Author 
Message 
TAGS:

Hide Tags

GMAT Instructor
Joined: 04 Jul 2006
Posts: 1253
Location: Madrid

How many positive integers less than 1000 are multiples of 5 [#permalink]
Show Tags
Updated on: 30 Apr 2015, 03:34
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
Official Answer and Stats are available only to registered users. Register/ Login.
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
Joined: 01 Jan 2007
Posts: 308

Re: How many positive integers less than 1000 are multiples of 5 [#permalink]
Show Tags
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 20078 = 122 multiples.
So the answere is C.
Javed.
Cheers!



Manager
Joined: 27 Feb 2007
Posts: 68

Re: How many positive integers less than 1000 are multiples of 5 [#permalink]
Show Tags
15 Apr 2007, 06:48
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, 1994928=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
Joined: 11 Feb 2007
Posts: 346

Re: How many positive integers less than 1000 are multiples of 5 [#permalink]
Show Tags
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
Joined: 01 Jan 2007
Posts: 308

Re: How many positive integers less than 1000 are multiples of 5 [#permalink]
Show Tags
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, 1994928=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
Joined: 25 Mar 2007
Posts: 81

Re: How many positive integers less than 1000 are multiples of 5 [#permalink]
Show Tags
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
Joined: 27 Feb 2007
Posts: 68

Re: How many positive integers less than 1000 are multiples of 5 [#permalink]
Show Tags
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
Joined: 01 Feb 2016
Posts: 10

Re: How many positive integers less than 1000 are multiples of 5 [#permalink]
Show Tags
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)



Moderator
Joined: 22 Jun 2014
Posts: 1047
Location: India
Concentration: General Management, Technology
GPA: 2.49
WE: Information Technology (Computer Software)

Re: How many positive integers less than 1000 are multiples of 5 [#permalink]
Show Tags
18 Jun 2016, 07:15
multiple of 5 between 1 to 100 = (1005)/5 + 1 = 20 multiple of 5&4 that is 20 between 1 to 100 = (10020)/20 + 1 = 5 multiple of 5&7 that is 35 between 1 to 100 = (10035)/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 = 20070 = 130 we need to subtract 1 because question asks less than 1000.hence total multiple asked = 1301 = 129
_________________
 Target  720740 http://gmatclub.com/forum/informationonnewgmatesrreportbeta221111.html http://gmatclub.com/forum/listofoneyearfulltimembaprograms222103.html



BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2642
GRE 1: 323 Q169 V154

How many positive integers less than 1000 are multiples of 5 [#permalink]
Show Tags
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 => 1994928+7 => 129 Smash that D Unfortunately its taking me over 4 minutes Any Quickies here abhimahnaTry 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 GMATQuant(700+)AVERAGE GRE Scores At The Top Business Schools!



Manager
Joined: 02 Jul 2016
Posts: 111

Re: How many positive integers less than 1000 are multiples of 5 [#permalink]
Show Tags
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



Manager
Joined: 17 May 2015
Posts: 232

Re: How many positive integers less than 1000 are multiples of 5 [#permalink]
Show Tags
13 Oct 2016, 04:01
[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 [ 22.51 KiB  Viewed 15923 times ]



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3511
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: How many positive integers less than 1000 are multiples of 5 [#permalink]
Show Tags
13 Oct 2016, 08:28
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  4928+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 )



VP
Joined: 07 Dec 2014
Posts: 1020

Re: How many positive integers less than 1000 are multiples of 5 [#permalink]
Show Tags
14 Oct 2016, 15:04
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 1994928+7=129 D.



Manager
Joined: 20 Jan 2017
Posts: 61
Location: United States (NY)
GMAT 1: 750 Q48 V44 GMAT 2: 610 Q34 V41
GPA: 3.92

Re: How many positive integers less than 1000 are multiples of 5 [#permalink]
Show Tags
20 Jan 2017, 18:37
1)Multiples of 5: (9955)/5+1=198+1=199 2)Multiples of 5&4: 20: (98020)/20+1=960/20+1=48+1=49 3)Multiples of 5&7: 35: (98035)/35+1=945/35+1=27+1=28 4)Multiples of 5&4&7: 140: (980140)/140+1=840/140+1=6+1=7 5)Multiples of 5 but not 4 and not 7: 199(497)(287)7=129



Target Test Prep Representative
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
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 WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy 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






