GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Sep 2018, 21:43

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.

Close

Request Expert Reply

Confirm Cancel

In the first 1000 positive integers, how many integers exist such that

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
In the first 1000 positive integers, how many integers exist such that  [#permalink]

Show Tags

New post 14 Mar 2016, 09:04
2
21
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

51% (02:41) correct 49% (02:48) wrong based on 231 sessions

HideShow timer Statistics

In the first 1000 positive integers, how many integers exist such that they leave a remainder 4 when divided by 7, and a remainder 9 when divided by 11?

A. 10
B. 11
C. 12
D. 13
E. 14

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Most Helpful Community Reply
Verbal Forum Moderator
User avatar
V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2107
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
GMAT ToolKit User Reviews Badge CAT Tests
Re: In the first 1000 positive integers, how many integers exist such that  [#permalink]

Show Tags

New post 14 Mar 2016, 11:19
3
3
When integer A is divided by 7 , it leaves a remainder of 4
A= 7 q +4
A can take values 4 , 11 , 18 , 25 , 32 , 39 , 46 , 53 , 60
When integer A is divided by 11 , it leaves a remainder of 9
A= 11 p + 9
A can take values 9 , 20 , 31 , 42 , 53 , 64
The first integer which fulfills the given criteria is 53 . Similarly , we will get the next such after an interval of LCM of 7 and 11 , that is 77
The numbers are 53 , 120 .... and 977 (977= 77*12 + 53)

Number of such integers = 13

Answer D
_________________

When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
+1 Kudos if you find this post helpful

General Discussion
Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2648
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User Premium Member
Re: In the first 1000 positive integers, how many integers exist such that  [#permalink]

Show Tags

New post 17 Mar 2016, 05:27
1
Skywalker18 wrote:
When integer A is divided by 7 , it leaves a remainder of 4
A= 7 q +4
A can take values 4 , 11 , 18 , 25 , 32 , 39 , 46 , 53 , 60
When integer A is divided by 11 , it leaves a remainder of 9
A= 11 p + 9
A can take values 9 , 20 , 31 , 42 , 53 , 64
The first integer which fulfills the given criteria is 53 . Similarly , we will get the next such after an interval of LCM of 7 and 11 , that is 77
The numbers are 53 , 120 .... and 977 (977= 77*12 + 53)

Number of such integers = 13

Answer D



Hey i solve the question on the same approach..
But it is taking way too much time..
Any other methods?
_________________


MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Manager
Manager
User avatar
Joined: 19 Dec 2015
Posts: 111
Location: United States
GMAT 1: 720 Q50 V38
GPA: 3.8
WE: Information Technology (Computer Software)
Re: In the first 1000 natural numbers, how many integers exist such that t  [#permalink]

Show Tags

New post 11 Jun 2016, 08:46
1
1
First number in this series = 53
last number in the series = 977

The series will be an arithmetic progression with first term = 53, last term = 977, and difference = 11*7 = 77
general formula for nth term => a(n) = a(1) + (n-1)d => 977 = 53 + (n-1)*77 => n-1 = 12 => n=13. Hence D.
Manager
Manager
avatar
G
Joined: 14 Oct 2012
Posts: 174
Premium Member Reviews Badge
Re: In the first 1000 positive integers, how many integers exist such that  [#permalink]

Show Tags

New post 30 Jul 2017, 11:02
My 2 cents -

If you have any question please let me know -
Attachments

my 2 cents.png
my 2 cents.png [ 3.39 MiB | Viewed 9681 times ]

VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1088
In the first 1000 positive integers, how many integers exist such that  [#permalink]

Show Tags

New post Updated on: 20 Aug 2017, 21:28
1
Bunuel wrote:
In the first 1000 positive integers, how many integers exist such that they leave a remainder 4 when divided by 7, and a remainder 9 when divided by 11?

