NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 13:35 It is currently 24 Apr 2024, 13:35
Decision Tracker
My Rewards
New posts
New comers' posts

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

How many integers are there between 1 and 1000, inclusive, that are

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
manalq8
Manager
Manager
Joined: 12 Apr 2011
Status:D-Day is on February 10th. and I am not stressed
Affiliations: American Management association, American Association of financial accountants
Posts: 118
Own Kudos [?]: 1850 [45]
Given Kudos: 52
Location: Kuwait
Concentration: finance and international business
Schools:Columbia university
 Q18  V17 GMAT 2: 320  Q18  V19 GMAT 3: 620  Q42  V33
GPA: 3.48
Send PM
How many integers are there between 1 and 1000, inclusive, that are [#permalink] New post   Updated on: 17 Mar 2024, 23:45
2
Kudos
43
Bookmarks
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

72% (02:44) correct 28% (02:46) wrong based on 472 sessions
Hide Show timer Statistics
How many integers are there between 1 and 1000, inclusive, that are not divisible by either 11 or 35?

A. 884
B. 890
C. 892
D. 910
E. 945

Experience a GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
GMAT Club Tests Check Our Products Try Free Tests
­
ShowHide Answer
Official Answer
A

Originally posted by manalq8 on 16 Jan 2012, 09:56.
Last edited by Bunuel on 17 Mar 2024, 23:45, edited 2 times in total.
Edited the question.
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92902
Own Kudos [?]: 618803 [19]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
How many integers are there between 1 and 1000, inclusive, that are [#permalink] New post   16 Jan 2012, 12:17
3
Kudos
16
Bookmarks
Expert Reply
Official Solution:

How many integers are there between 1 and 1000, inclusive, that are not divisible by either 11 or 35?

A. 884
B. 890
C. 892
D. 910
E. 945


Let's determine the number of multiples of 11 or 35 between 1 and 1000, inclusive, and subtract that number from 1000.

The number of multiples of an integer within a range can be calculated using the following formula:

\(\frac{\text{last multiple in the range - first multiple in the range} }{\text{multiple} }+1\)

Thus:

• The number of multiples of 11 in the given range is \(\frac{ last - first}{multiple}+1=\frac{990-11}{11}+1=90\);

• The number of multiples of 35 in the given range is \(\frac{ last - first }{ multiple}+1=\frac{980-35}{35}+1=28\);

• The number of multiples of both 11 and 35 is 2 (since \(11*35=385\) and \(385*2=770\));

Observe that the two numbers 385 and 770 are included in the count of multiples of 11 and the count of multiples of 35. To avoid double-counting, we need to subtract these numbers once from the total count of multiples of 11 and 35. Therefore, the number of multiples of either 11 or 35 in the given range is \(90+28-2=116\).

Consequently, the count of numbers that are not divisible by either 11 or 35 is \(1000-116=884\).


Answer: A­
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14817
Own Kudos [?]: 64899 [6]
Given Kudos: 426
Location: Pune, India
Send PM
Re: How many integers are there between 1 and 1000, inclusive, that are [#permalink] New post   17 Jan 2012, 04:12
5
Kudos
1
Bookmarks
Expert Reply
manalq8 wrote:
What is the number of integers from 1 to 1000 (inclusive) that are divisible by neither 11 nor by 35?


884
890
892
910
945

what's the quickest way to solve this questions do you think?
I will provide the my approach and the OA once I see yours

thanks alot


Normally, I would use the method used by Bunuel. It's the most accurate. But if you are looking for a speedy solution, you can use another method which will sometimes give you an estimate. Looking at the options (most of them are spread out), I wont mind trying it. (Mind you, the method is accurate here since the numbers start from 1.)

In 1000 consecutive numbers, number of multiples of 11 = 1000/11 = 90 (Ignore decimals)
In 1000 consecutive numbers, number of multiples of 35 = 1000/35 = 28
Number of multiples of 11*35 i.e. 385 = 1000/385 = 2

Number of integers from 1 to 1000 that are divisible by neither 11 nor by 35 = 1000 - (90 + 28 - 2) {Using the concept of sets here) = 884

Think: Why did I say the method is approximate in some cases?
Think what happens if the given range is 11 to 1010 both inclusive (again 1000 numbers)
What is the number of multiples in this case?
General Discussion
avatar
gmatDeep
Intern
Intern
Joined: 28 Feb 2012
Posts: 14
Own Kudos [?]: 26 [3]
Given Kudos: 3
GMAT 1: 700 Q48 V39
WE:Information Technology (Computer Software)
Send PM
Re: How many integers are there between 1 and 1000, inclusive, that are [#permalink] New post   09 Apr 2012, 22:19
2
Kudos
Hello,

Calculate the no. of terms from 1 to 1000 (inclusive) that are divisible by 11 or 35 or both.

