January 26, 2019 January 26, 2019 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions. January 27, 2019 January 27, 2019 07:00 AM PST 09:00 AM PST Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 31 Oct 2011
Posts: 230

What is the total number of positive integers that are less
[#permalink]
Show Tags
24 Feb 2012, 22:11
Question Stats:
62% (02:02) correct 38% (02:01) wrong based on 407 sessions
HideShow timer Statistics
What is the total number of positive integers that are less than 100 and that have no positive factor in common with 100 other than 1? A. 30 B. 40 C. 50 D. 60 E. 70
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 52460

Re: PT #8 PS 2 Q 20
[#permalink]
Show Tags
24 Feb 2012, 22:45
eybrj2 wrote: What is the total number of positive integers that are less than 100 and that have no positive factor in common with 100 other than 1?
A. 30 B. 40 C. 50 D. 60 E. 70 Since 100=2^2*5^2 then a number not to have a positive factor in common with 100 other than 1 should not have 2 and/or 5 as a factors. # of multiples of 2 in the range (982)/2+1=49 (check this: totallybasic94862.html#p730075); # of multiples of 5 in the range (955)/5+1=19; # of multiples of both 2 and 5, so multiples of 10, in the range (9010)/10+1=9 (to get the overlap of above two sets); Hence there are total of 49+199=59 numbers which are multiples of 2 or 5; Total positive integers less than 100 is 99, so there are 9959=40 numbers which have no positive factor in common with 100 other than 1. Answer: B. Hope it's clear.
_________________
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? Extrahard Quant Tests with Brilliant Analytics




Intern
Joined: 19 Feb 2012
Posts: 4

wHAT IS THE TOTAL NUMBER OF POSITIVE INTEGERS THAT ARE LESS
[#permalink]
Show Tags
04 Mar 2012, 03:31
wHAT IS THE TOTAL NUMBER OF POSITIVE INTEGERS THAT ARE LESS than 100 and that have no positive factor in common with 100 other than 1? A)30 B)40 C)50 D)60 E)70



Math Expert
Joined: 02 Sep 2009
Posts: 52460

Re: wHAT IS THE TOTAL NUMBER OF POSITIVE INTEGERS THAT ARE LESS
[#permalink]
Show Tags
04 Mar 2012, 03:46



Intern
Joined: 22 Feb 2010
Posts: 37

Re: PT #8 PS 2 Q 20
[#permalink]
Show Tags
16 May 2013, 10:25
Bunuel wrote: eybrj2 wrote: What is the total number of positive integers that are less than 100 and that have no positive factor in common with 100 other than 1?
A. 30 B. 40 C. 50 D. 60 E. 70 Since 100=2^2*5^2 then a number not to have a positive factor in common with 100 other than 1 should not have 2 and/or 5 as a factors. # of multiples of 2 in the range (982)/2+1=49 (check this: totallybasic94862.html#p730075); # of multiples of 5 in the range (955)/5+1=19; # of multiples of both 2 and 5, so multiples of 10, in the range (9010)/10+1=9 (to get the overlap of above two sets); Hence there are total of 49+199=59 numbers which are multiples of 2 or 5; Total positive integers less than 100 is 99, so there are 9959=40 numbers which have no positive factor in common with 100 other than 1. Answer: B. Hope it's clear. The approach taken by you is correct. I took a slightly long approach. I took the numbers as: 3,5,7,9,11..All the odd numbers starting with 3 till 99. Such numbers total to 49 Then, I took all the numbers divisible by 5. These numbers will have their factor common with 100. The count of such numbers is 19. In between the above two sets, we have few numbers in common  5, 15, 25 ..10 in total. Now, I am confused here. We have the following: Set 1  49 Set 2  19 Set 3  10 Total numbers = 4919 = 30 How do we deal with Set 3? We should add it to the above figure, but don't know the exact reasons..where is the overlapping of data that should cause us to add it to the figure of 30. Please help.



