It is currently 25 Feb 2018, 01:52

### 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

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

# Events & Promotions

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

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178
How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

### Show Tags

20 Dec 2012, 05:35
2
KUDOS
16
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:00) correct 33% (01:03) wrong based on 1618 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
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 43900
Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

### Show Tags

20 Dec 2012, 05:36
3
KUDOS
Expert's post
1
This post was
BOOKMARKED
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.

_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 13758
Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

### Show Tags

19 Mar 2014, 20:27
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.
_________________
Current Student
Joined: 25 Sep 2012
Posts: 281
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

### Show Tags

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

Time Taken - 00:46
Difficulty level - 600
Manager
Joined: 07 Apr 2014
Posts: 132
Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

### Show Tags

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?
Math Expert
Joined: 02 Sep 2009
Posts: 43900
Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

### Show Tags

13 Sep 2014, 06:12
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?
_________________
Intern
Joined: 22 Nov 2012
Posts: 22
Location: United States
Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

### Show Tags

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!
_________________

GMAT,
It is not finished untill I win!!!

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11074
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

### Show Tags

29 Mar 2015, 18:01
3
KUDOS
Expert's post
2
This post was
BOOKMARKED
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

# 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/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Senior Manager Joined: 02 Dec 2014 Posts: 370 Location: Russian Federation Concentration: General Management, Economics GMAT 1: 640 Q44 V33 WE: Sales (Telecommunications) Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink] ### Show Tags 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!" Retired Moderator Joined: 29 Oct 2013 Posts: 282 Concentration: Finance GPA: 3.7 WE: Corporate Finance (Retail Banking) Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink] ### Show Tags 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 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 Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 11074 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 How many prime numbers between 1 and 100 are factors of 7,15 [#permalink] ### Show Tags 01 Dec 2015, 20:52 4 This post received KUDOS Expert's post 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 # 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/

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

Last edited by EMPOWERgmatRichC on 01 May 2016, 10:26, edited 1 time in total.
Retired Moderator
Joined: 29 Oct 2013
Posts: 282
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

### Show Tags

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

_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Manager
Joined: 30 Dec 2015
Posts: 90
GPA: 3.92
WE: Engineering (Aerospace and Defense)
How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

### Show Tags

01 May 2016, 09:11
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
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11074
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

### Show Tags

01 May 2016, 10:30
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

# 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/

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

Manager
Joined: 30 Dec 2015
Posts: 90
GPA: 3.92
WE: Engineering (Aerospace and Defense)
Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

### Show Tags

01 May 2016, 11:40
EMPOWERgmatRichC wrote:
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

Rich,

Thanks for clarifying with an example.
_________________

If you analyze enough data, you can predict the future.....its calculating probability, nothing more!

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2016
Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

### Show Tags

02 May 2016, 06:22
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.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Retired Moderator
Joined: 12 Aug 2015
Posts: 2430
GRE 1: 323 Q169 V154
Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

### Show Tags

03 Dec 2016, 20:08

Great Question.
So many nice takeaways.
When i saw the first line i rushed to write the prime factors between 1-100
2
3
5
7
11
13
17
19
23
29
31
37
41
43
47
53
59
61
67
71
73
79
83
89
97
101

But wait.
It would be a HUGE task to check for each of these numbers.
And GMAT would never ask us that.
noted i prime factored 7150
and saw that it has only four prime factors which are all in the range (1,100)
Hence E

Great Question

_________________

Getting into HOLLYWOOD with an MBA

Stone Cold's Mock Tests for GMAT-Quant(700+)

Retired Moderator
Joined: 12 Aug 2015
Posts: 2430
GRE 1: 323 Q169 V154
Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

### Show Tags

09 Jan 2017, 19:19
NoHalfMeasures wrote:
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

Hi.
Actually there is a formulae.
In oder to check to check whether a given number is prime or not => We just need to check the divisibility with all the primes less than or equal to the square root of that number.
Question in case is 143
$$√143$$ = 11.something
So we need to check the divisibility with primes less than or equal to 11.somthing => 2,3,5,7,11

Another example => Say 211
Here $$√211$$ = 14.something
Hence we need to check the divisibility with all the primes less than or equal to 14.something => 2,3,5,7,11,13
211 is actually a prime number as every divisibly test fails.

Regards
Stone Cold

_________________

Getting into HOLLYWOOD with an MBA

Stone Cold's Mock Tests for GMAT-Quant(700+)

Intern
Joined: 28 Feb 2017
Posts: 13
How to assume if the GMAT is asking for a unique # of [things]? [#permalink]

### Show Tags

02 Mar 2017, 12:43
How many prime numbers between 1 and 100 are factors of 7,150?

A. One
B. Two
C. Three
D. Four
E. Five

I correctly factored 7,150 into 13 x 11 x 5 x 5 x 2. So there are 5 prime factors in total, 4 of which are unique. The correct answer is 4. So the GMAT must have been asking for the # of unique factors? I'm just having a little trouble convincing myself how the language in the question stem translates to unique vs. total.

Math Expert
Joined: 02 Sep 2009
Posts: 43900
Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

### Show Tags

02 Mar 2017, 14:12
v0latility wrote:
How many prime numbers between 1 and 100 are factors of 7,150?

A. One
B. Two
C. Three
D. Four
E. Five

I correctly factored 7,150 into 13 x 11 x 5 x 5 x 2. So there are 5 prime factors in total, 4 of which are unique. The correct answer is 4. So the GMAT must have been asking for the # of unique factors? I'm just having a little trouble convincing myself how the language in the question stem translates to unique vs. total.

Merging topics. Please refer to the discussion above.
_________________
Re: How many prime numbers between 1 and 100 are factors of 7,15   [#permalink] 02 Mar 2017, 14:12

Go to page    1   2    Next  [ 26 posts ]

Display posts from previous: Sort by