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# 10 students took a chemistry exam that was graded on a scale

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Intern
Joined: 30 Jun 2010
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10 students took a chemistry exam that was graded on a scale  [#permalink]

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30 Jun 2010, 20:00
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Difficulty:

25% (medium)

Question Stats:

74% (01:55) correct 26% (01:59) wrong based on 410 sessions

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10 students took a chemistry exam that was graded on a scale of 0 to 100. Five of the students were in Dr. Adams’ class and the other five students were in Dr. Brown’s class. Is the median score for Dr. Adams’ students greater than the median score for Dr. Brown’s students?

(1) The range of scores for students in Dr. Adams’ class was 40 to 80, while the range of scores for students in Dr. Brown’s class was 50 to 90.

(2) If the students are paired in study teams such that each student from Dr. Adams’ class has a partner from Dr. Brown’s class, there is a way to pair the 10 students such that the higher scorer in each pair is one of Dr. Brown’s students.
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Joined: 29 Apr 2010
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Re: 10 students took a chemistry exam that was graded on a scale  [#permalink]

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30 Jun 2010, 22:39
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This is a Yes/No Data Sufficiency question that never requires you to identify the specific values of the medians-- just to answer a question about their relative values.

Remember that the median--as opposed to the mean--only depends on the value of the middle term (or 2 middle terms if you have an even number of elements in your list, but each class has an odd number of students here) when all the terms are listed in order. For example:

For the set {1, 1, 1, 2, 100} -- median = 1
For the set {1, 1, 1, 1, 1} -- median = 1
For the set {-1000, -100, 1, 20, 99999}-- yup, median still equals 1.

Statement 1 tells you about the RANGE of scores in class A(dams). Range only involves the endpoints of the list. The middle term could be ANY number within that range. For example:
{40, 40, 40, 40, 80} -- median = 40
{40, 50, 60, 70, 80} -- median = 60
{40, 80, 80, 80, 80} -- median = 80

Likewise, a range of 50 to 90 could give you any of the following for class B(rown):
{50, 50, 50, 50, 90} -- median = 50
{50, 51, 62, 84, 90} -- median = 62
{50, 90, 90, 90, 90} -- median = 90

In order for the statement to be sufficient to answer the question, you would have to be say whether all possible medians for all possible set As were always greater than (or always less than) the medians for all possible set Bs. Since we have a "sometimes it might be, sometimes it might not" situation, this statement is INSUFFICIENT.

Statement 2, however, tells you that it's possible to pair up each student so that each score in set A corresponds to a HIGHER score in set B.

So if you listed out the elements in set A in ascending order: { p, q, r, s, t}
then set B must contain:
{#bigger than p, #bigger than q, #bigger than r, #bigger than s, #bigger than t}

What is the median of set A? The middle term-- r. What's the median of set B? Something bigger than r. Even though I have NO IDEA what those numbers are, if I put them in order I know that the middle term of set B will have to be greater than the middle term of set A. SUFFICIENT.

Hope this helps.
_________________

JP Park | Manhattan GMAT Instructor | Los Angeles

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##### General Discussion
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Joined: 29 Jan 2011
Posts: 275
DS - MGMAT 10 students took a chemistry exam  [#permalink]

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Updated on: 20 Jun 2011, 22:27
1

10 students took a chemistry exam that was graded on a scale of 0 to 100. Five of the students were in Dr. Adams’ class and the other five students were in Dr. Brown’s class. Is the median score for Dr. Adams’ students greater than the median score for Dr. Brown’s students?

(1) The range of scores for students in Dr. Adams’ class was 40 to 80, while the range of scores for students in Dr. Brown’s class was 50 to 90.

(2) If the students are paired in study teams such that each student from Dr. Adams’ class has a partner from Dr. Brown’s class, there is a way to pair the 10 students such that the higher scorer in each pair is one of Dr. Brown’s students.

Originally posted by siddhans on 20 Jun 2011, 06:27.
Last edited by siddhans on 20 Jun 2011, 22:27, edited 1 time in total.
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20 Jun 2011, 06:40
2
siddhans wrote:

10 students took a chemistry exam that was graded on a scale of 0 to 100. Five of the students were in Dr. Adams’ class and the other five students were in Dr. Brown’s class. Is the median score for Dr. Adams’ students greater than the median score for Dr. Brown’s students?

(1) The range of scores for students in Dr. Adams’ class was 40 to 80, while the range of scores for students in Dr. Brown’s class was 50 to 90.

(2) If the students are paired in study teams such that each student from Dr. Adams’ class has a partner from Dr. Brown’s class, there is a way to pair the 10 students such that the higher scorer in each pair is one of Dr. Brown’s students.

Statement1 -
Given
Dr. Adams’ class Range is 40-80
Dr. Brown’s class Range is 50 to 90

Case 1
Scores in Dr. Adams’ class can be 40,50,75,80,80 so median is 75
Scores in Dr. Brown’s class can be 50,60,70,80,90 so median is 70

Case 2
Scores in Dr. Adams’ class can be 40,50,75,80,80 so median is 75
Scores in Dr. Brown’s class can be 50,60,80,85,90 so median is 80

Hence Insuff

Statement 2
What can be concluded that all students of Dr Brown's Class have scores higher than all the students of Dr Adam's Class. So Median of Dr Adam' Class is less than Median of Dr Brown's Class. So we get a definite answer as No. Hence suff

Ans B
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Re: 10 students took a chemistry exam that was graded on a scale  [#permalink]

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15 Nov 2016, 10:10
1
parker wrote:
This is a Yes/No Data Sufficiency question that never requires you to identify the specific values of the medians-- just to answer a question about their relative values.

Remember that the median--as opposed to the mean--only depends on the value of the middle term (or 2 middle terms if you have an even number of elements in your list, but each class has an odd number of students here) when all the terms are listed in order. For example:

For the set {1, 1, 1, 2, 100} -- median = 1
For the set {1, 1, 1, 1, 1} -- median = 1
For the set {-1000, -100, 1, 20, 99999}-- yup, median still equals 1.

Statement 1 tells you about the RANGE of scores in class A(dams). Range only involves the endpoints of the list. The middle term could be ANY number within that range. For example:
{40, 40, 40, 40, 80} -- median = 40
{40, 50, 60, 70, 80} -- median = 60
{40, 80, 80, 80, 80} -- median = 80

Likewise, a range of 50 to 90 could give you any of the following for class B(rown):
{50, 50, 50, 50, 90} -- median = 50
{50, 51, 62, 84, 90} -- median = 62
{50, 90, 90, 90, 90} -- median = 90

In order for the statement to be sufficient to answer the question, you would have to be say whether all possible medians for all possible set As were always greater than (or always less than) the medians for all possible set Bs. Since we have a "sometimes it might be, sometimes it might not" situation, this statement is INSUFFICIENT.

Statement 2, however, tells you that it's possible to pair up each student so that each score in set A corresponds to a HIGHER score in set B.

So if you listed out the elements in set A in ascending order: { p, q, r, s, t}
then set B must contain:
{#bigger than p, #bigger than q, #bigger than r, #bigger than s, #bigger than t}

What is the median of set A? The middle term-- r. What's the median of set B? Something bigger than r. Even though I have NO IDEA what those numbers are, if I put them in order I know that the middle term of set B will have to be greater than the middle term of set A. SUFFICIENT.

Hope this helps.

I remember totally freaking out when this question appeared in my Mock and I thought whoa I am so bad and I will never get it correct. but careful examination of of the question stem and playing with variables helped me get the correct answer. Now looking at your explanation boosted me further as I had moved in the exact way. YAY! Thanks these little victories means a lot in this painful journey.
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Re: 10 students took a chemistry exam that was graded on a scale  [#permalink]

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10 Sep 2017, 23:39
ace001 wrote:
10 students took a chemistry exam that was graded on a scale of 0 to 100. Five of the students were in Dr. Adams’ class and the other five students were in Dr. Brown’s class. Is the median score for Dr. Adams’ students greater than the median score for Dr. Brown’s students?

(1) The range of scores for students in Dr. Adams’ class was 40 to 80, while the range of scores for students in Dr. Brown’s class was 50 to 90.

(2) If the students are paired in study teams such that each student from Dr. Adams’ class has a partner from Dr. Brown’s class, there is a way to pair the 10 students such that the higher scorer in each pair is one of Dr. Brown’s students.

Nice question

All statement 2 is basically saying is that for every student in Dr. Adams class, a student in Dr. Browns class scored higher- so if both classes have the same number of people then the median will naturally be higher even if you minimize the potential scores of Dr. Browns class

Dr A. [10,20,30,40,50]

Dr B [20,30,40,50,60]

The median is clearly higher

B
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Re: 10 students took a chemistry exam that was graded on a scale  [#permalink]

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13 Sep 2017, 00:39
Pretty much a dead giveway with B
for A) we don't know the exact scores so Median can be higher for either Dr A or Dr B
B) says each time the score for Dr B is higher --> therefore Me is higher
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Re: 10 students took a chemistry exam that was graded on a scale  [#permalink]

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02 Aug 2019, 02:13
Another way to make this question less of a giveaway and with slightly more difficulty would be to have 2 pairs (out of the 5) of students where Brown's student scores lower than the other student; we would then need to determine further if the medians actually differ enough.

E.g. student pairing (Adam on top, Brown below as arranged), with scoring from 1-10:
1 2 3 4 5
2 1 2 5 6 ---->>> (Median, Adam) = 3 > 2 (Median, Brown)

vs

1 2 3 4 5
4 3 1 3 6 ---->>> (Median, Adam) = 3 NOT > 3 (Median, Brown)
Re: 10 students took a chemistry exam that was graded on a scale   [#permalink] 02 Aug 2019, 02:13
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