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

It is currently 23 Jun 2018, 14:37

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

How many positive integers less than 1000 are multiples of 5

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

Hide Tags

7 KUDOS received
GMAT Instructor
avatar
B
Joined: 04 Jul 2006
Posts: 1253
Location: Madrid
CAT Tests
How many positive integers less than 1000 are multiples of 5 [#permalink]

Show Tags

New post Updated on: 30 Apr 2015, 03:34
7
33
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

43% (02:12) correct 57% (02:07) wrong based on 550 sessions

HideShow timer Statistics

How many positive integers less than 1000 are multiples of 5 but NOT of 4 or 7?

(A) 114
(B) 121
(C) 122
(D) 129
(E) 136

Originally posted by kevincan on 14 Apr 2007, 23:34.
Last edited by Bunuel on 30 Apr 2015, 03:34, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Senior Manager
Senior Manager
avatar
Joined: 01 Jan 2007
Posts: 308
Re: How many positive integers less than 1000 are multiples of 5 [#permalink]

Show Tags

New post 15 Apr 2007, 01:42
kevincan wrote:
How many positive integers less than 1000 are multiples of 5 but NOT of 4 or 7?

(A) 114 (B) 121 (C) 122 (D) 129 (E) 136


There are 1000/5=200 multiples of 5 . now we have to find the number of multiples of 5 and 4 that is 20 between 0 to 1000 and 5 and 7 that is 35 between 0 to 1000.

multiples of 20=1000/20=50 multiples. and multiples of 35= 1000/35 =28.5 so 28 multiples of 35.

So multiples of 5 between o to 1000 not including multiples of 20 and 35 are equal to 200-78 = 122 multiples.
So the answere is C.

Javed.

Cheers!
9 KUDOS received
Manager
Manager
User avatar
Joined: 27 Feb 2007
Posts: 68
Re: How many positive integers less than 1000 are multiples of 5 [#permalink]

Show Tags

New post 15 Apr 2007, 06:48
9
11
It's 129 (D)

There are 199 multiples of 5 that are less than 1000.

Now we have to exclude the multiples of 4 and 7 from these 199 numbers.

Let's first find out the numbers below 1000 that are multiples of 5 as well as 4. (that is, multiples of 20). There are 49 such numbers.

Ditto for 5 as well as 7. There are 28 such numbers.

Subtracting these numbers from 199, we get, 199-49-28=122.

However, there will be some numbers which are multiples of both 4 and 7 which have been subtracted twice in the above calculation.

There are 7 such numbers (multiples of 20 as well as 35, that is multiples of 140).

Thus the required number is 122+7 = 129.
Senior Manager
Senior Manager
avatar
Joined: 11 Feb 2007
Posts: 346
Re: How many positive integers less than 1000 are multiples of 5 [#permalink]

Show Tags

New post 15 Apr 2007, 06:49
Javed's method seems to be straight forward and correct.

Although in a counting problem such as this, B is tempting because it's very close to C and it might make you think that you forgot to subtract 1 from somewhere...

What is the OA?
Senior Manager
Senior Manager
avatar
Joined: 01 Jan 2007
Posts: 308
Re: How many positive integers less than 1000 are multiples of 5 [#permalink]

Show Tags

New post 15 Apr 2007, 10:08
rakesh.id wrote:
It's 129 (D)

There are 199 multiples of 5 that are less than 1000.

Now we have to exclude the multiples of 4 and 7 from these 199 numbers.

Let's first find out the numbers below 1000 that are multiples of 5 as well as 4. (that is, multiples of 20). There are 49 such numbers.

Ditto for 5 as well as 7. There are 28 such numbers.

Subtracting these numbers from 199, we get, 199-49-28=122.

However, there will be some numbers which are multiples of both 4 and 7 which have been subtracted twice in the above calculation.

There are 7 such numbers (multiples of 20 as well as 35, that is multiples of 140).

Thus the required number is 122+7 = 129.


I agree with your explanation. Answere is 129.

