|
Author |
Message |
|
TAGS:
|
|
|
Director
Joined: 29 Aug 2005
Posts: 891
Followers: 6
Kudos [?]:
87
[2] , given: 7
|
How many prime numbers between 1 and 100 are factors of 7150 [#permalink]
 13 Apr 2009, 01:39
2
This post received
KUDOS
Question Stats:
67% (01:43) correct
32% (00:45) wrong based on 9 sessions
How many prime numbers between 1 and 100 are factors of 7,150? A. One B. Two C. Three D. Four E. Five
|
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11594
Followers: 1799
Kudos [?]:
9584
[4] , given: 826
|
Re: How many prime numbers between 1 and 100 are factors of 7150 [#permalink]
13 Feb 2012, 19:22
4
This post received
KUDOS
pratk wrote: I also got 2,5,7,11 and 13 but it took me more than the two minutes to break down 143 into 11 and 13. 2,5 and 7 were the easier ones. I'm sure many will agree at in times of stress, the mind starts to play tricks. At first I stopped after 7 and thought that 143 cannot be factored further and chose C as the answer i.e. 3 prime factors but then got the other two in over the two mins.
Therefore, is there a quick way to get the prime factors of a large number?
Thanks. Generally there is no easy way to check whether some very large number is a prime (well if it doesn't have some small primes, which are easy to check). You'll need a computer to do this. Next, the GMAT won't give you a large number to factorize if there is no shortcut for that. For example in our original question after you find 2, 5, and 7, just check for the next prime 11: 143/11=13. You can also use divisibility rule for 11: if you sum every second digit and then subtract all other digits and the answer is divisible by 11, then the number is divisible by 11. So, for 143: (1+3)-4=0 --> 0 is divisible by 11 thus 143 is divisible by 11. Or, you can notice that 143=130+13= 13*10+ 13, so 143 must be divisible by 13. So, as you can see there are plenty of shortcuts to get prime factorization of the numbers from the GMAT problems. For more on divisibility rules and on verifying the primality check Number Theory chapter of Math Book: math-number-theory-88376.htmlHope it helps.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 3111
Location: Pune, India
Followers: 572
Kudos [?]:
2012
[3] , given: 92
|
Re: How many prime numbers between 1 and 100 are factors of 7150 [#permalink]
14 Feb 2012, 00:19
3
This post received
KUDOS
pratk wrote: I also got 2,5,7,11 and 13 but it took me more than the two minutes to break down 143 into 11 and 13. 2,5 and 7 were the easier ones. I'm sure many will agree at in times of stress, the mind starts to play tricks. At first I stopped after 7 and thought that 143 cannot be factored further and chose C as the answer i.e. 3 prime factors but then got the other two in over the two mins.
Therefore, is there a quick way to get the prime factors of a large number?
Thanks. Sadly, you will need to check for all prime numbers till the square root of the given number. We don't know the square root of 143 but we can approximate it. 143 is very close to 144. The square root of 144 is 12 so you will need to check for all prime numbers less than 12. If none of the prime numbers less than 12 is a factor of 143, then you can say that 143 is prime. So the question is not over till you don't check for 11 too. So basically, you need to check for all prime factors less than \sqrt{n} to figure out whether n is prime. If you are not sure why, check out these posts for details on factors: http://www.veritasprep.com/blog/2010/12 ... ly-number/http://www.veritasprep.com/blog/2010/12 ... t-squares/
_________________
Karishma
Veritas Prep | GMAT Instructor
My Blog
Save 10% on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.
Veritas Prep Reviews
|
|
|
|
|
|
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 3111
Location: Pune, India
Followers: 572
Kudos [?]:
2012
[1] , given: 92
|
Re: How many prime numbers between 1 and 100? [#permalink]
18 Jan 2012, 05:24
1
This post received
KUDOS
jgonza8 wrote: Hate to play devil's advocate here, but the question doesn't clarify how many UNIQUE prime numbers are factors of 7150. (Which would change the answer to five). Am I missing something? Yes, you are! Read the question again: How many prime numbers between 1 and 100 are factors of 7,150? The prime numbers between 1 and 100 are 2, 3, 5, 7, 11, 13, 17, 19... etc 5 appears only once between 1 and 100 so there is absolutely no confusion. Out of these 25 prime numbers, only 4 are factors of 7150: 2, 5, 11 and 13
_________________
Karishma
Veritas Prep | GMAT Instructor
My Blog
Save 10% on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.
Veritas Prep Reviews
|
|
|
|
|
|
Manager
Joined: 13 Feb 2012
Posts: 149
Location: Italy
Concentration: General Management, Entrepreneurship
GMAT 1: 560 Q36 V34
GPA: 3.1
WE: Sales (Transportation)
Followers: 4
Kudos [?]:
-1
[0], given: 85
|
Re: How many prime numbers between 1 and 100 are factors of 7150 [#permalink]
24 Jul 2012, 10:25
Had the same doubt about the "unique prime factors thing"; thanks for the clarification.
_________________
"The Burnout" - My Debrief
Kudos if I helped you 
Andy
|
|
|
|
|
|
Intern
Joined: 25 Dec 2008
Posts: 19
Schools: HBS, Stanford
Followers: 0
Kudos [?]:
1
[0], given: 2
|
Re: How many prime numbers between 1 and 100? [#permalink]
13 Apr 2009, 04:05
7,150 = 2 * 5 * 5 * 11 * 13
so there are 4 distinct prime numbers that are below 100, so answer D.
|
|
|
|
|
|
Intern
Joined: 04 Jan 2010
Posts: 6
Followers: 0
Kudos [?]:
0
[0], given: 2
|
Re: How many prime numbers between 1 and 100? [#permalink]
16 Jan 2012, 12:09
Hate to play devil's advocate here, but the question doesn't clarify how many UNIQUE prime numbers are factors of 7150. (Which would change the answer to five). Am I missing something?
|
|
|
|
|
|
Senior Manager
Status: D-Day is on February 10th. and I am not stressed
Affiliations: American Management association, American Association of financial accountants
Joined: 12 Apr 2011
Posts: 278
Location: Kuwait
Schools: Columbia university
Followers: 4
Kudos [?]:
13
[0], given: 52
|
Re: How many prime numbers between 1 and 100? [#permalink]
16 Jan 2012, 12:11
prime factorization is the idea behind this.
_________________
Sky is the limit
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11594
Followers: 1799
Kudos [?]:
9584
[0], given: 826
|
Re: How many prime numbers between 1 and 100? [#permalink]
16 Jan 2012, 12:33
|
|
|
|
|
|
Manager
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 190
Location: India
Concentration: Finance, International Business
WE: Information Technology (Investment Banking)
Followers: 3
Kudos [?]:
14
[0], given: 1
|
Re: How many prime numbers between 1 and 100 are factors of 7150 [#permalink]
17 Jan 2012, 04:17
Ans is D = 7150 = 2*5*5*11*13
so the prime numbers are 2,5,11,13
|
|
|
|
|
|
Intern
Joined: 14 Nov 2011
Posts: 12
Followers: 0
Kudos [?]:
0
[0], given: 1
|
Re: How many prime numbers between 1 and 100 are factors of 7150 [#permalink]
13 Feb 2012, 19:09
I also got 2,5,7,11 and 13 but it took me more than the two minutes to break down 143 into 11 and 13. 2,5 and 7 were the easier ones. I'm sure many will agree at in times of stress, the mind starts to play tricks. At first I stopped after 7 and thought that 143 cannot be factored further and chose C as the answer i.e. 3 prime factors but then got the other two in over the two mins.
Therefore, is there a quick way to get the prime factors of a large number?
Thanks.
|
|
|
|
|
|
Manager
Joined: 16 Dec 2011
Posts: 52
GMAT Date: 04-23-2012
Followers: 0
Kudos [?]:
0
[0], given: 12
|
Re: How many prime numbers between 1 and 100 are factors of 7150 [#permalink]
13 Feb 2012, 22:09
Good explanaation bunel thanks Posted from my mobile device 
|
|
|
|
|
|
Manager
Joined: 17 Sep 2011
Posts: 214
Followers: 0
Kudos [?]:
11
[0], given: 8
|
Re: How many prime numbers between 1 and 100 are factors of 7150 [#permalink]
14 Feb 2012, 00:22
The answer is D. There are 4 prime factors.
_________________
_________________
Giving +1 kudos is a better way of saying 'Thank You'.
|
|
|
|
|
|
Intern
Joined: 14 Nov 2011
Posts: 12
Followers: 0
Kudos [?]:
0
[0], given: 1
|
Re: How many prime numbers between 1 and 100 are factors of 7150 [#permalink]
14 Feb 2012, 20:16
Thanks for the explanation and the additional posts Bunuel and Karishma..
|
|
|
|
|
|
|
Re: How many prime numbers between 1 and 100 are factors of 7150
[#permalink]
14 Feb 2012, 20:16
|
|
|
|
|
|
|
|
|
|
|
close