Math Expert
Joined: 02 Sep 2009
Posts: 52460

Re: PT #8 PS 2 Q 20
[#permalink]
Show Tags
16 May 2013, 22:55
holidevil wrote: Bunuel wrote: eybrj2 wrote: What is the total number of positive integers that are less than 100 and that have no positive factor in common with 100 other than 1?
A. 30 B. 40 C. 50 D. 60 E. 70 Since 100=2^2*5^2 then a number not to have a positive factor in common with 100 other than 1 should not have 2 and/or 5 as a factors. # of multiples of 2 in the range (982)/2+1=49 (check this: totallybasic94862.html#p730075); # of multiples of 5 in the range (955)/5+1=19; # of multiples of both 2 and 5, so multiples of 10, in the range (9010)/10+1=9 (to get the overlap of above two sets); Hence there are total of 49+199=59 numbers which are multiples of 2 or 5; Total positive integers less than 100 is 99, so there are 9959=40 numbers which have no positive factor in common with 100 other than 1. Answer: B. Hope it's clear. The approach taken by you is correct. I took a slightly long approach. I took the numbers as: 3,5,7,9,11..All the odd numbers starting with 3 till 99. Such numbers total to 49 Then, I took all the numbers divisible by 5. These numbers will have their factor common with 100. The count of such numbers is 19. In between the above two sets, we have few numbers in common  5, 15, 25 ..10 in total. Now, I am confused here. We have the following: Set 1  49 Set 2  19 Set 3  10 Total numbers = 4919 = 30 How do we deal with Set 3? We should add it to the above figure, but don't know the exact reasons..where is the overlapping of data that should cause us to add it to the figure of 30. Please help. Not clear what are you doing here. There are 50 odd numbers from 1 to 100, not 49. Next, why are you subtracting from that the number of multiples of 5?
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 611

Re: What is the total number of positive integers that are less
[#permalink]
Show Tags
17 May 2013, 01:52
eybrj2 wrote: What is the total number of positive integers that are less than 100 and that have no positive factor in common with 100 other than 1?
A. 30 B. 40 C. 50 D. 60 E. 70 Basically the question asks about the total no of coprime factors of 100. Bunuel has already explained the method, however, for just knowing something new, there is another method to do this : 100 = Find out all the prime factors = 2 and 5. Thus total no of coprime integers to 100, and less than 100 = (11/2)(11/5)*100 = 1/2*4/5*100 = 40. So, if I have to find out the total no of coprime factors for 48, that would be > Total prime factors of 48 = 2,3. Thus the co=prime factors less than 48 = (11/2)(11/3)*48 = 1/2*2/3*48 = 16. This includes 1, which is coprime to 48. This is not some thumb rule, there is a proper derivation for this.Though, it is beyond the scope of GMAT.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Intern
Joined: 19 May 2013
Posts: 2

Re: What is the total number of positive integers that are less
[#permalink]
Show Tags
23 Jun 2013, 16:26
Total number of odd integers is 50 of which 10 integers are divisible by 5.
So the correct answer is (B) 40



Intern
Joined: 25 Apr 2013
Posts: 16
Location: India
GPA: 4
WE: Engineering (Transportation)

Re: What is the total number of positive integers that are less
[#permalink]
Show Tags
01 Mar 2014, 05:27
Formula : Number of integers less N and are coprime to N is given by : N(11/a)(11/b)(11/c).....where a, b, c are prime factors of N.. In the given equation, the prime factors of 100 are 2 and 5. Hence the number will be 100(11/2)(11/5) = 40. Hope it helps...



SVP
Joined: 06 Sep 2013
Posts: 1705
Concentration: Finance

Re: What is the total number of positive integers that are less
[#permalink]
Show Tags
28 Mar 2014, 08:07
I did it like this:
There are 50 odd numbers There are 10 multiples of 5 among those 50 odd numbers
Therefore 5010 = 40
Answer is B
Could someone confirm if this method is OK
Cheers J



Manager
Joined: 10 Feb 2014
Posts: 62

What is the total number of positive integers that are less
[#permalink]
Show Tags
27 Jun 2014, 06:39
Another way to solve this problem: Since 100=2^2*5^2 then an integer to not have a positive factor in common with 100 other than 1 should not have 2 and/or 5 as a factors Positive integers that do not have 2 and/or 5 as factors would be (all odd numbers MINUS odd numbers that end in 5) # of odds < 100 = 50 # of odd numbers that end in 5 (5, 15, 25, 35, 45, 55, 65, 75, 85, and 95) = 10
Ans = 50  10 = 40



Manager
Status: Oh GMAT ! I give you one more shot :)
Joined: 14 Feb 2013
Posts: 77
Location: United States (MI)
Concentration: General Management, Technology
GMAT 1: 580 Q44 V28 GMAT 2: 690 Q49 V34
GPA: 3.5
WE: Information Technology (Computer Software)

