7^9 - 4 is divided by 7?
A)1
B)2
C)3
D)4
E)5
A)1
B)2
C)3
D)4
E)5
\(\frac{7^9 - 4}{7}\)
\(= Rem ( 0 - 4 )\)
So, We have remainder -4
Thus, the value of the remainder will be \(7 - 4 = 3\)
Answer, must be (C) 3
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Re: What is the remainder when 7^9 - 4 is divided by 7?
[#permalink]
14 Apr 2017, 07:29
14 Apr 2017, 07:29
Bunuel wrote:
amathews wrote:
What is the remainder when 7^9 - 4 is divided by 7?
A)1
B)2
C)3
D)4
E)5
A)1
B)2
C)3
D)4
E)5
7^9 - 4 = {a multiple of 7} - 4, so it's 4 less than a multiple of 7 (3, 10, 17, ...), so the remainder is 3.
Answer: C.
When it is 7^8 -4 then what would be remainder. Thanks in advance.
Re: What is the remainder when 7^9 - 4 is divided by 7?
[#permalink]
14 Apr 2017, 07:35
14 Apr 2017, 07:35
Expert Reply
Chemerical71 wrote:
Bunuel wrote:
amathews wrote:
What is the remainder when 7^9 - 4 is divided by 7?
A)1
B)2
C)3
D)4
E)5
A)1
B)2
C)3
D)4
E)5
7^9 - 4 = {a multiple of 7} - 4, so it's 4 less than a multiple of 7 (3, 10, 17, ...), so the remainder is 3.
Answer: C.
When it is 7^8 -4 then what would be remainder. Thanks in advance.
It seems that you did not understand the explanation. The remainder of 7^n - 4 divided by 7 where n is a positive integer is always 3.
_________________
New to the GMAT CLUB Forum?
My Signature Questions' Collection:
What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
- Posting Rules: QUANTITATIVE | VERBAL.
Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant
Questions' Bank By Tags and Difficulty: GMAT Club's Complete Questions' Bank
My Signature Questions' Collection:
What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 4843
Location: India
GMAT 1: 690 Q50 V34 
WE:Engineering (Transportation)
Re: What is the remainder when 7^9 - 4 is divided by 7?
[#permalink]
15 Aug 2020, 08:45
15 Aug 2020, 08:45
Asked: What is the remainder when 7^9 - 4 is divided by 7?
(7^9-4)mod7 = -4mod7 = 3mod7
IMO C
_________________
(7^9-4)mod7 = -4mod7 = 3mod7
IMO C
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Email: kinshook.chaturvedi@gmail.com
Intern
Joined: 12 Jan 2017
Posts: 9
Concentration: Technology, Strategy
WE:Information Technology (Computer Software)
Re: What is the remainder when 7^9 - 4 is divided by 7?
[#permalink]
22 Aug 2020, 08:56
22 Aug 2020, 08:56
1
Kudos
Can anyone please explain it again in simple terms. I am still not able to understand it. May be i am missing something here.
GMAT Tutor
Joined: 05 Apr 2011
Status:Tutor - BrushMyQuant
Posts: 1486
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Re: What is the remainder when 7^9 - 4 is divided by 7?
[#permalink]
20 Oct 2022, 09:10
20 Oct 2022, 09:10
Expert Reply
Top Contributor
We need to find What is the remainder when \(7^9\) - 4 is divided by 7
\(7^9\) - 4 = \(7^9\) - 4 - 3 + 3 = \(7^9\) - 7 + 3 = 7*(\(7^8\) - 1) + 3 = (Multiple of 7) + 3
Theory: Remainder of a + b by a number say 7 is same as remainder of a by 7 + remainder of b by 7
=> Remainder of 7*(\(7^8\) - 1) + 3 by 7 is same as remainder of 7*(\(7^8\) - 1) by 7 + remainder of 3 by 7
=> 0 + 3 = 3
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Remainders
_________________
\(7^9\) - 4 = \(7^9\) - 4 - 3 + 3 = \(7^9\) - 7 + 3 = 7*(\(7^8\) - 1) + 3 = (Multiple of 7) + 3
Theory: Remainder of a + b by a number say 7 is same as remainder of a by 7 + remainder of b by 7
=> Remainder of 7*(\(7^8\) - 1) + 3 by 7 is same as remainder of 7*(\(7^8\) - 1) by 7 + remainder of 3 by 7
=> 0 + 3 = 3
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Remainders
_________________
Ankit
to My YouTube Channel to ENCOURAGE me to Keep Putting Regular Updates!!!
How to Solve :
Work Rate || Probability: Coin Toss || Probability: Dice Roll || Prime Numbers || Circles || Equilateral Triangle in a Circle || Arithmetic and Geometric Progression || Divisibility Rules || Absolute Value || Inequalities Basics || Inequalities (Problems) || Functions and Custom Characters || LCM and GCD || Remainders || Remainder Problems || Stem & Leaf Plot || Box And Whisker Plot || Statistics || Reflection of a line
How to start GMAT preparations? || How to Improve Quant Score? || OG Links || Gmatclub Topic Tags || My GMAT debrief || GMAT Quant Tutor
to My YouTube Channel to ENCOURAGE me to Keep Putting Regular Updates!!!How to Solve :
Work Rate || Probability: Coin Toss || Probability: Dice Roll || Prime Numbers || Circles || Equilateral Triangle in a Circle || Arithmetic and Geometric Progression || Divisibility Rules || Absolute Value || Inequalities Basics || Inequalities (Problems) || Functions and Custom Characters || LCM and GCD || Remainders || Remainder Problems || Stem & Leaf Plot || Box And Whisker Plot || Statistics || Reflection of a line
How to start GMAT preparations? || How to Improve Quant Score? || OG Links || Gmatclub Topic Tags || My GMAT debrief || GMAT Quant Tutor
gmatclubot
Re: What is the remainder when 7^9 - 4 is divided by 7? [#permalink]
20 Oct 2022, 09:10
Moderators:
|
|
||
