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

 It is currently 13 Dec 2018, 17:01

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

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

Events & Promotions

Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

December 14, 2018

December 14, 2018

09:00 AM PST

10:00 AM PST

10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.
• The winning strategy for 700+ on the GMAT

December 13, 2018

December 13, 2018

08:00 AM PST

09:00 AM PST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

M15-16

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51185

Show Tags

15 Sep 2014, 23:55
14
00:00

Difficulty:

75% (hard)

Question Stats:

64% (02:28) correct 36% (02:57) wrong based on 123 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
Joined: 02 Sep 2009
Posts: 51185

Show Tags

15 Sep 2014, 23:55
4
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 $$100-75=25$$.

_________________
Intern
Joined: 24 Jun 2015
Posts: 46

Show Tags

09 Jul 2015, 07:40
Bunuel wrote:
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 $$0.2A=0.25B$$, or: $$A=1.25B$$.

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 $$100-75=25$$.

Hi Bunuel,

I got this answer right but it took me almost 5 minutes.... I dont know If I am too slow but I think I did it in a normal pace.... How can this problem be solved faster? Usually I am good with overlapping sets using double matrix, but this problem has different restrictions that makes it a harder... Could you help me?

Thanks a lot.

Regards

Luis Navarro
Looking for 700
Senior Manager
Joined: 15 Sep 2011
Posts: 326
Location: United States
WE: Corporate Finance (Manufacturing)

Show Tags

19 Jul 2015, 08:03
1
The third statement concludes with "or: A=1.25B". "Or" in math isn't quite the same as "or" in english. Indeed, "Or" represents an alternative to the expression, but it's not logical with the noun it modifies. That is, "or: A=1.25B" isn't the number of those who read A and B anymore, but the ratio of A and B. I know what you meant, but the logic could be enhanced. Perhaps you could add " .20A = .25B, and therefore, A=1.25B." Otherwise the meaning isn't as clear as it could be.

Thanks,
Math Expert
Joined: 02 Sep 2009
Posts: 51185

Show Tags

20 Jul 2015, 04:04
mejia401 wrote:
The third statement concludes with "or: A=1.25B". "Or" in math isn't quite the same as "or" in english. Indeed, "Or" represents an alternative to the expression, but it's not logical with the noun it modifies. That is, "or: A=1.25B" isn't the number of those who read A and B anymore, but the ratio of A and B. I know what you meant, but the logic could be enhanced. Perhaps you could add " .20A = .25B, and therefore, A=1.25B." Otherwise the meaning isn't as clear as it could be.

Thanks,

Edited as suggested. Thank you!
_________________
Intern
Joined: 19 Sep 2014
Posts: 24
GPA: 3.96

Show Tags

19 Aug 2015, 07:07
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
Joined: 02 Sep 2009
Posts: 51185

Show Tags

19 Aug 2015, 09:05
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
Joined: 26 Mar 2013
Posts: 1911

Show Tags

20 Aug 2015, 06:24
7
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
>> !!!

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

Intern
Joined: 10 May 2015
Posts: 28

Show Tags

06 Sep 2015, 19:55
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. I actually thought the question implied that the no of people reading both A and B is 0.2 A + 0.25 B. Can it not be the case upon reading the question? Please throw some light on this.
Board of Directors
Joined: 17 Jul 2014
Posts: 2620
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)

Show Tags

31 Oct 2015, 20:27
0.2A = 0.25B, this can be inferred from the question.
this can be rewritten as 0.8A = 1B, or total who reads A = 1.25B and those who read only A = B
now we have B-0.75B = 0.25B
the only left to find out is B.
we have 0.25B both, 0.75B both, and B - those who read only A. We have 2B=200 or B=100. The difference thus must be 100-75 = 25.
Intern
Joined: 20 Aug 2016
Posts: 49
GMAT 1: 570 Q46 V23
GMAT 2: 610 Q49 V25
GMAT 3: 620 Q45 V31
WE: Information Technology (Other)

Show Tags

24 Sep 2016, 02:47
Isn't it should be A+B-2(both) as both part is common to both A and B?
Math Expert
Joined: 02 Sep 2009
Posts: 51185

Show Tags

25 Sep 2016, 22:37
Saps wrote:
Isn't it should be A+B-2(both) as both part is common to both A and B?

What should be A + B - 2(both) ? If it's the number of students who read only book A or only book B, then yes.
_________________
Intern
Joined: 06 Sep 2016
Posts: 2
GMAT 1: 660 Q49 V33

Show Tags

06 Dec 2016, 01:43
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
Joined: 08 Jun 2015
Posts: 436
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
GPA: 3.33

Show Tags

18 Jan 2017, 05:13
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
Status: Single
Affiliations: None
Joined: 25 Dec 2016
Posts: 10
Sricharan: A

Show Tags

20 Jan 2017, 09:46
I think this is a high-quality question and the explanation is clear enough.
Intern
Joined: 29 Aug 2012
Posts: 2

Show Tags

02 May 2017, 05:43
1
very simple ! 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
Manager
Joined: 14 May 2015
Posts: 51

Show Tags

02 May 2017, 15:14

0.20A=0.25B
B=4/5 A

200 =0.8A+0.6A+0.2A
A= 125

Intern
Joined: 09 Dec 2013
Posts: 27

Show Tags

07 Apr 2018, 12:35
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.
M15-16 &nbs [#permalink] 07 Apr 2018, 12:35
Display posts from previous: Sort by

M15-16

Moderators: chetan2u, Bunuel

 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®.