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# How many prime numbers between 1 and 100 are factors of 7,15

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How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]  20 Dec 2012, 05:35
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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
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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]  20 Dec 2012, 05:36
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Expert's post
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.

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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]  19 Mar 2014, 20:27
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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]  19 Mar 2014, 21:17
7150 = 715*5 = 13*55*5*2 = 13*11*5*5*2
The only mistake one could do is count 5 twice

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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]  12 Sep 2014, 22:31
Bunuel wrote:
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.

when they didn't mention distinct prime number. why we shouldn't consider 5 twice?
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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]  13 Sep 2014, 06:12
Expert's post
luckyme17187 wrote:
Bunuel wrote:
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.

when they didn't mention distinct prime number. why we shouldn't consider 5 twice?

The questions asks about the number of primes which are factors of 7,150. Why should we count any prime more than once?
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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]  29 Mar 2015, 14:06
Bunuel
Bunuel wrote:
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.

Bunuel,

Do you have any fast tricks to understand that 7,150 is divisible by 11 and 13?

The only silly mistake I made was to miss 11 and 13 as prime factors of 7150.

Thank you!
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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]  29 Mar 2015, 18:01
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Expert's post
Hi elisabettaportioli,

The speed with which you 'prime-factor' 7150 into its 'pieces' is likely going to be influenced by the 'first' number you factor out.

Looking at 7150, you could easily start with a 2 (because 7150 is even), a 5 (because 7150 ends in a 0) or a 10 (also since it ends in a 0).

I actually started with 50, since 50 divides into 100 twice.....7100 = (71x2) fifties....

So 7150 = 142 fifties + 1 fifty =
(50)(143)

The (50) can be quickly broken down into (2)(5)(5)

Now, looking at the 143, we know that NO even numbers will divide in (since even numbers do NOT divide into odd numbers). If you know the 'rule of 3', then you know that 3 does NOT divide in. Since 3 doesn't divide in, 9 won't divide in either. 5 won't divide in for obvious reasons. Thus, we're really left with just a handful of possibilities:

1) 143 might be prime
2) 7, 11 and/or 13 might divide in

It's pretty easy to eliminate 7 as an option (it divides into 14, but not 3). Once you find that 11 divides in, you end up with the 13 by default.

GMAT assassins aren't born, they're made,
Rich
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# Rich Cohen

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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ Senior Manager Joined: 02 Dec 2014 Posts: 251 Location: Russian Federation Concentration: General Management, Economics WE: Sales (Telecommunications) Followers: 0 Kudos [?]: 51 [0], given: 320 Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink] 20 Jun 2015, 12:11 I noticed from past Quant problems that GMAT likes to use number 143. So it is better to remember that 143=11*13. _________________ "Are you gangsters?" - "No we are Russians!" Senior Manager Joined: 29 Oct 2013 Posts: 275 Concentration: Finance Schools: Johnson GMAT 1: 750 Q V GPA: 3.7 WE: Corporate Finance (Retail Banking) Followers: 12 Kudos [?]: 267 [0], given: 179 Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink] 01 Dec 2015, 05:16 EMPOWERgmatRichC, Bunuel, VeritasPrepKarishma: I stopped at 143 as felt it was a prime number after trying 3, 5, 7 n 9. I didnt go to 11. If i had taken that one extra step I would have gotten it right. But how far one should go? Here it is 11 but on some other questions it could be 17, 19, 23 etc. Is there a neat formula too tell all prime factors of a number? thanks _________________ Please consider giving 'kudos' if you like my post and want to thank EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 5587 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 224 Kudos [?]: 1588 [1] , given: 152 Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink] 01 Dec 2015, 20:52 1 This post received KUDOS Expert's post Hi MensaNumber, When you say that you tried 3, 5, 7 and 9, what actual 'work' did you do? I ask because your Quant skills are clearly strong (you have a Q48 to prove it), so I would guess that you would have figured out rather quickly that those single-digit primes wouldn't divide into 143. Since those smaller primes don't divide in, there can't be that many left to check out (and checking EITHER 11 or 13 would have been enough work to correctly answer the question). At it's core, this is a test of 'thoroughness' - it's true that most people wouldn't think to try dividing 11, but most people can't score Q48+, so you have to decide what 'extra work' (if any) YOU'RE willing to do to be thorough, prove that your answer is correct and pick up those extra points. GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]  01 Dec 2015, 22:41
Hi empowergmatrichc:

Thanks for you reply. I think I agree - ultimately it comes down to conscientiousness and this one quality determines who will be extraordinary successful and who will be just successful in GMAT/life.

EMPOWERgmatRichC wrote:
Hi MensaNumber,

When you say that you tried 3, 5, 7 and 9, what actual 'work' did you do? I ask because your Quant skills are clearly strong (you have a Q48 to prove it), so I would guess that you would have figured out rather quickly that those single-digit primes wouldn't divide into 143.

Since those smaller primes don't divide in, there can't be that many left to check out (and checking EITHER 11 or 13 would have been enough work to correctly answer the question). At it's core, this is a test of 'thoroughness' - it's true that most people wouldn't think to try dividing 11, but most people can't score Q48+, so you have to decide what 'extra work' (if any) YOU'RE willing to do to be thorough, prove that your answer is correct and pick up those extra points.

GMAT assassins aren't born, they're made,
Rich

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Re: How many prime numbers between 1 and 100 are factors of 7,15   [#permalink] 01 Dec 2015, 22:41
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