Javed

Cheers!
Manager
Manager
avatar
Joined: 25 Mar 2007
Posts: 81
Re: How many positive integers less than 1000 are multiples of 5 [#permalink]

Show Tags

New post 15 Apr 2007, 12:12
multiples of 5: 5(1,2,3,4,5......, 199), 199 in total < 1000
multiples of 4 and 5: 20(1,2,3,4,5,....,49) 49 in total < 1000
multiples of 5 and 7: 35(1,2,3,4,5,....,28) 28 in total < 1000

199 - 49 - 28 = 122

The double counts include multiples of 20,35 (2*2*5, 7*5)
70,140,350,700,770,910,980

122 + 7(doubles) =129
Manager
Manager
User avatar
Joined: 27 Feb 2007
Posts: 68
Re: How many positive integers less than 1000 are multiples of 5 [#permalink]

Show Tags

New post 15 Apr 2007, 13:51
alfyG wrote:
multiples of 5: 5(1,2,3,4,5......, 199), 199 in total < 1000
multiples of 4 and 5: 20(1,2,3,4,5,....,49) 49 in total < 1000
multiples of 5 and 7: 35(1,2,3,4,5,....,28) 28 in total < 1000

199 - 49 - 28 = 122

The double counts include multiples of 20,35 (2*2*5, 7*5)
70,140,350,700,770,910,980

122 + 7(doubles) =129


I think the double counts given by you are incorrect. 70, for example, is not a multiple of 4 and 5.

The double counts are: 140, 280, 420, 560, 700, 840, 980
Intern
Intern
avatar
Joined: 01 Feb 2016
Posts: 10
Re: How many positive integers less than 1000 are multiples of 5 [#permalink]

Show Tags

New post 15 Jun 2016, 23:50
Did I understand the concept correctly?

To find multiples of a number X less that Y, we divide Y/X. If Y/X has no remainder then no. of multiples if Y/X - 1. If Y/X has remainder then no. of multiples is quotient of Y/X. Eg

no. of multiples of 5 less than 1000 = 1000/5 - 1=199. (If 1000 was included then we wouldnt have subtracted 1)
No. of multiples of 3 less than 1000 = 1000/3 = 333

To find common multiples of two nos U and V up to some no. W (eg common multiples of 20 and 35 less than 1000), we find the first common multiple (in this case 140). No all multiples of 140 less than 1000 would be common multiples of 20 and 35 less than 1000 (140, 280, 420, 560, 700, 840, 980, total 7)
2 KUDOS received
Moderator
avatar
V
Joined: 22 Jun 2014
Posts: 1047
Location: India
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20
GPA: 2.49
WE: Information Technology (Computer Software)
GMAT ToolKit User Premium Member
Re: How many positive integers less than 1000 are multiples of 5 [#permalink]

Show Tags

New post 18 Jun 2016, 07:15
2
multiple of 5 between 1 to 100 = (100-5)/5 + 1 = 20

multiple of 5&4 that is 20 between 1 to 100 = (100-20)/20 + 1 = 5

multiple of 5&7 that is 35 between 1 to 100 = (100-35)/35 + 1 = 2

Total multiple of 20 and 35 between 1 to 100 = 7

multiple of 5 between 1 to 1000 = 20*10 = 200

multiple of 20 and 35 between 1 to 1000 = 7*10 = 70

multiple of 5 BUT not of 4&7 between 1 to 1000 = 200-70 = 130

we need to subtract 1 because question asks less than 1000.

hence total multiple asked = 130-1 = 129
_________________

---------------------------------------------------------------
Target - 720-740
http://gmatclub.com/forum/information-on-new-gmat-esr-report-beta-221111.html
http://gmatclub.com/forum/list-of-one-year-full-time-mba-programs-222103.html

BSchool Forum Moderator
User avatar
D
Joined: 12 Aug 2015
Posts: 2642
GRE 1: 323 Q169 V154
GMAT ToolKit User Premium Member
How many positive integers less than 1000 are multiples of 5 [#permalink]

Show Tags

New post 23 Aug 2016, 10:58
here is my approach ->
Multiples of 5=> 199
Multiples of 4 and 5 i.e of 20 => 49
Multiples of 7 and 5 i.e 35 => 28
Multiples of all 5,4,& i.e multiples of 140=> 7


Required value => 199-49-28+7 => 129
Smash that D

Unfortunately its taking me over 4 minutes

Any Quickies here abhimahna
Try your hand on this one
_________________


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
avatar
B
Joined: 02 Jul 2016
Posts: 111
Re: How many positive integers less than 1000 are multiples of 5 [#permalink]

Show Tags

New post 13 Oct 2016, 03:07
I am not able to understand why 7 has been added in the end...
Can somebody explain this to me...
Of possible please explain with the help of Venn diagram

Posted from my mobile device
1 KUDOS received
Manager
Manager
avatar
D
Joined: 17 May 2015
Posts: 232
CAT Tests
Re: How many positive integers less than 1000 are multiples of 5 [#permalink]

Show Tags

New post 13 Oct 2016, 04:01
1
[quote="suramya26"]I am not able to understand why 7 has been added in the end...
Can somebody explain this to me...
Of possible please explain with the help of Venn diagram




Hope this will help.

