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# Half of the workers in Palabras bookstore have read the latest book by

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Math Expert
Joined: 02 Sep 2009
Posts: 59722
Half of the workers in Palabras bookstore have read the latest book by  [#permalink]

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06 Sep 2016, 04:52
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Question Stats:

67% (02:53) correct 33% (03:25) wrong based on 75 sessions

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Half of the workers in Palabras bookstore have read the latest book by J. Saramago, and 5/8 of the workers have read the latest book by H. Kureishi. The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book. If there are 40 workers in the Palabras bookstore, how many of them have read both books?

A. 13
B. 12
C. 9
D. 8
E. 7

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Senior Manager
Joined: 23 Apr 2015
Posts: 279
Location: United States
WE: Engineering (Consulting)
Re: Half of the workers in Palabras bookstore have read the latest book by  [#permalink]

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06 Sep 2016, 08:29
Bunuel wrote:
Half of the workers in Palabras bookstore have read the latest book by J. Saramago, and 5/8 of the workers have read the latest book by H. Kureishi. The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book. If there are 40 workers in the Palabras bookstore, how many of them have read both books?

A. 13
B. 12
C. 9
D. 8
E. 7

Let Jo be people who read only book by JS, Ho be people who read book only by HK and JH be people who read both.Question is to find HK
Given
$$Jo + HK = \frac{1}{2} * 40 = 20$$
$$Ho + HK = \frac{5}{8}*40 = 25$$
Read neither be N and it's
$$N = 20 - HK - 1$$
and the total set should be equal to 40
$$40 = 20 + 25 + N - HK$$

This will give HK = 12.
Intern
Joined: 17 Jun 2016
Posts: 42
Re: Half of the workers in Palabras bookstore have read the latest book by  [#permalink]

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06 Sep 2016, 11:46
Not getting this one
Senior Manager
Joined: 23 Apr 2015
Posts: 279
Location: United States
WE: Engineering (Consulting)
Half of the workers in Palabras bookstore have read the latest book by  [#permalink]

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06 Sep 2016, 12:05
shonakshi wrote:
Not getting this one

Excuse me for my messy abstraction. But this problem is just overlapping set with 2 groups.
Think of venn diagram with 2 circles/groups and an overlapping region.
The region outside the circles is the people who read none.

Let A be people who read only one author and B be other group who read other author alone and x be who reads both AnB.
U be the universal group of 40.
Question is to find x.

$$A +x = \frac{1}{2} * U = 20$$
$$B + x= \frac{5}{8} * U = 25$$
So A + B + 2x = 45 is one equation.
Next about the people who read none, they are outside the circle.
$$U - (A + B + x) = 40 - (A + B+ x) = A - 1$$
$$=> 40 - (45- x) = A -1 => A - x = -4,$$
solve this with the first equation to find x.
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Joined: 21 Jul 2016
Posts: 1
Re: Half of the workers in Palabras bookstore have read the latest book by  [#permalink]

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07 Sep 2016, 07:07
shonakshi wrote:
Not getting this one

See this problem as set theory, and it will become easy to solve.
Attachments

solution.jpg [ 163.05 KiB | Viewed 1398 times ]

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9876
Location: Pune, India
Re: Half of the workers in Palabras bookstore have read the latest book by  [#permalink]

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07 Sep 2016, 08:27
3
Bunuel wrote:
Half of the workers in Palabras bookstore have read the latest book by J. Saramago, and 5/8 of the workers have read the latest book by H. Kureishi. The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book. If there are 40 workers in the Palabras bookstore, how many of them have read both books?

A. 13
B. 12
C. 9
D. 8
E. 7

There are total 40 workers.

"Half of the workers in Palabras bookstore have read the latest book by J. Saramago,"

"5/8 of the workers have read the latest book by H. Kureishi."
So (5/8) * 40 = 25 have read Kureishi

"The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book"
If B workers have read both books, 20 - B have read Saramago but not Kureishi.
So, (20 - B - 1) have read neither.

Total = n(A) + n(B) - Both + Neither
40 = 20 + 25 - B + (20 - B - 1)
B = 12

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Karishma
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Intern
Joined: 02 Sep 2016
Posts: 2
Re: Half of the workers in Palabras bookstore have read the latest book by  [#permalink]

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07 Sep 2016, 09:26
I think it is easier to tackle this kind of question with a grid.

Intern
Joined: 21 Apr 2019
Posts: 33
Re: Half of the workers in Palabras bookstore have read the latest book by  [#permalink]

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23 Nov 2019, 09:08
A = 1/2 (40) B= 5/8(40) so..those who have not read becomes
AUB = ( 1/2 (40) + 3/8 (40)) -1
AnB = 20+25 - [(20+15)-1]
=11

Can anybody tell me what i am doing wrong here ?
Intern
Joined: 19 Oct 2019
Posts: 1
Re: Half of the workers in Palabras bookstore have read the latest book by  [#permalink]

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25 Nov 2019, 05:01
Let ppl who like both = A, J. Saramago as B and H. Kureishi as C.

40- ((20-A)-1)= 20+ 25- A
=> 21+A= 45-A
=> 2A= 24
therefore, A= 12
Re: Half of the workers in Palabras bookstore have read the latest book by   [#permalink] 25 Nov 2019, 05:01
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