Re: What is the total number of positive integers that are less
[#permalink]
Show Tags
27 Aug 2014, 16:43
My approach: All even integers and 100 have 2 as a common factor. Similarly all multiples of 5 and 100 have 5 as a common factor. Rest all the integers and 100 are coprimes. In between 1 and 10 there are 4 such integers (1, 3, 7, 9), which have no common factor with 100 except 100 and 1. And for all numbers less than 100, we have 10 such sets 110, 1120, 2130 .... 91100 So total number of integers less than 100 that have no common factors with 100 = 4 * 10 = 40 Option B.
_________________
Life is a highway I wanna ride it all night long



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1823
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: What is the total number of positive integers that are less
[#permalink]
Show Tags
28 Aug 2014, 01:20
\(100 = 2^2 * 5^2\) We require to find out numbers which do not have 2 & 5 as factors Total odd numbers from 1 to 99 = 50 (These do not have 2 as factors) However the above 50 numbers have 5, 15.... upto 95 (Total = 10) factors of 5 Removing the same 5010 = 40 Answer = B
_________________
Kindly press "+1 Kudos" to appreciate



Intern
Joined: 20 Jul 2014
Posts: 3

Needing to find easier solution of this numbers question...
[#permalink]
Show Tags
27 Sep 2014, 22:40
Question: What is the total number of positive integers that are less than 100 and that have no positive factor in common with 100 other than 1?
My way: First I eliminated 1 and 100, then I eliminated 2,4,5,10,20,25,50 since they're all factors of 100. Now I don't know how to go next. Since you have to eliminate all the factors of 100, I don't know if I need to eliminate all 2's, all 4's, all 5's and so on...
Please help...



Math Expert
Joined: 02 Sep 2009
Posts: 52460

Re: What is the total number of positive integers that are less
[#permalink]
Show Tags
28 Sep 2014, 01:20
LEOMODE wrote: Question: What is the total number of positive integers that are less than 100 and that have no positive factor in common with 100 other than 1?
My way: First I eliminated 1 and 100, then I eliminated 2,4,5,10,20,25,50 since they're all factors of 100. Now I don't know how to go next. Since you have to eliminate all the factors of 100, I don't know if I need to eliminate all 2's, all 4's, all 5's and so on...
Please help... Merging similar topics. Please refer to the discussion above. P.S. Please read carefully and follow: rulesforpostingpleasereadthisbeforeposting133935.html Pay attention to rules 1, 2, 3, 7, and 8. Thank you.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8810
Location: Pune, India

Re: What is the total number of positive integers that are less
[#permalink]
Show Tags
09 Jun 2016, 20:34
eybrj2 wrote: What is the total number of positive integers that are less than 100 and that have no positive factor in common with 100 other than 1?
A. 30 B. 40 C. 50 D. 60 E. 70 Another way to think about it: Let's consider numbers from 1 to 100 (since it eases the calculations). Coprime with 100 means that they should have no factor of 2 and/or 5. In the first 100 positive integers, 50 are divisible by 2 (including 100). So we remove these 50 and are left with 50 numbers not divisible by 2. Next, in the first 100 numbers, 100/5 = 20 are divisible by 5. Out of these 20, 10 are even so we have already removed them. We need to remove another 10 with are odd multiples of 5. We are left with 50  10 = 40. Answer (B)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Intern
Joined: 13 Jul 2016
Posts: 37

Re: What is the total number of positive integers that are less
[#permalink]
Show Tags
01 Nov 2016, 11:59
eybrj2 wrote: What is the total number of positive integers that are less than 100 and that have no positive factor in common with 100 other than 1?
A. 30 B. 40 C. 50 D. 60 E. 70 For those familiar with Euler's phi function: phi(100) = phi(2 squared) * phi(5 squared) = (2) * (25  5) = 40



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2726
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: What is the total number of positive integers that are less
[#permalink]
Show Tags
17 Mar 2018, 04:12
eybrj2 wrote: What is the total number of positive integers that are less than 100 and that have no positive factor in common with 100 other than 1?
A. 30 B. 40 C. 50 D. 60 E. 70 100 = 2^2 * 5^2 i.e the Solutions must not contain any factor of 2 and 5 in order to satisfy the given constraints in the question. Number of multiples of 2 from 1 to 100 = 100/2 = 50 Number of multiples of 5 from 1 to 100 = 100/5 = 20 Number of multiples of 10 from 1 to 100 = 100/10 = 10 So Total number that are multiple of either of 2 or 5 = 50+2010 = 60 Remaining number = 100  60 = 40 Answer: Option B
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION




Re: What is the total number of positive integers that are less &nbs
[#permalink]
17 Mar 2018, 04:12






