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

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Manager
Joined: 30 May 2013
Posts: 168
Location: India
Concentration: Entrepreneurship, General Management
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Of 200 surveyed students, 20% of those who read book A  [#permalink]

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26 Sep 2013, 22:14
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Difficulty:

65% (hard)

Question Stats:

67% (02:42) correct 33% (02:02) wrong based on 231 sessions

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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: 47967
Re: Of 200 surveyed students, 20% of those who read book A  [#permalink]

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27 Sep 2013, 00:47
3
4
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.

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GMAT Date: 11-06-2013
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Re: Of 200 surveyed students, 20% of those who read book A  [#permalink]

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26 Sep 2013, 23:35
7
2
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)
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Collection of some good questions on Number System

##### General Discussion
Intern
Joined: 06 Feb 2013
Posts: 21
Re: Of 200 surveyed students, 20% of those who read book A  [#permalink]

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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
Manager
Joined: 29 Apr 2013
Posts: 97
Location: India
Concentration: General Management, Strategy
GMAT Date: 11-06-2013
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Re: Of 200 surveyed students, 20% of those who read book A  [#permalink]

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29 Sep 2013, 07:05
3
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.

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Collection of some good questions on Number System

Intern
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Posts: 21
Re: Of 200 surveyed students, 20% of those who read book A  [#permalink]

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29 Sep 2013, 07:07
Thanks! it's clear now
Math Expert
Joined: 02 Sep 2009
Posts: 47967
Re: Of 200 surveyed students, 20% of those who read book A  [#permalink]

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

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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

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Quant.xlsx [9.35 KiB]

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

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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.

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.
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Joined: 29 May 2017
Posts: 8
Re: Of 200 surveyed students, 20% of those who read book A  [#permalink]

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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
Intern
Joined: 26 Feb 2017
Posts: 27
Re: Of 200 surveyed students, 20% of those who read book A  [#permalink]

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12 Feb 2018, 14:44
rrsnathan 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

~A- who dont read book A
~B= who dont read book B

A ~A Total

B 0.2x 0.8x-0.2x=0.6x 0.2x*4=0.8x

~B x-0.2x=0.8x 0 0.8x

Total x 0.6x 200

1.6x=200
so 0.2x=200/8=25
Re: Of 200 surveyed students, 20% of those who read book A &nbs [#permalink] 12 Feb 2018, 14:44
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