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17 Feb 2020, 08:37
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C
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Difficulty:
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76% (02:29) correct
24%
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wrong
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The average weight of students in a class of 20 was 80 pounds. Five new students joined and the weight increased to 84 pounds. If weights of the five new students are in integers, weight of no two students is same, and the lightest new student weighs 84 pounds, what is the highest possible weight of the heaviest new student?
A. 100
B. 116
C. 158
D. 164
E. 172
Are You Up For the Challenge: 700 Level Questions
A. 100
B. 116
C. 158
D. 164
E. 172
Are You Up For the Challenge: 700 Level Questions
17 Feb 2020, 09:05
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Answer is C.
First we take the sum of the the 20 terms and multiply by the terms by the average (20*80) total of 1600
Adding 5 students to the class that increases the average student wait of the class to 84 lbs. Makes the new sum 2,100 (25*84).
2,100-1,600=500. The five new students added 500 lbs and the lightest weighted student is 84 lbs. No student is the same weight, the next smallest numbers are 85,86,87. Adding those numbers with 84 gives us a sum of 342 lbs lowest weight for the first four students. Making the heaviest student, at most, 158 lbs. (500-158 lbs)
Sounds wordy/lengthy and I’m sure that there may be easier solutions but this took approximately 90 seconds, and allows you to see it clearly.
In summary:
Old total- 80*20 = 1,600
New total- 84*25= 2,100
New total-old total= 500
Lowest student weight-84
Weight of other students- 85,86,87
New total- weight of first four students= 500-342=158
C. 158 lbs is our answer.
Posted from my mobile device
First we take the sum of the the 20 terms and multiply by the terms by the average (20*80) total of 1600
Adding 5 students to the class that increases the average student wait of the class to 84 lbs. Makes the new sum 2,100 (25*84).
2,100-1,600=500. The five new students added 500 lbs and the lightest weighted student is 84 lbs. No student is the same weight, the next smallest numbers are 85,86,87. Adding those numbers with 84 gives us a sum of 342 lbs lowest weight for the first four students. Making the heaviest student, at most, 158 lbs. (500-158 lbs)
Sounds wordy/lengthy and I’m sure that there may be easier solutions but this took approximately 90 seconds, and allows you to see it clearly.
In summary:
Old total- 80*20 = 1,600
New total- 84*25= 2,100
New total-old total= 500
Lowest student weight-84
Weight of other students- 85,86,87
New total- weight of first four students= 500-342=158
C. 158 lbs is our answer.
Posted from my mobile device
18 Feb 2020, 03:17
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total weight of 20 students ; 1600
and of 25 students ; 2100 lbs
net ∆ ; sum of 5 students; 500 lbs
least weight ; 84 lbs
so max can be ; 500-(84+85+86+87) ; 158
IMO C
and of 25 students ; 2100 lbs
net ∆ ; sum of 5 students; 500 lbs
least weight ; 84 lbs
so max can be ; 500-(84+85+86+87) ; 158
IMO C
Bunuel
