At Princeton Community High School there are 440 students, all of whom

Question

At Princeton Community High School there are 440 students, all of whom were assigned to read Atlas Shrugged and The Grapes of Wrath over the summer. Of the students in the junior class, 31 read Atlas Shrugged, 31 read both books and 1 read neither. If the junior class makes up one quarter of the school then how many students in the junior class read The Grapes of Wrath?

A. 109
B. 57
C. 47
D. 5
E. 1

A. 109
B. 57
C. 47
D. 5
E. 1

vitaliyGMAT · Answer

I read this “31 read Atlas Shrugged” as “Altas Shrugged only”

440/4 = 31 (Atlas only) + 31 (Both) + 1 (neither) + X(Grapes)

X = 110 – 63 = 47

chetan2u · Answer

Hi,
You cannot ADD 'only' if it is not given.
So 31 read Atlas and 31 read both, so there is no one who read ONLY Atlas shrugged...

1 did not read either, so he is the only one who did not read ' The grapes...'
Total students=1/4 * 440=110..
Number of students who read 'the grapes...'=110-1=109..
A

vitaliyGMAT · Answer

Yes you are right. I seems I’ve interpreted the question on my own will. If it’s not stated directly than our set of “Read Only Atlas” is empty and answer should be A.
Thanks

AR15J · Answer

number of the students in junior class=440/4=110

In junior class,

The number of the students who read Atlas Shrugged n(A) =31

let's say the number of the students who read The Grapes of wrath n(B)=x

the number of the students who read both n(A and B)=31

the number of the students who did not read any=1

Number of the students who read aleast one book n(A or B)=110-1=109

n(A or B)=n(A)+ n(B)-n(A and B)
109=31+x-31

x=109

Correct answer is A

+1 Kudos if you like the post

ScottTargetTestPrep · Answer

We are given that 440 students were assigned to read Atlas Shrugged and The Grapes of Wrath. We are also given that of the students in the junior class, 31 read Atlas Shrugged, 31 read both books, and 1 read neither book, and that juniors make up 1/4 of the students in the school.

We can use the following formula:

Total juniors = (# juniors who read Atlas Shrugged) + (# juniors who read The Grapes of Wrath) - (# who read both) + (# who read neither)

1/4 x (440) = 31 + G - 31 + 1

110 = G + 1

109 = G

Thus, 109 students read The Grapes of Wrath.

Answer: A

FlyingCycle · Answer

Here's how I did it. using matrix method solves this within 15 secs or lesser. The more you get used to it the faster you become. Some of the questions you can also do mentally (not recommended

)

MathRevolution · Answer

Total: 440

Junior class makes up one quarter:  \frac{1}{ 4}  * 440 = 110

Let us assign variables: Atlas shrugged(A) and Grapes of Wrath(G)

31 read Atlas Shrugged, 31 read both books and 1 read neither. Therefore,

110 - 1 = 31 + G - 31

=> G = 109

Answer A

At Princeton Community High School there are 440 students, all of whom

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