Thanks.
Attachments

HowManyIntegers.jpg
HowManyIntegers.jpg [ 22.51 KiB | Viewed 15923 times ]

Board of Directors
User avatar
G
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3511
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: How many positive integers less than 1000 are multiples of 5 [#permalink]

Show Tags

New post 13 Oct 2016, 08:28
3
kevincan wrote:
How many positive integers less than 1000 are multiples of 5 but NOT of 4 or 7?

(A) 114
(B) 121
(C) 122
(D) 129
(E) 136


Numbers less than 1000 = { 1 , 2 , 3 , 4 ............999 }

Numbers upto 999 Divisible by 5 is \(\frac{999}{5}\) = 199

Numbers upto 999 Divisible by 20 (Multiple of 5 & 4) is \(\frac{999}{5}\) = 49
Numbers upto 999 Divisible by 35 (Multiple of 5 & 7) is \(\frac{999}{5}\) = 28
Numbers upto 999 Divisible by 140 (Multiple of 5 ,4 & 7) is \(\frac{999}{5}\) = 7
Quote:
So, Total number of positive integers less than 1000 are multiples of 5 but NOT of 4 or 7


=> 199 - 49-28+7 = 129

Hence answer will be (D) 129...

_________________

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 )

1 KUDOS received
VP
VP
avatar
G
Joined: 07 Dec 2014
Posts: 1020
Re: How many positive integers less than 1000 are multiples of 5 [#permalink]

Show Tags

New post 14 Oct 2016, 15:04
1
1
kevincan wrote:
How many positive integers less than 1000 are multiples of 5 but NOT of 4 or 7?

(A) 114
(B) 121
(C) 122
(D) 129
(E) 136



995/5=all multiples of 5=199
980/20=all multiples of 5 and 4=49
980/35=all multiples of 5 and 7=28
980/140=duplicate multiples of 5, 4 and 7=7
199-49-28+7=129
D.
Manager
Manager
User avatar
B
Joined: 20 Jan 2017
Posts: 61
Location: United States (NY)
Schools: CBS '20 (A)
GMAT 1: 750 Q48 V44
GMAT 2: 610 Q34 V41
GPA: 3.92
Reviews Badge
Re: How many positive integers less than 1000 are multiples of 5 [#permalink]

Show Tags

New post 20 Jan 2017, 18:37
1)Multiples of 5: (995-5)/5+1=198+1=199
2)Multiples of 5&4: 20: (980-20)/20+1=960/20+1=48+1=49
3)Multiples of 5&7: 35: (980-35)/35+1=945/35+1=27+1=28
4)Multiples of 5&4&7: 140: (980-140)/140+1=840/140+1=6+1=7
5)Multiples of 5 but not 4 and not 7: 199-(49-7)-(28-7)-7=129
Expert Post
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2779
Location: United States (CA)
Re: How many positive integers less than 1000 are multiples of 5 [#permalink]

Show Tags

New post 05 Feb 2018, 10:20
kevincan wrote:
How many positive integers less than 1000 are multiples of 5 but NOT of 4 or 7?

(A) 114
(B) 121
(C) 122
(D) 129
(E) 136


Let’s first determine the number of multiples of 5 from 5 to 995, inclusive:

(995 - 5)/5 + 1 = 199

If a number is a multiple of 5, but not a multiple of 4, then it’s not a multiple of 20. So let’s determine the number of multiples of 20 less than 1000:

(980 - 20)/20 + 1 = 49

If a number is a multiple of 5, but not a multiple of 7, then it’s not a multiple of 35. So let’s determine the number of multiples of 35 less than 1000:

(980 - 35)/35 + 1 = 28

Thus, we need to subtract 49 and 28 from 199:

199 - 49 - 28 = 122

However, we “over” subtracted from 199; for example, we subtracted 980 twice, as it is a multiple of 20 and also a multiple of 35. In other words, we “over” subtracted the number of numbers that are multiples of 5, 4 and 7, i.e., a multiple of the LCM of 5, 4, 7, which is 140. So we have to determine the number of multiples of 140 less than 100 and add that number back to 122:

(980 - 140)/140 + 1 = 7

Thus, the number of positive integers less than 1000 which are a multiple of 5 but not 4 or 7 is 122 + 7 = 129.

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

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

Re: How many positive integers less than 1000 are multiples of 5   [#permalink] 05 Feb 2018, 10:20
Display posts from previous: Sort by

How many positive integers less than 1000 are multiples of 5

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


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®.