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Learn what truly sets the UC Riverside MBA apart and how it helps in your professional growth
26 May 2017, 05:14
Kudos
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It rained for 12 days during the rainy season. The day with the least rainfall was 0.4 inches, and the day with the most rainfall was 9.4 inches. If the total average rainfall of 12 days was 4.0 inches, what is the maximum possible value of the median rainfall, in inches?
A. 4.8
B. 5.2
C. 5.5
D. 5.8
E. 6.1
A. 4.8
B. 5.2
C. 5.5
D. 5.8
E. 6.1
26 May 2017, 05:14
Kudos
Bookmarks
Official Solution:
It rained for 12 days during the rainy season. The day with the least rainfall was 0.4 inches, and the day with the most rainfall was 9.4 inches. If the total average rainfall of 12 days was 4.0 inches, what is the maximum possible value of the median rainfall, in inches?
A. 4.8
B. 5.2
C. 5.5
D. 5.8
E. 6.1
The day with the least rainfall was 0.4 inches, and the day with the most rainfall was 9.4 inches, so if you put this in an increasing order, you get \(0.4 + ( ) + ( ) + ( ) + ( ) + ( ) + ( ) + ( ) + ( ) + ( ) + ( ) + 9.4 = 12 * 4.0 = 48\). However, since the question is about the maximum value of the median, the rest of the number should become the least. In order for that to happen, it should be \(0.4 + 0.4 + 0.4 + 0.4 + 0.4 + M + M + M + M + M + M + 9.4 = 12 * 4.0 = 48\). By solving this, you get from \(0.4 * 5 + 6M + 9.4 = 48\) and \(6M = 48 - 9.4 - 2 = 36,6\), to \(M = \frac{36.6}{6} = 6.1\). Therefore, the answer is E.
Answer: E
It rained for 12 days during the rainy season. The day with the least rainfall was 0.4 inches, and the day with the most rainfall was 9.4 inches. If the total average rainfall of 12 days was 4.0 inches, what is the maximum possible value of the median rainfall, in inches?
A. 4.8
B. 5.2
C. 5.5
D. 5.8
E. 6.1
The day with the least rainfall was 0.4 inches, and the day with the most rainfall was 9.4 inches, so if you put this in an increasing order, you get \(0.4 + ( ) + ( ) + ( ) + ( ) + ( ) + ( ) + ( ) + ( ) + ( ) + ( ) + 9.4 = 12 * 4.0 = 48\). However, since the question is about the maximum value of the median, the rest of the number should become the least. In order for that to happen, it should be \(0.4 + 0.4 + 0.4 + 0.4 + 0.4 + M + M + M + M + M + M + 9.4 = 12 * 4.0 = 48\). By solving this, you get from \(0.4 * 5 + 6M + 9.4 = 48\) and \(6M = 48 - 9.4 - 2 = 36,6\), to \(M = \frac{36.6}{6} = 6.1\). Therefore, the answer is E.
Answer: E
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