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11 Feb 2020, 00:04
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D
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Difficulty:
45%
(medium)
Question Stats:
64% (01:43) correct
36%
(01:57)
wrong
based on 291
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A certain school has 250 students. All these students took a psychometric test that scored them on a scale 1 to 10. Is the average score of these students greater than the median score?
(1) At least 140 students scored less than average
(2) Sum of all the scores is 360 times Median score
(1) At least 140 students scored less than average
(2) Sum of all the scores is 360 times Median score
16 Feb 2020, 09:06
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If you list the scores in increasing order, the median here will be the average of the 125th and 126th highest scores. If we know 140 scores were below the average, the 125th and 126th highest both must be, so the median must be, and Statement 1 is sufficient.
If S is the sum of the scores, S/250 is the average score. If M is the median, Statement 2 tells us S = 360M, so M = S/360. S/250, the average, is definitely larger than S/360, the median, since it has a smaller denominator (and since S is positive). So Statement 2 is also sufficient.
The answer is D.
If S is the sum of the scores, S/250 is the average score. If M is the median, Statement 2 tells us S = 360M, so M = S/360. S/250, the average, is definitely larger than S/360, the median, since it has a smaller denominator (and since S is positive). So Statement 2 is also sufficient.
The answer is D.
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