1. No of terms divisible by 11 -> 1000/11 = 90
2. No of terms divisible by 35 -> 1000/35 = 28
3. No of terms divisible by 11 and 35 -> 1000/(11*35) = 2

Answer = 1000- (90+28-2) = 884.
User avatar
Divyadisha
Current Student
Joined: 18 Oct 2014
Posts: 680
Own Kudos [?]: 1763 [0]
Given Kudos: 69
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
Send PM
GMAT ToolKit User
Re: How many integers are there between 1 and 1000, inclusive, that are [#permalink] New post   16 Jul 2016, 05:22
manalq8 wrote:
What is the number of integers from 1 to 1000 (inclusive) that are divisible by neither 11 nor by 35?

A. 884
B. 890
C. 892
D. 910
E. 945


Number divisible by 11:-
1000/11= 90

numbers divisible by 35:-
1000/35= 28

Numbers divisible by both 11 and 35= 2

Total numbers divisible by both 11 and 28= 90+28-2= 116 (because we counted 2 in both 90 and 28)

Total numbers not divisible by 11 or 35= 1000-116= 884

A is the answer
User avatar
B
law258
Senior Manager
Senior Manager
Joined: 05 Sep 2016
Status:DONE!
Posts: 274
Own Kudos [?]: 101 [0]
Given Kudos: 283
Send PM
Re: How many integers are there between 1 and 1000, inclusive, that are [#permalink] New post   29 Nov 2016, 20:03
Numbers divisible by 11: 1001/11 = 91
Numbers divisible by 35: 1001/35 = 28
Numbers divisible by 11x35: 1001/385 = 2

1001-(91+28)+2 = 884

A.
User avatar
gmatmartell
Intern
Intern
Joined: 17 Mar 2024
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 0
Location: United States
Send PM
Re: How many integers are there between 1 and 1000, inclusive, that are [#permalink] New post   17 Mar 2024, 20:54
law258 wrote:
Numbers divisible by 11: 1001/11 = 91
Numbers divisible by 35: 1001/35 = 28
Numbers divisible by 11x35: 1001/385 = 2

1001-(91+28)+2 = 884

A.

­Can you explain why you check for numbers dividible by 11x35?

Thank
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92902
Own Kudos [?]: 618803 [0]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: How many integers are there between 1 and 1000, inclusive, that are [#permalink] New post   17 Mar 2024, 23:48
Expert Reply
gmatmartell wrote:
law258 wrote:
Numbers divisible by 11: 1001/11 = 91
Numbers divisible by 35: 1001/35 = 28
Numbers divisible by 11x35: 1001/385 = 2

1001-(91+28)+2 = 884

A.

­Can you explain why you check for numbers dividible by 11x35?

Thank

­
I updted the solution HERE. Hope now it's clear.
User avatar
S
ruis
Manager
Manager
Joined: 17 Sep 2023
Posts: 130
Own Kudos [?]: 53 [0]
Given Kudos: 476
Send PM
Re: How many integers are there between 1 and 1000, inclusive, that are [#permalink] New post   31 Mar 2024, 10:07
Bunuel wrote:
Official Solution:

How many integers are there between 1 and 1000, inclusive, that are not divisible by either 11 or 35?

A. 884
B. 890
C. 892
D. 910
E. 945


Let's determine the number of multiples of 11 or 35 between 1 and 1000, inclusive, and subtract that number from 1000.

The number of multiples of an integer within a range can be calculated using the following formula:


\(\frac{\text{last multiple in the range - first multiple in the range} }{\text{multiple} }+1\)

Thus:


• The number of multiples of 11 in the given range is \(\frac{ last - first}{multiple}+1=\frac{990-11}{11}+1=90\);

• The number of multiples of 35 in the given range is \(\frac{ last - first }{ multiple}+1=\frac{980-35}{35}+1=28\);

• The number of multiples of both 11 and 35 is 2 (since \(11*35=385\) and \(385*2=770\));

Observe that the two numbers 385 and 770 are included in the count of multiples of 11 and the count of multiples of 35. To avoid double-counting, we need to subtract these numbers once from the total count of multiples of 11 and 35. Therefore, the number of multiples of either 11 or 35 in the given range is \(90+28-2=116\).

Consequently, the count of numbers that are not divisible by either 11 or 35 is \(1000-116=884\).


Answer: A­

­Hello Bunuel. Could you please help me understand a quick way to find out the greatest multiple of 35? How did you got within less than 2 minutes to 980?
It would help me a lot when using this method with big numbers like these.
User avatar
D
GMATCoachBen
Tutor
Joined: 21 Mar 2017
Status:Professional GMAT Trainer
Affiliations: GMAT Coach
Posts: 386
Own Kudos [?]: 846 [1]
Given Kudos: 198
Location: United States (WA)
GMAT 1: 760 Q50 V44
GMAT 2: 770 Q51 V44
GMAT 3: 770 Q50 V44
GMAT 4: 770 Q50 V45 (Online)
GMAT 5: 780 Q51 V48
Send PM
Re: How many integers are there between 1 and 1000, inclusive, that are [#permalink] New post   31 Mar 2024, 10:37
1
Kudos
Expert Reply
ruis wrote:
Bunuel wrote:
Official Solution:

How many integers are there between 1 and 1000, inclusive, that are not divisible by either 11 or 35?

A. 884
B. 890
C. 892
D. 910
E. 945


Let's determine the number of multiples of 11 or 35 between 1 and 1000, inclusive, and subtract that number from 1000.

The number of multiples of an integer within a range can be calculated using the following formula:




\(\frac{\text{last multiple in the range - first multiple in the range} }{\text{multiple} }+1\)

Thus:




• The number of multiples of 11 in the given range is \(\frac{ last - first}{multiple}+1=\frac{990-11}{11}+1=90\);

• The number of multiples of 35 in the given range is \(\frac{ last - first }{ multiple}+1=\frac{980-35}{35}+1=28\);

• The number of multiples of both 11 and 35 is 2 (since \(11*35=385\) and \(385*2=770\));

Observe that the two numbers 385 and 770 are included in the count of multiples of 11 and the count of multiples of 35. To avoid double-counting, we need to subtract these numbers once from the total count of multiples of 11 and 35. Therefore, the number of multiples of either 11 or 35 in the given range is \(90+28-2=116\).

Consequently, the count of numbers that are not divisible by either 11 or 35 is \(1000-116=884\).


Answer: A­

­Hello Bunuel. Could you please help me understand a quick way to find out the greatest multiple of 35? How did you got within less than 2 minutes to 980?
It would help me a lot when using this method with big numbers like these.

­ruis You can divide 1000 by 35, and then subtract the remainder, 20, from 1000:



 ­
User avatar
S
ruis
Manager
Manager
Joined: 17 Sep 2023
Posts: 130
Own Kudos [?]: 53 [0]
Given Kudos: 476
Send PM
Re: How many integers are there between 1 and 1000, inclusive, that are [#permalink] New post   31 Mar 2024, 10:57
GMATCoachBen wrote:
ruis wrote:
Bunuel wrote:
Official Solution:

How many integers are there between 1 and 1000, inclusive, that are not divisible by either 11 or 35?

A. 884
B. 890
C. 892
D. 910
E. 945


Let's determine the number of multiples of 11 or 35 between 1 and 1000, inclusive, and subtract that number from 1000.

The number of multiples of an integer within a range can be calculated using the following formula:




\(\frac{\text{last multiple in the range - first multiple in the range} }{\text{multiple} }+1\)

Thus:




• The number of multiples of 11 in the given range is \(\frac{ last - first}{multiple}+1=\frac{990-11}{11}+1=90\);

• The number of multiples of 35 in the given range is \(\frac{ last - first }{ multiple}+1=\frac{980-35}{35}+1=28\);

• The number of multiples of both 11 and 35 is 2 (since \(11*35=385\) and \(385*2=770\));

Observe that the two numbers 385 and 770 are included in the count of multiples of 11 and the count of multiples of 35. To avoid double-counting, we need to subtract these numbers once from the total count of multiples of 11 and 35. Therefore, the number of multiples of either 11 or 35 in the given range is \(90+28-2=116\).

Consequently, the count of numbers that are not divisible by either 11 or 35 is \(1000-116=884\).


Answer: A­

­Hello Bunuel. Could you please help me understand a quick way to find out the greatest multiple of 35? How did you got within less than 2 minutes to 980?
It would help me a lot when using this method with big numbers like these.

­ruis You can divide 1000 by 35, and then subtract the remainder, 20, from 1000:



 ­


Thats awesome! Thanks :)

Posted from my mobile device
GMAT Club Bot
gmatclubot
Re: How many integers are there between 1 and 1000, inclusive, that are [#permalink]
31 Mar 2024, 10:57
Moderators:
Bunuel
Math Expert
92902 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions