Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 05 Dec 2013, 08:08

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# How many prime numbers between 1 and 100 are factors of 7150

Author Message
TAGS:
Director
Joined: 29 Aug 2005
Posts: 885
Followers: 6

Kudos [?]: 119 [2] , given: 7

How many prime numbers between 1 and 100 are factors of 7150 [#permalink]  13 Apr 2009, 00:39
2
KUDOS
00:00

Difficulty:

35% (medium)

Question Stats:

61% (01:43) correct 38% (00:50) wrong based on 220 sessions
How many prime numbers between 1 and 100 are factors of 7,150?

A. One
B. Two
C. Three
D. Four
E. Five
[Reveal] Spoiler: OA
Intern
Joined: 25 Dec 2008
Posts: 18
Schools: HBS, Stanford
Followers: 0

Kudos [?]: 1 [0], given: 2

Re: How many prime numbers between 1 and 100? [#permalink]  13 Apr 2009, 03:05
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, 11:09
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: 275
Location: Kuwait
Schools: Columbia university
Followers: 4

Kudos [?]: 19 [0], given: 52

Re: How many prime numbers between 1 and 100? [#permalink]  16 Jan 2012, 11:11
prime factorization is the idea behind this.
_________________

Sky is the limit

Math Expert
Joined: 02 Sep 2009
Posts: 15068
Followers: 2517

Kudos [?]: 15448 [0], given: 1551

Re: How many prime numbers between 1 and 100? [#permalink]  16 Jan 2012, 11:33
Expert's post
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?

How many prime numbers between 1 and 100 are factors of 7,150?
A. One
B. Two
C. Three
D. Four
E. Five

Make prime factorization of 7,150 --> 7,150=2*5^2*11*13. So 4 prime numbers between 1 and 100 (namely 2, 5, 11, and 13) are factors of 7,150 (you shouldn't count one prime factor twice).

_________________
Manager
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 182
Location: India
WE: Information Technology (Investment Banking)
Followers: 3

Kudos [?]: 15 [0], given: 1

Re: How many prime numbers between 1 and 100 are factors of 7150 [#permalink]  17 Jan 2012, 03:17
Ans is D = 7150 = 2*5*5*11*13
so the prime numbers are 2,5,11,13
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 3736
Location: Pune, India
Followers: 803

Kudos [?]: 3170 [1] , given: 136

Re: How many prime numbers between 1 and 100? [#permalink]  18 Jan 2012, 04:24
1
KUDOS
Expert's post
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 $100 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 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, 18:09 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. Math Expert Joined: 02 Sep 2009 Posts: 15068 Followers: 2517 Kudos [?]: 15448 [4] , given: 1551 Re: How many prime numbers between 1 and 100 are factors of 7150 [#permalink] 13 Feb 2012, 18:22 4 This post received KUDOS Expert's post 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.html Hope it helps. _________________ Manager Joined: 16 Dec 2011 Posts: 51 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, 21:09 Good explanaation bunel thanks Posted from my mobile device Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 3736 Location: Pune, India Followers: 803 Kudos [?]: 3170 [4] , given: 136 Re: How many prime numbers between 1 and 100 are factors of 7150 [#permalink] 13 Feb 2012, 23:19 4 This post received KUDOS Expert's post 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$100 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: 17 Sep 2011
Posts: 212
Followers: 0

Kudos [?]: 13 [0], given: 8

Re: How many prime numbers between 1 and 100 are factors of 7150 [#permalink]  13 Feb 2012, 23:22
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, 19:16
Thanks for the explanation and the additional posts Bunuel and Karishma..
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 [?]: 0 [0], given: 85

Re: How many prime numbers between 1 and 100 are factors of 7150 [#permalink]  24 Jul 2012, 09:25
Had the same doubt about the "unique prime factors thing"; thanks for the clarification.
_________________

"The Burnout" - My Debrief

Kudos if I helped you

Andy

Director
Joined: 09 Sep 2013
Posts: 554
Followers: 67

Kudos [?]: 10 [0], given: 0

Re: How many prime numbers between 1 and 100 are factors of 7150 [#permalink]  01 Dec 2013, 14:39
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: How many prime numbers between 1 and 100 are factors of 7150   [#permalink] 01 Dec 2013, 14:39
Similar topics Replies Last post
Similar
Topics:
How many prime numbers between 1 and 100 are factors of 6 30 Apr 2006, 07:12
How many prime numbers between 1 and 100 are factors of 4 24 Aug 2006, 23:23
How many different prime numbers are factors of the positive 4 22 Oct 2006, 22:37
HOw many prime numbers between 1 and 100 are factors of 4 12 May 2008, 07:52
2 How many prime numbers between 1 and 100 are factors of 7,15 1 20 Dec 2012, 05:35
Display posts from previous: Sort by