A. 10
B. 11
C. 12
D. 13
E. 14


let n=dividend
(n-4)/7=p
(n-11)/9=q
combining,
7p-11q=5
p=7
q=4
least value of n=53
let x=number of n-1
53+(7*11)x<1001
77x<948
x<12.3
x=12
12+1=13
D

Originally posted by gracie on 30 Jul 2017, 13:01.
Last edited by gracie on 20 Aug 2017, 21:28, edited 1 time in total.
Manager
Manager
avatar
B
Joined: 04 May 2014
Posts: 161
Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: In the first 1000 positive integers, how many integers exist such that  [#permalink]

Show Tags

New post 20 Aug 2017, 07:28
1
1
How did we get the last no in the series

FacelessMan wrote:
First number in this series = 53
last number in the series = 977

The series will be an arithmetic progression with first term = 53, last term = 977, and difference = 11*7 = 77
general formula for nth term => a(n) = a(1) + (n-1)d => 977 = 53 + (n-1)*77 => n-1 = 12 => n=13. Hence D.
Intern
Intern
avatar
Joined: 27 May 2018
Posts: 1
Re: In the first 1000 positive integers, how many integers exist such that  [#permalink]

Show Tags

New post 27 May 2018, 04:57
how can i solve within short time?

Posted from my mobile device
Intern
Intern
avatar
B
Joined: 27 Dec 2016
Posts: 2
Re: In the first 1000 positive integers, how many integers exist such that  [#permalink]

Show Tags

New post 31 Jul 2018, 08:23
How did we get the last number in the series?
Intern
Intern
avatar
B
Joined: 27 Aug 2014
Posts: 3
Re: In the first 1000 positive integers, how many integers exist such that  [#permalink]

Show Tags

New post 31 Jul 2018, 10:09
1
helishah142

977 is calculated by adding 53 to the last multiple of 77 that is < 1000 i.e. 53+ 77*12 = 977.

Hope it helps.
Intern
Intern
avatar
B
Joined: 04 Apr 2018
Posts: 1
Re: In the first 1000 positive integers, how many integers exist such that  [#permalink]

Show Tags

New post 31 Jul 2018, 10:51
Skywalker18 wrote:
When integer A is divided by 7 , it leaves a remainder of 4
A= 7 q +4
A can take values 4 , 11 , 18 , 25 , 32 , 39 , 46 , 53 , 60
When integer A is divided by 11 , it leaves a remainder of 9
A= 11 p + 9
A can take values 9 , 20 , 31 , 42 , 53 , 64
The first integer which fulfills the given criteria is 53 . Similarly , we will get the next such after an interval of LCM of 7 and 11 , that is 77
The numbers are 53 , 120 .... and 977 (977= 77*12 + 53)

Number of such integers = 13

Answer D


Please change the series.. 53, 130, ... I got confused when I read it.
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3515
Location: United States (CA)
Re: In the first 1000 positive integers, how many integers exist such that  [#permalink]

Show Tags

New post 10 Aug 2018, 19:07
Bunuel wrote:
In the first 1000 positive integers, how many integers exist such that they leave a remainder 4 when divided by 7, and a remainder 9 when divided by 11?

A. 10
B. 11
C. 12
D. 13
E. 14


We need to find the smallest integer that satisfies both conditions:

Numbers that leave a remainder of 4 when divided by 7 are:

4, 11, 18, 25, 32, 39, 46, 53, ...

Numbers that leave a remainder of 9 when divided by 11 are:

20, 31, 42, 53, …

We see that 53 is the first number that satisfies both conditions. To find the subsequent numbers that also satisfy both conditions we keep adding the LCM of 7 and 11, i.e., 77, to (and beginning with) 53. So the numbers, including 53, are:

53, 130, 207, 284, 361, 438, 515, 592, 669, 746, 823, 900, and 977

So there are a total of 13 such numbers.

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Senior Manager
Senior Manager
avatar
P
Joined: 31 Jul 2017
Posts: 461
Location: Malaysia
Schools: INSEAD Jan '19
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
CAT Tests
Re: In the first 1000 positive integers, how many integers exist such that  [#permalink]

Show Tags

New post 11 Aug 2018, 01:13
Bunuel wrote:
In the first 1000 positive integers, how many integers exist such that they leave a remainder 4 when divided by 7, and a remainder 9 when divided by 11?

A. 10
B. 11
C. 12
D. 13
E. 14


The Terms are -

53,130, .............. So, T(n) = 77n-24........ Only D satisfies.
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

GMAT Club Bot
Re: In the first 1000 positive integers, how many integers exist such that &nbs [#permalink] 11 Aug 2018, 01:13
Display posts from previous: Sort by

In the first 1000 positive integers, how many integers exist such that

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


cron
Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.