Steve took 5 history exams during a semester. Each score was : DS Archive
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# Steve took 5 history exams during a semester. Each score was

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Manager
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Steve took 5 history exams during a semester. Each score was [#permalink]

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18 Oct 2004, 08:08
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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.

Easy question of a type that I keep making stupid mistakes on ...
Manager
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18 Oct 2004, 08:19
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I'm thinking D

coz from 1 we can get alll the 5 different scores

from 2 we get the sum of of the last 2 to be 191

the max score possible is 100 hence the other score cannot be less than 91 which means for all possible values of the last 2 scores 87 remains the median
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18 Oct 2004, 10:02
guess it shud be B...St.1 alone is sufficient...
OA..???
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18 Oct 2004, 10:23
Also got D

1 - We can get the last socre by finding the missing score from avg,

2 - We know the sum of the last two tests is 194, and since test score can't be above 100, the last two tests are greater than 90 so 87 is the median.
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18 Oct 2004, 15:38
OA is D.

As people have said ...

(1) Tells us that the scores on the first 4 exams were 76, 87, 73, and 96, respectively. Average on the last 3 exams was 89 and 3*89 is 267. Subtracting the scores from the 3rd and 4th exam which we were told, 267 - 73 - 96 = 98. So the scores in increasing order were:
73, 76, 87, 96, 98
and the median is 87.
Thus, (1) is sufficient.

(2) Tells us that the scores on the first 3 exams were 76, 87, and 73, respectively. Also we are told that the his average score was 86 and thus the total score of all 5 exams is 86 * 5 = 430. Subtracting the first three exams scores, 430 - 76 - 87 - 73, leaves 194 as the sum of the last two exams scores. Since the highest score possible is 100 there is no possible way to distribute the score across the two exams (i.e. 100/94, 99/95, ...) and get anything other than 87 as the median.
Thus, (2) is sufficient.

OA is D
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18 Oct 2004, 17:16
after doing it I see the answer already posted, but since I did it, I'll just chime in and agree. answer is D.
18 Oct 2004, 17:16
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