Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 18 Jul 2019, 01:59

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Director
Director
avatar
Joined: 29 Aug 2005
Posts: 732
How many prime numbers between 1 and 100 are factors of 7150  [#permalink]

Show Tags

New post 13 Apr 2009, 01:39
9
24
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

66% (01:20) correct 34% (01:29) wrong based on 2704 sessions

HideShow timer Statistics


How many prime numbers between 1 and 100 are factors of 7,150?

A. One
B. Two
C. Three
D. Four
E. Five
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56261
Re: How many prime numbers between 1 and 100 are factors of 7150  [#permalink]

Show Tags

New post 13 Feb 2012, 19:22
11
4
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.
_________________
General Discussion
Intern
Intern
avatar
Joined: 04 Jan 2010
Posts: 5
Re: How many prime numbers between 1 and 100?  [#permalink]

Show Tags

New post 16 Jan 2012, 12:09
4
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?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56261
Re: How many prime numbers between 1 and 100?  [#permalink]

Show Tags

New post 16 Jan 2012, 12:33
2
5
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).

Answer: D.
_________________
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 9442
Location: Pune, India
Re: How many prime numbers between 1 and 100?  [#permalink]

Show Tags

New post 18 Jan 2012, 05:24
2
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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern
Intern
avatar
Joined: 14 Nov 2011
Posts: 10
Re: How many prime numbers between 1 and 100 are factors of 7150  [#permalink]

Show Tags

New post 13 Feb 2012, 19:09
4
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.
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 9442
Location: Pune, India
Re: How many prime numbers between 1 and 100 are factors of 7150  [#permalink]

Show Tags

New post 14 Feb 2012, 00:19
9
3
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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Senior Manager
Senior Manager
User avatar
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 410
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: How many prime numbers between 1 and 100 are factors of 7150  [#permalink]

Show Tags

New post 19 Jan 2015, 10:20
So, just to clarify this, if the question only asks for the factors we count all of the factors, no matter if there are repetitions.

Only when it specifically says that we need the "unique" factors should we diregard repeating factors.

Right?
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 9442
Location: Pune, India
Re: How many prime numbers between 1 and 100 are factors of 7150  [#permalink]

Show Tags

New post 19 Jan 2015, 22:14
pacifist85 wrote:
So, just to clarify this, if the question only asks for the factors we count all of the factors, no matter if there are repetitions.

Only when it specifically says that we need the "unique" factors should we diregard repeating factors.

Right?


Not really.
Take the example of factors of 8:

How many total factors does 8 have and what are they?
They are 1, 2, 4 and 8 - a total of 4 factors

We know that 8 = 2^3 but we don't say that factors are 8 are 1, 2, 2, 2, 4 and 8.

Similarly, if we are asked - how many prime factors does 8 have? I will answer only 1 (the prime factor is 2). The number of prime factors of 8 are not 3 (not 2, 2, 2). I know of people who are not very convinced with this and hence, I assume that GMAT will insert the word "unique" to remove all doubts.

On GMAT, I would expect it to be - How many unique prime factors does 8 have?

In the original question, there is no doubt since they ask "how many prime numbers are factors of..." The set of prime numbers does not have multiple entries and hence there is no doubt that we are talking about unique prime factors only.
_________________
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
Intern
User avatar
Joined: 22 Nov 2012
Posts: 20
Location: United States
GMAT ToolKit User
Re: How many prime numbers between 1 and 100 are factors of 7,15  [#permalink]

Show Tags

New post 29 Mar 2015, 15:06
Bunuel
Bunuel wrote:
Walkabout 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.

Answer: D.


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!
_________________
GMAT,
It is not finished untill I win!!!
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14567
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: How many prime numbers between 1 and 100 are factors of 7,15  [#permalink]

Show Tags

New post 29 Mar 2015, 19:01
5
2
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
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Retired Moderator
avatar
Joined: 29 Oct 2013
Posts: 257
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
GMAT ToolKit User
Re: How many prime numbers between 1 and 100 are factors of 7,15  [#permalink]

Show Tags

New post 01 Dec 2015, 06:16
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 contact me for super inexpensive quality private tutoring

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14567
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
How many prime numbers between 1 and 100 are factors of 7,15  [#permalink]

Show Tags

New post Updated on: 01 May 2016, 11:26
4
Hi NoHalfMeasures,

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
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

Originally posted by EMPOWERgmatRichC on 01 Dec 2015, 21:52.
Last edited by EMPOWERgmatRichC on 01 May 2016, 11:26, edited 1 time in total.
Manager
Manager
User avatar
S
Joined: 30 Dec 2015
Posts: 84
GPA: 3.92
WE: Engineering (Aerospace and Defense)
Premium Member
How many prime numbers between 1 and 100 are factors of 7,15  [#permalink]

Show Tags

New post 01 May 2016, 10:11
EMPOWERgmatRichC, Bunuel, VeritasPrepKarishma:

Here is my method (and I am guessing this is not the right approach, but wanted to confirm):

7150 = 7000 + 150
7000 = 7 * 1000 (so we have 7, 5 & 2)
150 = 3 * 50 (so we have 3, 5 & 2)

combining both we have 2, 3, 5 & 7 as prime numbers.

