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14 Mar 2018, 01:46
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D
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Difficulty:
75%
(hard)
Question Stats:
57% (02:21) correct
43%
(01:58)
wrong
based on 278
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Steve took 5 history exams during a semester. Each score was one of the integers 1 through 100 inclusive. What was Steve's median score for these 5 exams?
(1) Steve's scores on the first 4 exams where 76, 87, 73, and 96, respectively, and Steve's average (arithmetic mean) score on the last 3 exams was 89.
(2) Steve's scores on the first 3 exams were 76, 87, and 73, respectively, and Steve's average (arithmetic mean) on all 5 exams was 86.
(1) Steve's scores on the first 4 exams where 76, 87, 73, and 96, respectively, and Steve's average (arithmetic mean) score on the last 3 exams was 89.
(2) Steve's scores on the first 3 exams were 76, 87, and 73, respectively, and Steve's average (arithmetic mean) on all 5 exams was 86.
14 Mar 2018, 01:48
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Bunuel
20. Descriptive Statistics
- Theory
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14 Mar 2018, 01:55
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Bunuel
IMO D.
We want to find steve's median score on the 5 history tests.
Statement 1) Score on first 4 exams given and average of last 3 exams given. We can find the score of the last exam by using the total sum of average concept and hence median is well defined.
89* 3 ( total for last 3 exams ) = 73 + 96 + last exam.
Hence sufficient.
Statement 2) Using same principle let the total score of last two exams be X.
86 * 5 = 76 + 87 + 73 + X
X = 194.
Since score is capped by 100. the lowest and highest scores with the 194 sum are 94 and 100.
Median is well defined.
Hence sufficient.
Therefore D.
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