It is currently 16 Oct 2017, 19:13

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

Of 200 surveyed students, 20% of those who read book A

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

Hide Tags

2 KUDOS received
Manager
Manager
avatar
Joined: 30 May 2013
Posts: 185

Kudos [?]: 87 [2], given: 72

Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.82
GMAT ToolKit User
Of 200 surveyed students, 20% of those who read book A [#permalink]

Show Tags

New post 26 Sep 2013, 22:14
2
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

67% (02:51) correct 33% (01:54) wrong based on 167 sessions

HideShow timer Statistics

Of 200 surveyed students, 20% of those who read book A also read book B and 25% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B?

A. 20
B. 25
C. 30
D. 35
E. 40
[Reveal] Spoiler: OA

Kudos [?]: 87 [2], given: 72

7 KUDOS received
Manager
Manager
User avatar
Joined: 29 Apr 2013
Posts: 99

Kudos [?]: 296 [7], given: 53

Location: India
Concentration: General Management, Strategy
GMAT Date: 11-06-2013
WE: Programming (Telecommunications)
Re: Of 200 surveyed students, 20% of those who read book A [#permalink]

Show Tags

New post 26 Sep 2013, 23:35
7
This post received
KUDOS
Total students = A + B - BOTH

where, A = students who read book A
B = students who read book B

BOTH = 0.2A (20% of those who read book A also read book B)
BOTH = 0.25B (25% of those who read book B also read book A)

So, 0.2A = 0.25B
A = 1.25B

Replacing A with 1.25B and BOTH with 0.25B in the original equation, we get
Total = A + B - BOTH
200 = 1.25B + B - 0.25B
200 = 2B
B=100

So, BOTH = 0.25B = 0.25 * 100 = 25

Again, Total = A + B -BOTH
200 = A + 100 - 25
A = 125

We have to find ONLY A - ONLY B
ONLY A = A - BOTH = 125 - 25 = 100
ONLY B = B - BOTH = 100 - 25 = 75


So ONLY A - ONLY B = 100 - 75 = 25 (Correct Answer : B)
_________________

Do not forget to hit the Kudos button on your left if you find my post helpful 8-)

Collection of some good questions on Number System

Kudos [?]: 296 [7], given: 53

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41875

Kudos [?]: 128460 [2], given: 12173

Re: Of 200 surveyed students, 20% of those who read book A [#permalink]

Show Tags

New post 27 Sep 2013, 00:47
2
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
m15 q16

Of 200 surveyed students, 20% of those who read book A also read book B and 25% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B?

A. 20
B. 25
C. 30
D. 35
E. 40

Say the number of students who read book A is A and the number of students who read book B is B.

Given that 20% of those who read book A also read book B and 25% of those who read book B also read book A, so the number of students who read both books is 0.2A=0.25B --> A=1.25B.

Since each student read at least one of the books then {total}={A}+{B}-{Both} --> 200=1.25B+B-0.25B --> B=100, A=1.25B=125 and {Both}=0.25B=25.

The number of students who read only book A is {A}-{Both}=125-25=100;
The number of students who read only book B is {B}-{Both}=100-25=75;

The difference is 100-75=25.

Answer: B.
_________________

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 [?]: 128460 [2], given: 12173

Intern
Intern
avatar
Joined: 06 Feb 2013
Posts: 23

Kudos [?]: 6 [0], given: 3

Re: Of 200 surveyed students, 20% of those who read book A [#permalink]

Show Tags

New post 29 Sep 2013, 06:38
Bunuel,

Could you please give an example of a problem where we would use Total= only A+ only B + both. Why aren't we using this formula in this problem?
thanks

Kudos [?]: 6 [0], given: 3

3 KUDOS received
Manager
Manager
User avatar
Joined: 29 Apr 2013
Posts: 99

Kudos [?]: 296 [3], given: 53

Location: India
Concentration: General Management, Strategy
GMAT Date: 11-06-2013
WE: Programming (Telecommunications)
Re: Of 200 surveyed students, 20% of those who read book A [#permalink]

Show Tags

New post 29 Sep 2013, 07:05
3
This post received
KUDOS
LinaNY wrote:
Bunuel,

Could you please give an example of a problem where we would use Total= only A+ only B + both. Why aren't we using this formula in this problem?
thanks


It depends on what information you have with you.

