In a classroom, 40% of the boys had read a particular book. What was

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In a classroom, 40% of the boys had read a particular book. What was the probability that a student who was randomly selected from the classroom was a girl who had read the book?

(1) Three-eighths of all students in the classroom had read the book
(2) 20 girls in the classroom had not read the book

GMATinsight · Answer

Total Students = B+G
Boys reader = 0.4B
Girls reader = ?

Question : Girl reader / Total Students = ?

Statement 1 : Three-eighths of all students in the classroom had read the book

Readers = (3/8)*(B+G) = o.4B + xG
But we can't find even the ratio of boys and girls hence

NOT SUFFICIENT

Statement 2 : 20 girls in the classroom had not read the book 
Girls Readers = G - 20

But this is what fraction of total students that is unknown hence

NOT SUFFICIENT

Combining

(3/8)*(B+G) = 0.4B + (G-20)

Still we can't find what fraction of all the students are girl readers hence

NOT SUFFICIENT

Answer: Option E

freedom128 · Answer

Boys: 40% read, 60% no
Q. Probability of a girl who reads among all class members?

Let's start with combining both (1) + (2) 
** 3/8 (Boys + Girls) read --> 5/8 (Boys + Girls) no
** 20 girls in the classroom had not read the book

CASE 1 
Boy/read = 40, Boy/no = 60, 
Girl/read=8, Girl/no = 20
Total class = 128 --> 3/8 (128) = 48 had read a book = 40 + 8 (ok!)
Probability (girl/read) = 8/128 = 1/16

CASE 2
Boy/read = 20, Boy/no = 30, 
Girl/read= 10, Girl/no = 20
Total class = 80 --> 3/8 (80) = 30 had read a book = 20 + 10 (ok!)
Probability (girl/read) = 10/80 = 1/8

Cases 1 and 2 don't yield the same probability. ---> NOT SUFFICIENT

Since (1)+(2) is NOT SUFFICIENT, eliminate (A),(B),(C),(D)

FINAL ANSWER IS (E)

exc4libur · Answer

…boys…girls
y…0.4b……
n…0.6b……

(1) insufic 
…boys…girls
y…0.4b……3/8(b+g)
n…0.6b……5/8(b+g)

(2) insufic 
…boys…girls
y…0.4b……
n…0.6b…20

(1/2) insufic
…boys…girls
y…0.4b………3/8(b+g)
n…0.6b…20…5/8(b+g)

0.6b+20=5/8(b+g)
4.8b+160=5b+5g
160-5g=b/5
b=800-25g
b>0, 20<g≤32=800/25
g=25, b=800-25*25=175, gy=5/25+175=5/200
g=30, b=800-25*30=50, gy=10/30+50=5/80

Ans (E)

Archit3110 · Answer

#1
Three-eighths of all students in the classroom had read the book
3/8 * total students have read book
but total students not know ; insufficient
#2
 20 girls in the classroom had not read the book
total students not know and no clarity on total students ; insuficient
from 1 &2 ; we cannot determine total students
IMO E: sufficient

In a classroom, 40% of the boys had read a particular book. What was the probability that a student who was randomly selected from the classroom was a girl who had read the book?

(1) Three-eighths of all students in the classroom had read the book
(2) 20 girls in the classroom had not read the book

unraveled · Answer

In a classroom, 40% of the boys had read a particular book. What was the probability that a student who was randomly selected from the classroom was a girl who had read the book?

(1) Three-eighths of all students in the classroom had read the book
Total number of students is not given plus number of boys and girls is also not given.

INSUFFICIENT.

(2) 20 girls in the classroom had not read the book
Total number of students is not given plus number of boys and girls is also not given.

INSUFFICIENT.

Together 1 and 2, its still the same information thus INSUFFICIENT. Let's check, however.
Refer snapshot.

Attachment:

Boys girls Book read.png [ 175.8 KiB | Viewed 5188 times ]

Answer E.

Jawad001 · Answer

In a classroom, 40% of the boys had read a particular book. What was the probability that a student who was randomly selected from the classroom was a girl who had read the book?

(1) Three-eighths of all students in the classroom had read the book
(2) 20 girls in the classroom had not read the book

Solution:
Let, total number of students = 100 
To find out:
The number of girl students + Read books = x

………………………….Boys…………………….......Girls…………………..Total
Read Books……….0.40b…………………………x=?....................
Not- Read books.***………………………....***……………………….
Total…………………..b..…………………………...g………………………100

From statement (1), 
Three-eighths of all students in the classroom had read the book =3/8*(100)
Putting the value in the following diagram:
………………………….Boys……………………Girls…………………………Total
Read Books……….0.40b……………………x=?.............................3/8(100) = 37.50
Not- Read books.***………………………..***…………………………..
Total……………………b………………………..100-b………………………100
Not Sufficient.

From statement (2), 
20 girls in the classroom had not read the book
………………………….Boys…………………….......Girls………………………….Total
Read Books……….0.40b…………………………x=?........................
Not- Read books.***…………………………..20…………………………...
Total…………………..b..………………………….100-b………………………100
Not Sufficient.

Combining both statements,
…………………………...Boys……………………Girls…………………………….....Total
Read Books……….0.40b…………………………x=?........................=37.50
Not- Read books.43.50…………………………..20………………………….= 63.50
Total…………………..b..………………………….100-b……………………….....=100

The value of x can be found out. Hence Sufficient.

Answer: C

madgmat2019 · Answer

(1) Three-eighths of all students in the classroom had read the book.......INSUFFICIENT
(2) 20 girls in the classroom had not read the book................INSUFFICIENT

let total books be x
 NoBooks Books Total
boys 0.4a a
girls 20 b
Total 3x/8 5x/8

combining both is also insufficient
OA:E

bumpbot · Answer

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In a classroom, 40% of the boys had read a particular book. What was

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