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26 May 2017, 04:47
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20 students including Tom take a test and Tom gets 5.8 pts higher than their average score. If the teacher gives all the 20 students an additional 10 pts question and Tom is the only one who solved it correctly, how many pts is tom's average score higher than the average score of the total 20 students?
A. 6.2
B. 10.4
C. 10.5
D. 15.3
E. 16.2
A. 6.2
B. 10.4
C. 10.5
D. 15.3
E. 16.2
26 May 2017, 04:48
Kudos
Bookmarks
Official Solution:
20 students including Tom take a test and Tom gets 5.8 pts higher than their average score. If the teacher gives all the 20 students an additional 10 pts question and Tom is the only one who solved it correctly, how many pts is tom's average score higher than the average score of the total 20 students?
A. 6.2
B. 10.4
C. 10.5
D. 15.3
E. 16.2
If the average (arithmetic mean) score of the total 20 students is m, then
Tom's score is \(m + 5.8\).
However, there is an additional 10pts question, and since Tom is the only person who got it right, the average (arithmetic mean) score of the total 20 students is becomes \(m + \frac{10}{20} = m + 0.5\), and Tom's score becomes \(m + 5.8 + 10 = m + 15.8\). Hence, the difference becomes \((m + 15.8) - (m + 0.5) = 15.3\), and therefore, D is the answer.
Answer: D
20 students including Tom take a test and Tom gets 5.8 pts higher than their average score. If the teacher gives all the 20 students an additional 10 pts question and Tom is the only one who solved it correctly, how many pts is tom's average score higher than the average score of the total 20 students?
A. 6.2
B. 10.4
C. 10.5
D. 15.3
E. 16.2
If the average (arithmetic mean) score of the total 20 students is m, then
Tom's score is \(m + 5.8\).
However, there is an additional 10pts question, and since Tom is the only person who got it right, the average (arithmetic mean) score of the total 20 students is becomes \(m + \frac{10}{20} = m + 0.5\), and Tom's score becomes \(m + 5.8 + 10 = m + 15.8\). Hence, the difference becomes \((m + 15.8) - (m + 0.5) = 15.3\), and therefore, D is the answer.
Answer: D
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