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Fifteen college seniors, none of whom took any math classes

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Bunuel
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Fifteen college seniors, none of whom took any math classes [#permalink] New post   11 Oct 2017, 22:12
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Fifteen college seniors, none of whom took any math classes in college, were selected for a clinical trial. An online GRE Math Course was made available to them, and these students were allowed to study for however many hours they wanted. Then, each took the GRE for their first time. The graph below records how many hours each student studied, using the online material, and that student’s GRE Quant score. The best-fit line model shows the best prediction, given such a student’s hours of study, of what her GRE Q score might be.

Image
1) Among the students in this trial who studied less than 25 hours, what is the highest GRE Quant score achieved?

(A) 146

(B) 149

(C) 154

(D) 157

(E) 165

Show: :: OA
C




2) For the students in this trial with the three highest scores, approximately what is the average number of hours they spend studying?

(A) 29

(B) 32

(C) 35

(D) 39

(E) 43

Show: :: OA
D




3) Among the students in this trial who studied for 20 hours or more, what fraction of them performed worse than expected, according to the best-fit line model? Express your answer as a fraction.



Show: :: OA
3/10



Show: ::
Attachment:
Hours-Studied-GRE-Q-score.jpg
Hours-Studied-GRE-Q-score.jpg [ 24.96 KiB | Viewed 8793 times ]


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Rajneesh Garg
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Re: Fifteen college seniors, none of whom took any math classes [#permalink] New post   13 Oct 2017, 03:58
Answer

1 - C
2 - D
3 - 3/10
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Bunuel
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Re: Fifteen college seniors, none of whom took any math classes [#permalink] New post   13 Oct 2017, 05:35
Rajneesh Garg wrote:
Answer

1 - C
2 - D
3 - 3/10


The OA's are already given. Please post solutions too. Thank you.
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IlCreatore
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Re: Fifteen college seniors, none of whom took any math classes [#permalink] New post   15 Oct 2017, 01:05
Q1: Among the points representing those students who study less than 25 hours, the highest is the second from the right whose score can be read on the y axis as 154 (C)

Q2: The three students with the highest GRE scores have studied roughly 28, 43 and 45 hours. Thus the mean is 28+43+45/3 = 38.6 which can be rounded to 39. (D)

Q3: To compute the ratio of those scoring less than expected, we can compute the denominator as the sum of the points after 20 hours of study and at the numerator those below the fit line. This leads to a ratio of 3/10
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Re: Fifteen college seniors, none of whom took any math classes [#permalink] New post   02 Sep 2021, 04:39
IlCreatore wrote:
Q1: Among the points representing those students who study less than 25 hours, the highest is the second from the right whose score can be read on the y axis as 154 (C)

Q2: The three students with the highest GRE scores have studied roughly 28, 43 and 45 hours. Thus the mean is 28+43+45/3 = 38.6 which can be rounded to 39. (D)

Q3: To compute the ratio of those scoring less than expected, we can compute the denominator as the sum of the points after 20 hours of study and at the numerator those below the fit line. This leads to a ratio of 3/10


Why did we have to consider the student who's marks came to what was expected, as his score was almost on the best fit line. Shouldn't the answer be \(\frac{2}{10}\) instead?
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Fifteen college seniors, none of whom took any math classes [#permalink] New post   02 Sep 2021, 05:25
Expert Reply
OE

1)

Quote:
We ignore all the points that are at 25 hours studied and more: that’s the point on the vertical 25-hour line and all the points to the right—all of those are ignored. The only ones we care about are the ones less than 25-hours. Of these, the highest is the one furthest to the right, at a height of 154. This person studied less than 25 hours and got a GRE Q score of 154.

Answer = (C)


2)
Quote:
The three highest scores, the three highest dots on the graph, are

a) person with Q = 165 who studied 45 hours
b) person with Q = 170 who studied 29 hours
c) person with Q = 169 who studied 44 hours
We don’t need a calculator. Subtract 30 from each hour amount for simplicity. Then we have hours of {15, –1, 14}. The sum of those is 28, and 28/3 = 9.33. Add back 30 now: that’s an average of 39.33. The closest answer choice is 39.

Answer = (D)



3)

Quote:
we have to look in the right part of the graph. We have to look at all the dots to the right of the 20-hour line: these are the only dots that count. Dots above the line are students who exceeded the prediction. Dots below the line are students who fell short of the prediction.


Attachment:
screenshot.89.jpg
screenshot.89.jpg [ 96.54 KiB | Viewed 4099 times ]


The gray dots on the left are out, because those are times less than 20 hours. Of the remaining dots, the 7 green dots are above the line and 3 red dots are below the line. Ten dots altogether are above the 20-hour line, and 3/10 performed worse than expected.

answer is 3/10
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