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

It is currently 12 Feb 2016, 04:22
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Set S is the set of all prime integers between 0 and 20. If

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
3 KUDOS received
Current Student
User avatar
Joined: 29 Jan 2005
Posts: 5239
Followers: 23

Kudos [?]: 257 [3] , given: 0

Set S is the set of all prime integers between 0 and 20. If [#permalink] New post 31 Aug 2006, 23:40
3
This post received
KUDOS
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

72% (03:28) correct 28% (02:47) wrong based on 265 sessions
Set S is the set of all prime integers between 0 and 20. If three numbers are chosen randomly from set S and each number can be chosen only once, what is the positive difference between the probability that the product of these three numbers is a number less than 31 and the probability that the sum of these three numbers is odd?

(A) 1/336
(B) 1/2
(C) 17/28
(D) 3/4
(E) 301/336
[Reveal] Spoiler: OA
5 KUDOS received
Director
Director
avatar
Joined: 13 Nov 2003
Posts: 790
Location: BULGARIA
Followers: 1

Kudos [?]: 32 [5] , given: 0

 [#permalink] New post 01 Sep 2006, 01:03
5
This post received
KUDOS
1
This post was
BOOKMARKED
The primes between 1-20 are 2,3,5,7,11,13,17,19 or 8 in total then 8C3=56 or we can form 56 triplets. The product of 2,3,5 only is less than 31 so the prob that the product is less than 31 is 1/56 . The prob that the sum is odd is 7C3/8C3 . Exclude 2 , because it is even and will make the sum even and select 3 out of 7( Odd only) the prob is 35/56. The required prob is 35/56-1/56=34/56=17/28
Director
Director
User avatar
Joined: 28 Dec 2005
Posts: 755
Followers: 1

Kudos [?]: 9 [0], given: 0

 [#permalink] New post 01 Sep 2006, 01:48
C for me.

P(product < 31) =1/8C3

P(sum is odd) = 7C3/8C3

Diff = 34/56 or 17/28
Senior Manager
Senior Manager
avatar
Joined: 14 Jul 2006
Posts: 281
Followers: 1

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

Re: PS Sets [#permalink] New post 01 Sep 2006, 03:49
GMATT73 wrote:
Set S is the set of all prime integers between 0 and 20. If three numbers are chosen randomly from set S and each number can be chosen only once, what is the positive difference between the probability that the product of these three numbers is a number less than 31 and the probability that the sum of these three numbers is odd?

(A) 1/336
(B) 1/2
(C) 17/28
(D) 3/4
(E) 301/336


Ans C The only time the product will be less than 31 is when 2,3,5

1/(8C3)

The only time an even sum would occur is when 2 is included in the mix

so excluding 2 7C3/8C3

The difference will be C
Current Student
User avatar
Joined: 29 Jan 2005
Posts: 5239
Followers: 23

Kudos [?]: 257 [0], given: 0

 [#permalink] New post 01 Sep 2006, 03:50
BG wrote:
The primes between 1-20 are 2,3,5,7,11,13,17,19 or 8 in total then 8C3=56 or we can form 56 triplets. The product of 2,3,5 only is less than 31 so the prob that the product is less than 31 is 1/56 . The prob that the sum is odd is 7C3/8C3 . Exclude 2 , because it is even and will make the sum even and select 3 out of 7( Odd only) the prob is 35/56. The required prob is 35/56-1/56=34/56=17/28


Scintillating :cool Don't you just love it when we can reinforce multiple concepts in one problem?

1. Rule of primes
2. Adding odd and even integers
3. Triplets
4. Dependent probabilty
5. Combinatorics
6. Positive sum (absolute value)
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 8221
Followers: 419

Kudos [?]: 111 [0], given: 0

Top 10 in overall
Re: Set S is the set of all prime integers between 0 and 20. If [#permalink] New post 19 Sep 2013, 00:59
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Intern
Intern
avatar
Joined: 14 Feb 2012
Posts: 29
Followers: 0

Kudos [?]: 4 [0], given: 6

Re: [#permalink] New post 31 Oct 2013, 01:08
BG wrote:
The primes between 1-20 are 2,3,5,7,11,13,17,19 or 8 in total then 8C3=56 or we can form 56 triplets. The product of 2,3,5 only is less than 31 so the prob that the product is less than 31 is 1/56 . The prob that the sum is odd is 7C3/8C3 . Exclude 2 , because it is even and will make the sum even and select 3 out of 7( Odd only) the prob is 35/56. The required prob is 35/56-1/56=34/56=17/28


Im not understanding how you come to 35/56?

Can someone please explain?
Current Student
User avatar
Joined: 06 Sep 2013
Posts: 2036
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 40

Kudos [?]: 435 [0], given: 355

GMAT ToolKit User
Re: [#permalink] New post 25 Nov 2013, 11:55
BG wrote:
The primes between 1-20 are 2,3,5,7,11,13,17,19 or 8 in total then 8C3=56 or we can form 56 triplets. The product of 2,3,5 only is less than 31 so the prob that the product is less than 31 is 1/56 . The prob that the sum is odd is 7C3/8C3 . Exclude 2 , because it is even and will make the sum even and select 3 out of 7( Odd only) the prob is 35/56. The required prob is 35/56-1/56=34/56=17/28


You got the answer but your procedure is flawed. You must INCLUDE 2 not exclude since you want the sum to be odd. Anyways you get the same combinatorics fraction.

Cheers
J :)
Senior Manager
Senior Manager
User avatar
Joined: 17 Sep 2013
Posts: 389
Concentration: Strategy, General Management
GMAT 1: 690 Q48 V37
GMAT 2: 730 Q51 V38
WE: Analyst (Consulting)
Followers: 16

Kudos [?]: 186 [0], given: 136

GMAT ToolKit User Top 10 in overall
Re: Re: [#permalink] New post 07 May 2014, 01:34
jlgdr wrote:
BG wrote:
The primes between 1-20 are 2,3,5,7,11,13,17,19 or 8 in total then 8C3=56 or we can form 56 triplets. The product of 2,3,5 only is less than 31 so the prob that the product is less than 31 is 1/56 . The prob that the sum is odd is 7C3/8C3 . Exclude 2 , because it is even and will make the sum even and select 3 out of 7( Odd only) the prob is 35/56. The required prob is 35/56-1/56=34/56=17/28


You got the answer but your procedure is flawed. You must INCLUDE 2 not exclude since you want the sum to be odd. Anyways you get the same combinatorics fraction.

Cheers
J :)


2+3+5= 10...?
3 numbers here..so all 3 odd is necessary

FYI if we use 2 here..i.e 2 is a necessary filler..then the no of ways you can get an even sum is 21..and probability is 7C2/8C3=21/56
Correct me if I am wrong
_________________

Appreciate the efforts...KUDOS for all
Don't let an extra chromosome get you down..:P

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 8221
Followers: 419

Kudos [?]: 111 [0], given: 0

Top 10 in overall
Re: Set S is the set of all prime integers between 0 and 20. If [#permalink] New post 01 Jun 2015, 21:28
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Intern
Intern
avatar
Joined: 28 Jun 2015
Posts: 6
Followers: 0

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

Re: Set S is the set of all prime integers between 0 and 20. If [#permalink] New post 23 Aug 2015, 22:48
S = 2,3,5,7,11,13,17,19
Size of S = 8

first number can be chosen in 8 ways
2nd number in 7 ways
3rd number 6 ways

so total outcomes = 8 x 7 x 6 = 336 possible triplets

for the sum to be odd all three must be odd = 7 x 6 x 5 = 210 ways

prob of odd = 210/336 = 5/8

prod less than 31 can only be possible if we have 2,3,5 this can be done in 3x2x1 ways = 6 ways
prob (sum<31) = 6/8x7x6 = 1/56

diff = 5/8 - 1/56 = 34/56 = 17/28
Manager
Manager
avatar
Joined: 07 Apr 2015
Posts: 187
Followers: 2

Kudos [?]: 42 [0], given: 185

Set S is the set of all prime integers between 0 and 20. If [#permalink] New post 24 Aug 2015, 00:47
I did it this way:

Primes between 0 and 20:
2, 3, 5, 7, 11, 13, 17, 19

I: Probability that the product of (x,yz) < 31:
Only possible way is 2*3*5 = 30, all other products are >31

=> \(1/8 * 1/7 * 1/6 * 3! = 3*2*1/336 = 1/56\)

II: Probability that the sum of (x+y+z) = odd:
There are numerous possibilities as long as 2 (the only even number) is not included.

=> \(7/8 * 6/7 * 5/6 = 5/8\)

III: I - II:

=> \(1/56 - 5/8 = |-17/28|\)
Intern
Intern
avatar
Joined: 27 Apr 2015
Posts: 21
Concentration: General Management, Entrepreneurship
GMAT 1: 730 Q50 V40
WE: Operations (Telecommunications)
Followers: 0

Kudos [?]: 5 [0], given: 27

Re: Set S is the set of all prime integers between 0 and 20. If [#permalink] New post 31 Aug 2015, 21:23
waltiebikkiebal wrote:
BG wrote:
The primes between 1-20 are 2,3,5,7,11,13,17,19 or 8 in total then 8C3=56 or we can form 56 triplets. The product of 2,3,5 only is less than 31 so the prob that the product is less than 31 is 1/56 . The prob that the sum is odd is 7C3/8C3 . Exclude 2 , because it is even and will make the sum even and select 3 out of 7( Odd only) the prob is 35/56. The required prob is 35/56-1/56=34/56=17/28


Im not understanding how you come to 35/56?

Can someone please explain?



We have a total of 8 prime nos between 1 and 20. To have an odd sum, the three nos should be odd. Out of the total 8 prime nos, there are 7 odd nos, so the no of ways to select 3 nos out of 7 would be 7C3.
Hence, the probability would be 7C3/8C3 = 35/56
Re: Set S is the set of all prime integers between 0 and 20. If   [#permalink] 31 Aug 2015, 21:23
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic D is the set of all the multiples of 3 between 20 and 100. E is the se honchos 2 09 Jul 2015, 22:58
Set S is the prime integers between 0 and 20. If three numbe sudharsansuski 4 03 Aug 2013, 06:28
5 Experts publish their posts in the topic Set S consists of all prime integers less than 10. If two ashiima 6 15 Dec 2011, 17:56
15 Experts publish their posts in the topic Set A consists of all even integers between 2 and 100 punyadeep 10 14 Mar 2011, 08:20
6 Experts publish their posts in the topic Set A consists of all prime numbers between 10 and 25; Set B punyadeep 14 14 Mar 2011, 08:05
Display posts from previous: Sort by

Set S is the set of all prime integers between 0 and 20. If

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.