GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 18 Sep 2018, 22:24

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

M70-28

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49231
M70-28  [#permalink]

Show Tags

New post 03 Sep 2018, 06:10
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

75% (00:28) correct 25% (05:38) wrong based on 4 sessions

HideShow timer Statistics

Of the 27 participants in a talent show, 13 are singers, 14 are musicians, and 9 are dancers. If 4 people are both singers and dancers, 3 are both singers and musicians and 1 person is all three, how many people are both dancers and musicians?


A. 0
B. 1
C. 2
D. 3
E. 4

_________________

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49231
Re M70-28  [#permalink]

Show Tags

New post 03 Sep 2018, 06:10
Official Solution:


Of the 27 participants in a talent show, 13 are singers, 14 are musicians, and 9 are dancers. If 4 people are both singers and dancers, 3 are both singers and musicians and 1 person is all three, how many people are both dancers and musicians?


A. 0
B. 1
C. 2
D. 3
E. 4


We’ll go for ALTERNATIVE because the numbers in the answers are easy to use.

Since we have three overlapping sets, we’ll draw a Venn diagram, and instead of going into redundant calculations, we’ll try the median answer (C) 2 and see whether it works out:

The third layer, consisting of all three groups, is made up of 1 person. This makes the number of people who are singers and musicians (but not dancers) 3 – 1 = 2, and the number of singer-dancers (but not musicians) 4 – 1 = 3. The number of people who only sing is 13 – 1 – 2 – 3 = 7. Now, if answer (C) is correct, the number of those who only dance is 9 – 3 – 1 – 1 = 4, and the number of those who are only musicians is 14 – 2 – 1 – 1 = 10. So the overall number of participants is: 7 + 3 + 1 + 2 + 10 + 1 + 4 = 28, instead of 27. (C) is eliminated.

We can just check a random answer, but note that the answer we need to check is actually a larger one in order to make both ‘just musicians’ and ‘just dancers’ groups smaller (and thus making the total number of participants smaller). Let’s see answer choice (D) 3:

As we’ve seen before, we have 1 person in all three groups; 2 who are singers and musicians (but not dancers); 3 singer-dancers (but not musicians); and 7 only sing. Now, if answer (D) is correct, the number of those who only dance is 9 – 3 – 1 – 2 = 3, and the number of those who are only musicians is 14 – 2 – 1 – 2 = 9. So the total number of participants is: 7 + 3 + 1 + 2 + 9 + 2 + 3 = 27. That’s our answer!


Answer: D
_________________

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

Intern
Intern
avatar
Joined: 11 Mar 2018
Posts: 2
Re: M70-28  [#permalink]

Show Tags

New post 07 Sep 2018, 08:02
shouldn't it be 4?
Re: M70-28 &nbs [#permalink] 07 Sep 2018, 08:02
Display posts from previous: Sort by

M70-28

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

Moderators: chetan2u, Bunuel

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.