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Source: Beat The GMAT — Data Sufficiency |
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ColumbiaVC
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goalevan
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S = 20
But S consists of students that scored lower than the mean, equal to the mean, and higher than the mean.
L + E + H = 20
L = ?
Statement 1) We are given that H = 12, but the students who scored exactly the mean score of 85 are still unknown, so we cannot simply take 20 - 12 = 8, only L + E = 20 - 12 = 8, where E is unknown. Insufficient.
Statement 2) The lowest eight scores had a 640/8 = 80 average. It could be that 4 students had a score of 85 and 4 students had a score of 75, and thus only 4 students scored below average. It could also be that all 8 students (and more from the other 12 students) had a score of 80. Insufficient.
Combined) From statement 2 we illustrated that the number of students who scored less than 80 can differ at least between 4 and 8. From statement 1 we know that L <= 8, but we still do not have enough information. Insufficient.
Two possibilities to illustrate:
{75,75,75,75, 85,85,85,85, 85,85,85,85, 85,85,85,85, 95,95,95,95}
The average is 85 and 4 students scored below the mean.
{80,80,80,80, 80,80,80,80, 80,80,90,90, 90,90,90,90, 90,90,90,90}
The average is 85 and 10 students scored below the mean.
E
But S consists of students that scored lower than the mean, equal to the mean, and higher than the mean.
L + E + H = 20
L = ?
Statement 1) We are given that H = 12, but the students who scored exactly the mean score of 85 are still unknown, so we cannot simply take 20 - 12 = 8, only L + E = 20 - 12 = 8, where E is unknown. Insufficient.
Statement 2) The lowest eight scores had a 640/8 = 80 average. It could be that 4 students had a score of 85 and 4 students had a score of 75, and thus only 4 students scored below average. It could also be that all 8 students (and more from the other 12 students) had a score of 80. Insufficient.
Combined) From statement 2 we illustrated that the number of students who scored less than 80 can differ at least between 4 and 8. From statement 1 we know that L <= 8, but we still do not have enough information. Insufficient.
Two possibilities to illustrate:
{75,75,75,75, 85,85,85,85, 85,85,85,85, 85,85,85,85, 95,95,95,95}
The average is 85 and 4 students scored below the mean.
{80,80,80,80, 80,80,80,80, 80,80,90,90, 90,90,90,90, 90,90,90,90}
The average is 85 and 10 students scored below the mean.
E