At the end, I am still getting the same number of prime numbers for 7150, albeit different values (maybe coincidence).

I will be trying this with the next similar questions I come across, till then any help....greatly appreciated.
_________________
If you analyze enough data, you can predict the future.....its calculating probability, nothing more!
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14567
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: How many prime numbers between 1 and 100 are factors of 7,15  [#permalink]

Show Tags

New post 01 May 2016, 11:30
Hi colorblind,

Unfortunately, that logic is NOT correct (and it was lucky that you ended up with the correct answer). Here's a simple example that proves the logic is NOT correct.

17 has one prime factor: 17

Using the logic you described...
17 = 10+7
10 has prime factors of 2 and 5 and 7 has one prime factor: 7

However, these prime factors (re: 2, 5 and 7) are NOT the same prime factors of 17 (re: 17) and the NUMBER of prime factors is also different.

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823
Re: How many prime numbers between 1 and 100 are factors of 7,15  [#permalink]

Show Tags

New post 02 May 2016, 07:22
1
Walkabout wrote:
How many prime numbers between 1 and 100 are factors of 7,150 ?

(A) One
(B) Two
(C) Three
(D) Four
(E) Five


We start by prime factoring 7,150.

7,150 = 715 x 10 = 143 x 5 x 10

At this point we must be careful. They WANT you to think that 143 is prime. Using our divisibility rules, however, we can determine that 143 is divisible by 11. A number is divisible by 11 if the sum of the odd-numbered place digits minus the sum of the even-numbered place digits is divisible by 11. We can test 143 to prove this:

1 + 3 – 4 = 4 – 4 = 0

Since zero is divisible by 11, we know that 143 is divisible by 11. We can now finish the prime factorization.

143 x 5 x 10 = 11 x 13 x 5 x 5 x 2

11 x 13 x 5^2 x 2

Thus we can see that there are 4 different prime factors in 7,150.

Answer is D.
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7599
GMAT 1: 760 Q51 V42
GPA: 3.82
How many prime numbers between 1 and 100 are factors of 7,15  [#permalink]

Show Tags

New post 09 Mar 2017, 17:01
elisabettaportioli wrote:
Bunuel
Bunuel wrote:
Walkabout 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.

Answer: D.


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!


One of the questions above is how to recognize easily if a number is a multiple of 11 or not.

Let \(N\) be an integer \(a_m a_{m-1} ... a_2 a_1 a_0\) written in 10 base notation.
Consider the difference between \(a_0 + a_2 + a_4 + ...\), the sum of digits at even numbered positions such as 0th, 2nd, 4th, ... and \(a_1 + a_3 + a5 + ...\), the sum of digits at odd numbered positions such 1st, 3rd, 5th, ... .
If \(( a_0 + a_2 + a_4 + ... ) - ( a_1 + a_3 + a5 + ... )\) is a multiple of 11, then \(N\) must be a multiple of 11.

Here, in this question, we have ( 7 + 5 ) - ( 1 + 0 ) = 12 - 1 = 11, which is a multiple of 11.
Thus 7150 must be a multiple of 11.

For 143, ( 1 + 3 ) - 4 is 0, which is also a multiple of 11.
Thus 143 is a multiple of 11.

Are you curious about why?
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
VP
VP
User avatar
D
Joined: 09 Mar 2016
Posts: 1273
Re: How many prime numbers between 1 and 100 are factors of 7,15  [#permalink]

Show Tags

New post 02 Jan 2018, 04:38
Walkabout wrote:
How many prime numbers between 1 and 100 are factors of 7,150 ?

(A) One
(B) Two
(C) Three
(D) Four
(E) Five



Hello Everyone :) Can anyone suggest divisibility rule by 7, 11, and 13 ? Thanks! :-)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56261
Re: How many prime numbers between 1 and 100 are factors of 7,15  [#permalink]

Show Tags

New post 02 Jan 2018, 04:50
Manager
Manager
avatar
S
Joined: 07 Feb 2017
Posts: 182
How many prime numbers between 1 and 100 are factors of 7150  [#permalink]

Show Tags

New post 27 Jun 2018, 18:35
The tag is 600-700 level. Why is the question labeled "hard" in the Official Guide 2018 Book's Onine Question Bank?
GMAT Club Bot
How many prime numbers between 1 and 100 are factors of 7150   [#permalink] 27 Jun 2018, 18:35

Go to page    1   2    Next  [ 21 posts ] 

Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne