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31 Dec 2020, 07:05
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
71% (02:00) correct
29%
(02:23)
wrong
based on 185
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Five students took a calculus test and received an average score of 82 and a median score of 84. If the greatest possible score is 100, what is the least possible score a student could have received?
(A) 42
(B) 56
(C) 64
(D) 78
(E) 84
(A) 42
(B) 56
(C) 64
(D) 78
(E) 84
rocky620
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31 Dec 2020, 07:24
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Let the scores be A, B, C, D, E (in ascending order) and C is the median score 84
Since the average is 82 total score will be 410
To minimize A, we will have to maximize everything.
D & E can be 100.
C+D+E = 84+100+100 = 284
A+B = 410-284 = 126
Since B cannot be greater than 84, the maximum value it can take is 84.
A+84 = 126
So, the least value of A can be 42.
Option A
Since the average is 82 total score will be 410
To minimize A, we will have to maximize everything.
D & E can be 100.
C+D+E = 84+100+100 = 284
A+B = 410-284 = 126
Since B cannot be greater than 84, the maximum value it can take is 84.
A+84 = 126
So, the least value of A can be 42.
Option A
31 Dec 2020, 07:41
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Given
To Find
Approach and Working Out
Correct Answer: Option A
- • Five students took a calculus test and received an average score of 82 and a median score of 84.
• The greatest possible score is 100.
To Find
- • The least possible score a student could have received.
Approach and Working Out
- • We have 5 students with a median of 84 and a mean of 82.
- o Total score = 5 × 82 = 410
o Median = 84, means at least 2 students should get 84.
o So, scores are x, 84, 84, y, z
o Now maximum score can be 100 so we can have a scenario of x, 84, 84, 100, 100.
o This would give the minimum value of x.
- o = 42
Correct Answer: Option A
