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

It is currently 13 Oct 2019, 15:59

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

M15-16

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58335
M15-16  [#permalink]

Show Tags

New post 16 Sep 2014, 00:55
16
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

68% (02:48) correct 33% (02:51) wrong based on 80 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

_________________
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58335
Re M15-16  [#permalink]

Show Tags

New post 16 Sep 2014, 00:55
4
1
Official Solution:

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 \(0.2A=0.25B\), and therefore \(A=1.25B\).

Since each student read at least one of the books then \(\{Total\}=\{A\}+\{B\}-\{Both\}\), hence \(200=1.25B+B-0.25B\), which gives \(B=100\), \(A=1.25B=125\) 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
_________________
Intern
Intern
avatar
Joined: 19 Sep 2014
Posts: 20
GPA: 3.96
GMAT ToolKit User Reviews Badge
Re M15-16  [#permalink]

Show Tags

New post 19 Aug 2015, 08:07
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Need help as to how the calculation for both which is 0.25B has been derived?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58335
Re: M15-16  [#permalink]

Show Tags

New post 19 Aug 2015, 10:05
1
schak2rhyme wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Need help as to how the calculation for both which is 0.25B has been derived?


From \(\{Total\}=\{A\}+\{B\}-\{Both\}\) we get that \(B=100\). Next, the stem says that "25% of those who read book \(B\) also read book \(A\).", thus 25% of those who read book \(B\) read both book A and book B. Therefore, \(\{Both\}=0.25B=0.25100=25\).

Hope it's clear.
_________________
SVP
SVP
User avatar
V
Joined: 26 Mar 2013
Posts: 2341
Reviews Badge CAT Tests
Re: M15-16  [#permalink]

Show Tags

New post 20 Aug 2015, 07:24
8
1
Bunuel wrote:
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


After constructing the matrix as attached:
From here: 0.2X=0.25Y......> 4x=5Y or the same X=1.25Y
Difference between reading only A and only B= 0.8X - 0.75Y, simplify and from above equation to 0.2(4X) - 0.75Y= 0.2*5Y -0.75 Y = Y-0.75Y= 0.25Y.......(1)
From the matrix: Y+0.8X=200…..> Y + 0.2 (4X)+Y=200……> 2Y=200…> Y=100.

Applying in (1)… Difference=0.25Y=25
Answer is B
>> !!!

You do not have the required permissions to view the files attached to this post.

Intern
Intern
avatar
B
Joined: 20 Aug 2016
Posts: 43
GMAT 1: 570 Q46 V23
GMAT 2: 610 Q49 V25
GMAT 3: 620 Q45 V31
WE: Information Technology (Other)
Reviews Badge
Re: M15-16  [#permalink]

Show Tags

New post 24 Sep 2016, 03:47
Isn't it should be A+B-2(both) as both part is common to both A and B?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58335
Re: M15-16  [#permalink]

Show Tags

New post 25 Sep 2016, 23:37
Intern
Intern
avatar
Joined: 06 Sep 2016
Posts: 2
GMAT 1: 660 Q49 V33
Reviews Badge
Re: M15-16  [#permalink]

Show Tags

New post 06 Dec 2016, 02:43
Twenty percent of A is common with Twenty five percent of B. Rest of A =80% ,Rest of B =75%
If we consider the common part as 1 part of A and 1 part of B, 4 parts of A and 3 parts of B are left. therefore the total number of parts is 8 and the difference between only A and only B is 1 part which is equal to 200/8 =25
Senior Manager
Senior Manager
User avatar
S
Joined: 08 Jun 2015
Posts: 420
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
GPA: 3.33
Reviews Badge
Re: M15-16  [#permalink]

Show Tags

New post 18 Jan 2017, 06:13
2
The ratio of A to B is 5 to 4.
We are given that each student chooses at least one book. The intersection of A & B is 'x' (assuming 5X choose A and 4X choose B).
There are a total of 200 students. The number of people reading just A is 4x. The number of people reading just B is 3X. X read both A & B.

