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03 Jan 2018, 20:47
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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54% (02:31) correct
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(02:09)
wrong
based on 263
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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.
04 Jan 2018, 09:15
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A
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.
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.
04 Jan 2018, 09:27
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Bunuel
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
a
