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

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08 Nov 2004, 06:43

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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 were 76, 87, 73 and 96, respectively, and Steve's average (arithmetic mean) score on the last 3 exams was 89
2- Steve's score 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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Statement 1: Gives you the first four scores and the average scores for the last three exams. So, using the average the last score can be determined. Once we have all the five scores, we can tell the median is 87.

Statement 2: Gives the first three scores and the average for all the five scores. So we have two unknowns the last two exam scores.

Using the average, we can see that 76+87+73+x+y = 86*5
=> x+y = 194.

But the scores have a range of 1 to 100 inclusive.

Assuming x =100, y = 94, so you can tell he did not get any lower than 94 in both the exams.

Key info is # of scores is an odd number.
Statement 1 is sufficient for reasons mentioned above.
As far as statement 2 is concerned all you need to know is whether the remaining unknowns (x & y) fall within or outside the [73,87] interval.
As x+y = 194 you know that min value for x or y is 94>87. Hence median is 87.

I have a small doubt regarding Statement 1. 5 scores are 73,76,87,96,x Avg of last three=89 87+96+x/3=89 x+183=267 x=84 5 scores are 73,76,84,87,96. Median is 84.

According to statement 2, median is 87.

Now, in DS two statements cannot have conflicting answers. So how come we are getting different answers?

I have a small doubt regarding Statement 1. 5 scores are 73,76,87,96,x Avg of last three=89 87+96+x/3=89 x+183=267 x=84 5 scores are 73,76,84,87,96. Median is 84.

According to statement 2, median is 87.

Now, in DS two statements cannot have conflicting answers. So how come we are getting different answers?

1 says: Steve's scores on the first 4 exams were 76, 87, 73 and 96, respectively. Means, the order must not be disturbed. 1st test:76 2nd test:87 3rd test:73 4th test:96 5th test:x

Average of last three: (73+96+x)/3=89 169+x=267 x=98