At a certain university, 120 students were asked to take a surprise qu

Question

At a certain university, 120 students were asked to take a surprise quiz to check their awareness of history and civil rights. The score distribution of the students is tabulated below:

If 70 students scored greater than 30% in both tests, what was the number of students who scored less than 30% in both the history and the civil rights sections of the quiz?

A. 6
B. 14
C. 16
D. 50
E. Insufficient data to determine a unique answer

Show Spoiler

Attachment:

1.png [ 10.3 KiB | Viewed 2642 times ]

Show Answer

Official Answer

A

chetan2u · Answer

Now we have three different categories...
1)  m>80 %
2)  30\leq{m}\leq{80} 
3)  m<30 %

The question should have read AT LEAST 30 % in 'If 70 students scored  greater than  at least 30% in both tests'.
If it is at least 30% we can draw overlapping sets as shown..
1) History - There are 70+30 or 100 students scoring at least 30%, so 100-70 or 30 score at least 30% in only history.
2) Civil rights - There are 44+40 or 84 students scoring at least 30%, so 84-70 or 14 score at least 30% in only civi rights.
Total students scoring 30% or more in at least one subject will be 30+70+14=114.

Thus, students scoring <30% in both subjects will be 120-114=6.

A

In present format, it will be E, as we do not know how many get exact 30%.

yashikaaggarwal · Answer

Sir I partially able to understand question itself. Can you brief a little?
Moreover is this the official OA, or there are some changes meant to be done in Question?

Posted from my mobile device

ScottTargetTestPrep · Answer

Solution:

According to the table, 70 + 30 = 100 students scored higher than 30% in the History section (which includes the students who also scored higher than 30% in Civil Rights as well). Since 70 students scored greater than 30% in both tests, there are 100 - 70 = 30 students who scored higher than 30% in History but scored less than 30% in Civil Rights.

Similarly, there are 44 + 40 = 84 students who scored higher than 30% for the Civil Rights section (which includes the ones who scored over 30% in the History section as well). Again since 70 students scored higher than 30% in both tests, there are 84 - 70 = 14 students who scored higher than 30% in only the Civil Rights section.

Notice that we have the following formula:

Total # of students = #higher than 30% in only History + #higher than 30% in only Civil Rights + #higher than 30% in both sections + #did not score higher than 30% in either section

Since the total number of students is 120, only History is 30, only Civil Rights is 14 and both is 70, we have:

120 = 30 + 14 + 70 + #neither

#neither = 120 - 114 = 6

Notice that “students who did not score higher than 30% in either section” is precisely the number of students who scored less than 30% in both sections. Thus, the answer is 6.

Answer: A

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

At a certain university, 120 students were asked to take a surprise qu

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

At a certain university, 120 students were asked to take a surprise qu

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards