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Class A and Class B took the same test. For class A, the median score

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Class A and Class B took the same test. For class A, the median score [#permalink]

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New post 03 Jan 2018, 19:47
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CHALLENGE PROBLEM



Class A and Class B took the same test. For class A, the median score is 80, and the average (arithmetic mean) score is 82; for class B, the median score is 78, and the average (arithmetic mean) score is 74. Combining the two classes A and B together, is the average (arithmetic mean) of the combination greater than its median?

(1) Class A has 37 students and Class B has 40 students.
(2) Class A and Class B together have 77 students.
[Reveal] Spoiler: OA

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Re: Class A and Class B took the same test. For class A, the median score [#permalink]

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New post 04 Jan 2018, 08:15
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Median of A:80 and median of B= 78.
let x be the sum of no. of class A students and m be the sum of no. of class B students.
x/37 = 82 and m/40= 74
As no. of students is more or less same mean would be little less than 78.

median would be 39th term.
Individually since class A has 37 students 19 students will have marks less than equal to 80.
Individually since class B has 40 students 20 students will have marks less than equal to 78.

Now aligning it in ascending order.

39th term would be 80( median of class A).

So suffucient.
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Class A and Class B took the same test. For class A, the median score [#permalink]

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New post 04 Jan 2018, 08:27
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Bunuel wrote:

CHALLENGE PROBLEM



Class A and Class B took the same test. For class A, the median score is 80, and the average (arithmetic mean) score is 82; for class B, the median score is 78, and the average (arithmetic mean) score is 74. Combining the two classes A and B together, is the average (arithmetic mean) of the combination greater than its median?

(1) Class A has 37 students and Class B has 40 students.
(2) Class A and Class B together have 77 students.


Class A : median - 80 and mean - 82
Class B : median - 78 and mean - 74

is combined mean>median

(1) Class A has 37 students and Class B has 40 students.
Since class B has more strength, the average of combined class will be closer to average of class B
so between 74 and 82, average will be closer to 74 or < \(\frac{74+82}{2} =78\), so <78..
Median has to be between 78 and 80, so no requirement of calculating exact value..
as Mean< Median
sufficient

(2) Class A and Class B together have 77 students
if class A is 1 and class B is 76, mean will be closer to 82 and median will be closer to 80.. so mean>median
if class A is 76 and class B is 1, mean will be closer to 74 and median will be closer to 78.. so mean<median
insuff

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Class A and Class B took the same test. For class A, the median score   [#permalink] 04 Jan 2018, 08:27
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