If you know the values of TOTAL, ONLY A and ONLY B and you need to calculate the value of BOTH, then you can use the formula:
Total= only A+ only B + both

But if you don't know the values of ONLY A and ONLY B (like in this case where we are able to deduce the values of A and B but not of ONLY A and ONLY B), the we should use the following formula:
Total= A+ B - BOTH.

So use of formula varies depending on the information available.

I hope I have addressed your query :-D
_________________

Do not forget to hit the Kudos button on your left if you find my post helpful 8-)

Collection of some good questions on Number System

Kudos [?]: 296 [3], given: 53

Intern
Intern
avatar
Joined: 06 Feb 2013
Posts: 23

Kudos [?]: 6 [0], given: 3

Re: Of 200 surveyed students, 20% of those who read book A [#permalink]

Show Tags

New post 29 Sep 2013, 07:07
Thanks! it's clear now :)

Kudos [?]: 6 [0], given: 3

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41875

Kudos [?]: 128460 [0], given: 12173

Re: Of 200 surveyed students, 20% of those who read book A [#permalink]

Show Tags

New post 29 Sep 2013, 11:33
LinaNY wrote:
Bunuel,

Could you please give an example of a problem where we would use Total= only A+ only B + both. Why aren't we using this formula in this problem?
thanks


PS: a-polling-company-found-that-of-300-households-surveyed-102377.html
DS: a-data-company-recently-conducted-a-survey-to-determine-wh-154001.html

Theory on Overlapping Sets:
advanced-overlapping-sets-problems-144260.html
how-to-draw-a-venn-diagram-for-problems-98036.html

All DS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=45
All PS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=65

Hope this helps.
_________________

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 [?]: 128460 [0], given: 12173

Intern
Intern
avatar
Joined: 04 Apr 2012
Posts: 10

Kudos [?]: 8 [0], given: 2

Schools: Katz '18 (S)
GMAT 1: 640 Q49 V28
Re: Of 200 surveyed students, 20% of those who read book A [#permalink]

Show Tags

New post 12 Oct 2014, 05:54
Y+.8X=200
.2X=.25Y

X=125 Y=100


We have to find

(x-.2x)-(y-.25y)

100-75==>25 Ans
Attachments

File comment: See attach Matrix
Quant.xlsx [9.35 KiB]
Downloaded 59 times

To download please login or register as a user

Kudos [?]: 8 [0], given: 2

Manager
Manager
User avatar
B
Joined: 18 Mar 2015
Posts: 98

Kudos [?]: 4 [0], given: 107

Location: India
Schools: ISB '19
GMAT 1: 600 Q47 V26
GPA: 3.59
Re: Of 200 surveyed students, 20% of those who read book A [#permalink]

Show Tags

New post 09 Sep 2017, 06:04
Bunuel wrote:
m15 q16



Since each student read at least one of the books then {total}={A}+{B}-{Both} --> 200=1.25B+B-0.25B --> B=100, A=1.25B=125 and {Both}=0.25B=25.

The number of students who read only book A is {A}-{Both}=125-25=100;
The number of students who read only book B is {B}-{Both}=100-25=75;

The difference is 100-75=25.

Answer: B.

Hi Bunuel ,I know it must be little silly to ask but how did you get both =0.25 B.. Even I could come upto A(=5/4)B but couldn't understand what to write for "both". Please elaborate.

Kudos [?]: 4 [0], given: 107

Intern
Intern
avatar
B
Joined: 29 May 2017
Posts: 4

Kudos [?]: 0 [0], given: 96

Re: Of 200 surveyed students, 20% of those who read book A [#permalink]

Show Tags

New post 06 Oct 2017, 10:57
Given : 0.2X=0.25Y = n(X&Y)
Or X/5=Y/4 =n(X&Y)
Y=4X/5
Total=X+Y-n(X&Y)
200=X+4X/5-X/5
8X/5=200
X=125
Y=4*125/5=100
X-Y=125-100=25

Kudos [?]: 0 [0], given: 96

Re: Of 200 surveyed students, 20% of those who read book A   [#permalink] 06 Oct 2017, 10:57
Display posts from previous: Sort by

Of 200 surveyed students, 20% of those who read book A

  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®.