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

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Bunuel
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At a certain university, 120 students were asked to take a surprise qu [#permalink] At a certain university, 120 students were asked to take a surprise qu   05 Jun 2020, 08:11
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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


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At a certain university, 120 students were asked to take a surprise qu [#permalink] At a certain university, 120 students were asked to take a surprise qu   05 Jun 2020, 21:05
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Bunuel
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


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The attachment 1.png is no longer available


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%.
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Re: At a certain university, 120 students were asked to take a surprise qu [#permalink] At a certain university, 120 students were asked to take a surprise qu   08 Jun 2020, 11:07
chetan2u
Bunuel
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


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%.

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?

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Re: At a certain university, 120 students were asked to take a surprise qu [#permalink] At a certain university, 120 students were asked to take a surprise qu   10 Jun 2020, 13:48
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Bunuel
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


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Attachment:
1.png

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
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Re: At a certain university, 120 students were asked to take a surprise qu [#permalink] At a certain university, 120 students were asked to take a surprise qu   18 May 2024, 09:06
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Re: At a certain university, 120 students were asked to take a surprise qu [#permalink]
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