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A group of 7 students have a combined score of 280 on an aptitude test. If 4 of the students have a score of 60, 50, 30 and 20 respectively, what is the median score of the students on the aptitude test?
(1) Out of the remaining three students, two students have a combined score of 80 on the aptitude test.
(2) Out of the remaining three students, one student has a score of 40 on the aptitude test.
Are You Up For the Challenge: 700 Level Questions
(1) Out of the remaining three students, two students have a combined score of 80 on the aptitude test.
(2) Out of the remaining three students, one student has a score of 40 on the aptitude test.
Are You Up For the Challenge: 700 Level Questions
04 Feb 2022, 05:50
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Bunuel
Given values \(20 ,30,50,60 \)
Total of given values \(= 160 \) hence remaining \(3\) students \(= 280-160= 120\)
Median is the fourth value when arranged in ascending order.
(1) Out of the remaining three students, two students have a combined score of \(80\) on the aptitude test.
So the remaining third student must have had a score of \(40\), lets incoporate this value and see
\( \{20 \hspace{1mm}, 30 \hspace{1mm}, 40 \hspace{1mm}, 50 \hspace{1mm}, 60 \}\)
We see the fourth value is \(40 \), now no matter however we try to distribute the remaining \(2\) students score that total \(80\), the fourth value always remains \(40,\) hence the median always remains \(40.\)
Lets test with a couple of examples.
Let the \(3\) remaining scores be \( (40,10,70)\) then
\(\{10\hspace{1mm}, 20\hspace{1mm}, 30\hspace{1mm}, 40 \hspace{1mm}, 50 \hspace{1mm}, 60 \hspace{1mm},70 \}= \) Median \(40\)
If Scores are \((40,20, 60 )\)
\( \{20 \hspace{1mm}, 20\hspace{1mm}, 30 \hspace{1mm}, 40\hspace{1mm}, 50 \hspace{1mm}, 60\hspace{1mm}, 60 \} =\) Median \(40\)
....
If Scores are \((40, 40, 40)\)
\( \{20\hspace{1mm}, 30\hspace{1mm}, 40 \hspace{1mm}, 40\hspace{1mm}, 40\hspace{1mm}, 50\hspace{1mm}, 60 \} =\)Median \(40\)
Median always remains \(40\)
SUFF.
(2) Out of the remaining three students, one student has a score of \(40\) on the aptitude test.
This says the same thing as statement 1
SUFF.
Ans D.
RenB
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28 Oct 2023, 04:40
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Official Solution-
The 40-x and 40+x idea really helped!
Steps 1 & 2: Understand Question and Draw Inferences
. Let the scores of the students be {a, b, c, d, e, f, g}
. a + b + c + d +e + f +g =280
o a=60
o b=50
o c=30
o d=20
o This means, a + b + c + d = 160
o So, e + f+ g = 280-160 =120
To Find: Median score of the students
o Need the scores of the other 3 students
Step 3: Analyze Statement 1 independently
1. Out of the remaining three students, two students have a combined score of 80 on the aptitude test.
. Say, e + f = 80
o So, g = 120 - 80 = 40
. As e +f = 80, we can write e = 40 + x and f = 40-x, where 0 ≤x ≤40
o For all the cases, 40 ≤e ≤80 and 0≤f ≤ 40.
. Thus, we can rearrange the scores in scending order as {20, 30, f, 40, e, 50, 60}.
o For all the values of e and f, 40 will be the median score of the students.
Sufficient to answer.
Step 4: Analyze Statement 2 independently
2.Out of the remaining three students, one of the students has a score of 40 on the aptitude test.
. Say, g = 40
o So,e + f = 120-40 = 80
. As e + f = 80, we can write e = 40 + x and f = 40-x, where 0 ≤x≤ 40
o For all the cases, 40 ≤e ≤80 and 0 ≤f ≤ 40.
. Thus, we can rearrange the scores in ascending order as {20, 30, f, 40, e, 50, 60].
o For all the values of e and f, 40 will be the median score of the students.
Sufficient to answer.
