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# Steve took 5 history exams during a semester. Each score was one of th

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Math Expert
Joined: 02 Sep 2009
Posts: 58415
Steve took 5 history exams during a semester. Each score was one of th  [#permalink]

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14 Mar 2018, 01:46
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Difficulty:

65% (hard)

Question Stats:

69% (02:16) correct 31% (01:54) wrong based on 40 sessions

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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.

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Re: Steve took 5 history exams during a semester. Each score was one of th  [#permalink]

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14 Mar 2018, 01:48
Bunuel wrote:
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.

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Re: Steve took 5 history exams during a semester. Each score was one of th  [#permalink]

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14 Mar 2018, 01:55
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Bunuel wrote:
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.

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.

Please give kudos if you liked the explanation.
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Re: Steve took 5 history exams during a semester. Each score was one of th   [#permalink] 14 Mar 2018, 01:55
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