8X = 200 --> X=25. 4X-3X=X=25.
_________________
" The few , the fearless "
Intern
Intern
avatar
B
Joined: 29 Aug 2012
Posts: 2
Reviews Badge
Re: M15-16  [#permalink]

Show Tags

New post 02 May 2017, 06:43
1
very simple 8-) ! m=ones who just read A , n=ones who just read B
0.2(m+x)=x ... m=4x
0.25(n+x)=x ... n=3x
200=m+x+n=8x ... x=25
m-n=x=25
Intern
Intern
avatar
B
Joined: 14 May 2015
Posts: 47
Re: M15-16  [#permalink]

Show Tags

New post 02 May 2017, 16:14
20% who read A also reads B.....read both(A+B)=0.20A
25% who read B also reads A.....read both(A+B)=0.25B

0.20A=0.25B
B=4/5 A

read only A= read A - read both(A+B)=A-0.2A=0.8A
read only B= read B - read both(A+B)=B-0.25B=0.75B=0.75*4/5A=0.6A [B=4/5 A]

Total= read only A + read only B + read both(A+B)
200 =0.8A+0.6A+0.2A
A= 125

read only A =0.8A=0.8*125=100
read only B=0.6A=0.6*125=75

read only A-read only B=100-75=25

Answer: B
Intern
Intern
avatar
B
Joined: 09 Dec 2013
Posts: 27
M15-16  [#permalink]

Show Tags

New post 07 Apr 2018, 13:35
Bunuel wrote:
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



My technique may not be the most accurate but this was logical to me in understanding while I was going through the complex solutions above
20% of A is 25% of B.
Think this way, out of the 200 students there are those who read A and those who read B and those who read both,
Lets name them Group X who read book A and Group Y who read book B. Since there are only 2 books we are talking about.
In both the groups there are students who also like to read the other groups book apart from their own group.
WHEN I SAY A & B I AM REFERRING TO THE BOOKS A & B
Group X
80% only A,20% A+B
Group Y
75% only B, 25% A+B
The number that is highlighted should be same for both groups.
Lets take :

X=100
80% of X is 80 ; 20% is 20 which is also 25% of Y so,
25% of Y is 20 ; 75% is 60 which makes 80
So total is 180 but we want 200

X=120
80% of X is 96 ; 20% is 24 which makes Y=80 because total should be 200
25% of Y is 20 ; This does not match because look at the highlighted part above, it has to be the same number of students

X=125
80% of X is 100 ; 20% is 25 ( now ask 25 is 25% of what?) 100 right
75% of Y is 75 ; 25% is 25 (its a match)

Therefore 100 who read only A -75 who read only B =25
P.S. This is just meant for understanding since it takes a lot of time while doing it in actual.
Intern
Intern
avatar
B
Joined: 31 May 2017
Posts: 11
GMAT ToolKit User Reviews Badge CAT Tests
Re: M15-16  [#permalink]

Show Tags

New post 25 Feb 2019, 05:42
Hi Bunuel, Can you show how this can be solved using the 2*2 matrix?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58335
Re: M15-16  [#permalink]

Show Tags

New post 25 Feb 2019, 05:57
Manager
Manager
avatar
B
Joined: 09 Nov 2018
Posts: 69
CAT Tests
Re M15-16  [#permalink]

Show Tags

New post 04 Aug 2019, 12:22
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Not able to understand the equations.
SVP
SVP
User avatar
V
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1687
Location: India
Concentration: International Business, Operations
Schools: INSEAD Jan '19
GPA: 3.01
WE: Engineering (Real Estate)
Reviews Badge CAT Tests
Re M15-16  [#permalink]

Show Tags

New post 20 Sep 2019, 05:32
I think this is a high-quality question and I agree with explanation.
_________________
"Do not watch clock; Do what it does. KEEP GOING."
GMAT Club Bot
Re M15-16   [#permalink] 20 Sep 2019, 05:32
Display posts from previous: Sort by

M15-16

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

Moderators: chetan2u, Bunuel






Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne