It is currently 19 Nov 2017, 00:20

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Set S consists of all prime integers less than 10. If two

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

Hide Tags

1 KUDOS received
Manager
Manager
avatar
Joined: 05 Mar 2011
Posts: 145

Kudos [?]: 67 [1], given: 3

Set S consists of all prime integers less than 10. If two [#permalink]

Show Tags

New post 15 Dec 2011, 18:56
1
This post received
KUDOS
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

74% (01:26) correct 26% (01:38) wrong based on 190 sessions

HideShow timer Statistics

Set S consists of all prime integers less than 10. If two numbers are chosen form set S at random, what is the probability that the product of these numbers will be greater than the product of the numbers which were not chosen?

(A) \(\frac{1}{3}\)
(B) \(\frac{2}{3}\)
(C) \(\frac{1}{2}\)
(D) \(\frac{7}{10}\)
(E) \(\frac{4}{5}\)
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 Feb 2012, 12:59, edited 1 time in total.
Edited the question

Kudos [?]: 67 [1], given: 3

Intern
Intern
avatar
Joined: 12 Oct 2011
Posts: 19

Kudos [?]: 22 [0], given: 5

Location: United States
GMAT 1: 720 Q50 V36
Reviews Badge
Re: probabilty [#permalink]

Show Tags

New post 15 Dec 2011, 19:22
S = {2,3,5,7}


chosen numbers =x,y
not chosen ones = a,b
such that xy < ab



chosen nos = a,b
not chosen ones = x,y
ab>xy


so the probability that product of chosen ones is more than not chosen ones is 1/2

[Reveal] Spoiler:
Option C

Kudos [?]: 22 [0], given: 5

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 12 Oct 2011
Posts: 255

Kudos [?]: 63 [1], given: 110

Re: probabilty [#permalink]

Show Tags

New post 15 Dec 2011, 22:57
1
This post received
KUDOS
1
This post was
BOOKMARKED
The set will be
S = {2, 3, 5, 7}
Two numbers can be chosen from the set of four numbers in 4C2 = 6 ways.
Chosen Numbers ----- Product ----- Numbers not chosen ----- Product
2, 3 -------------------- 6 --------------- 5, 7 -------------------- 35
2, 5 -------------------- 10 --------------- 3, 7 -------------------- 21
2, 7 -------------------- 14 --------------- 3, 5 -------------------- 15
3, 5 -------------------- 15 --------------- 2, 7 -------------------- 14
3, 7 -------------------- 21 --------------- 2, 5 -------------------- 10
5, 7 -------------------- 35 --------------- 2, 3 -------------------- 6

Thus, from the table above, it is obvious that there are just three possible combinations in which the product of the numbers chosen is greater than the product of the numbers not chosen.
Thus the required probability = 3/6 = 1/2

Hope this is helpful. :)

Kudos [?]: 63 [1], given: 110

Manager
Manager
avatar
Joined: 21 Sep 2011
Posts: 109

Kudos [?]: 16 [0], given: 18

Concentration: Entrepreneurship, General Management
GMAT 1: 530 Q42 V20
GMAT 2: 540 Q43 V28
GMAT 3: 680 Q48 V35
WE: Business Development (Hospitality and Tourism)
Re: probabilty [#permalink]

Show Tags

New post 16 Dec 2011, 00:33
IMO C.

Went with the same approach but i stopped after 4th step since 5 and 6 will definitely be greater in the chosen values side as the values are increasing that side and decreasing in the other side :)
_________________

KUDOS - if my post has helped you.

Kudos [?]: 16 [0], given: 18

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132643 [2], given: 12326

Re: Set S consists of all prime integers less than 10. If two [#permalink]

Show Tags

New post 04 Feb 2012, 13:01
2
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
ashiima wrote:
Set S consists of all prime integers less than 10. If two numbers are chosen form set S at random, what is the probability that the product of these numbers will be greater than the product of the numbers which were not chosen?

(A) \(\frac{1}{3}\)
(B) \(\frac{2}{3}\)
(C) \(\frac{1}{2}\)
(D) \(\frac{7}{10}\)
(E) \(\frac{4}{5}\)


Shortcut solution:

S={2, 3, 5, 7}

The simplest way would be to realize that we choose half of the numbers (basically we divide the group of 4 into two smaller groups of 2) and since a tie is not possible then the probability that the product of the numbers in either of subgroup is more than that of in another is 1/2 (the probability doesn't favor any of two subgroups).

Answer: C.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132643 [2], given: 12326

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15705

Kudos [?]: 282 [0], given: 0

Premium Member
Re: Set S consists of all prime integers less than 10. If two [#permalink]

Show Tags

New post 30 Oct 2017, 13:47
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

Kudos [?]: 282 [0], given: 0

Re: Set S consists of all prime integers less than 10. If two   [#permalink] 30 Oct 2017, 13:47
Display posts from previous: Sort by

Set S consists of all prime integers less than 10. If two

  new topic post reply 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 | Emoji artwork provided by EmojiOne

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®.