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02 Jul 2020, 01:41
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
76% (01:42) correct
24%
(01:18)
wrong
based on 49
sessions
History
Date
Time
Result
Not Attempted Yet
If the average test score of four students is 85, which of the following scores could a fifth student receive such that the average of all five scores is greater than 84 and less than 86?
I. 86
II. 85
III. 83
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
I. 86
II. 85
III. 83
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
chipsy
Joined: 05 Oct 2014
Last visit: 01 Sep 2021
Posts: 55
Given Kudos: 149
Concentration: Technology, Entrepreneurship
Schools: Tepper '23 Ross '23 McCombs '23 Tuck '23 NUS '23
02 Jul 2020, 01:55
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Average of test score of 4 students = 85 i.e. ((a+b+c+d)/4) = 85
If we add 85 as score of fifth student to above average , then average of all five scores remains same = 85
if we add 83 to the test score of 4 students, then average would decrease by 2/5 = 0.4 i.e. 84.6
if we add 86 to the test score of 4 students, then average would increase by 1/5 = 0.2 i.e. 85.2
so Option: E
If we add 85 as score of fifth student to above average , then average of all five scores remains same = 85
if we add 83 to the test score of 4 students, then average would decrease by 2/5 = 0.4 i.e. 84.6
if we add 86 to the test score of 4 students, then average would increase by 1/5 = 0.2 i.e. 85.2
so Option: E
02 Jul 2020, 20:43
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Ans: E
The natural way to solve it would be:
Total score for all 4 students: 340
I: 86: (340 + 86)/ 5=85.2
II: 85: Since the average of 4 was 85. If the fifth scores 85. The average should remain the same as 85
III: 83: (340 + 83)/5: 84.6
A faster way to solve it would be.
If average is of 4 people's score is 85. Ideally, if the 5th scores an 85 the average remains the same.
So 86 is basically 85 + 1 and 83 is 85 - 2
Averages of both opt I and opt III can be calculated as:
I: 85 + 1/5: 85 + 0.2: 85.2
III: 85 - 2/5: 85 - 0.4: 84.6
The natural way to solve it would be:
Total score for all 4 students: 340
I: 86: (340 + 86)/ 5=85.2
II: 85: Since the average of 4 was 85. If the fifth scores 85. The average should remain the same as 85
III: 83: (340 + 83)/5: 84.6
A faster way to solve it would be.
If average is of 4 people's score is 85. Ideally, if the 5th scores an 85 the average remains the same.
So 86 is basically 85 + 1 and 83 is 85 - 2
Averages of both opt I and opt III can be calculated as:
I: 85 + 1/5: 85 + 0.2: 85.2
III: 85 - 2/5: 85 - 0.4: 84.6
