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04 Nov 2021, 07:15
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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:
65%
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Question Stats:
62% (02:24) correct
38%
(02:26)
wrong
based on 236
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Each of the 5 friends contributed a different integral amount for a restaurant bill. The average payment made by all five them was $64. The person who paid the 2nd highest paid $124 and the average amount paid by two of them who paid the minimum was $23. What is the maximum possible highest amount paid by one of them?
A. 125
B. 127
C. 128
D. 130
E. more than 130
A. 125
B. 127
C. 128
D. 130
E. more than 130
Updated on: 04 Nov 2021, 10:15
Originally posted by sanjitscorps18 on 04 Nov 2021, 08:43.
Last edited by sanjitscorps18 on 04 Nov 2021, 10:15, edited 1 time in total.
Last edited by sanjitscorps18 on 04 Nov 2021, 10:15, edited 1 time in total.
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Bunuel, the wording of the question needs correction
The average payment made by all five them was 64.
Total amount paid = 64 x 5 = 320
The 2nd highest person paid 124, and the minimum two paid an average of 23. Hence we have the following
22, 24, M, 124, H (M is the median value and H is the highest value, also considering both the minimum payers paid 23 equally)
Now M + H = 320 - 124 - 46 = 150
Now H > 124 and we have to maximize H. In order to maximize H we have to minimize M. Least value to M can be 25.
Hence for minimum value of M (=23) we have
H + 25 = 150
=> maximum value of H = 150 - 25 = 125
Option A
The average payment made by all five them was 64.
Total amount paid = 64 x 5 = 320
The 2nd highest person paid 124, and the minimum two paid an average of 23. Hence we have the following
22, 24, M, 124, H (M is the median value and H is the highest value, also considering both the minimum payers paid 23 equally)
Now M + H = 320 - 124 - 46 = 150
Now H > 124 and we have to maximize H. In order to maximize H we have to minimize M. Least value to M can be 25.
Hence for minimum value of M (=23) we have
H + 25 = 150
=> maximum value of H = 150 - 25 = 125
Option A
04 Nov 2021, 09:42
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Each person paid a DIFFERENT Integral amount towards the bill. Let’s label the five friends A through E where the amount each paid:
A < B < C < D < E
Since the average is $64, the SUM paid by all 5 friends is = $320
A < B < C < D < E = $320
The person who paid the 2nd highest (D) paid = $124
And the average of the 2 friends who paid the least is $23 ———> meaning that A and B together paid $46
To maximize the amount paid by E, the assumed friend who paid the most, we want to keep A and B as close together as we possible can ———> because C has to pay at the very least $1 dollar more than B (because they all pay different integers amounts)
For instance, if we had A pay 1 dollar ——-> B would have to pay 45 dollars ——-> and C would have to pay at least 46 dollars
If instead, we apportioned 10 to A ——-> B would have to pay 36 ———> and C would have to pay at least 37.
As the amounts A and B pay come closer to being equal, we MINIMIZE the amount that we can apportion to C.
In other words, If we put A and B’s payments as close as possible, this will result in the smallest value we can apportion to C.
We can apportion 22 to A and 24 to B —-> this is the closest we can make the values, have them be Different Integral Values, and add up to $46.
And since C must pay a different integral amount, we can minimize C’s contribution by making it just $1 more than B’s ——>$25
(A = 22) < (B = 24) < (C= 25) < (D = 124) < (E = ?) ——-> amounts must SUM to $320
By apportioning the amounts above, we have fulfilled the conditions of the question and Maximized the highest possible payment that could have been made by friend E
MAX E = (320) - (22 + 24 + 25 + 124)
MAX E = (320) - (195)
MAX -E = $125
(A)
The highest amount a friend can pay is $125
Posted from my mobile device
A < B < C < D < E
Since the average is $64, the SUM paid by all 5 friends is = $320
A < B < C < D < E = $320
The person who paid the 2nd highest (D) paid = $124
And the average of the 2 friends who paid the least is $23 ———> meaning that A and B together paid $46
To maximize the amount paid by E, the assumed friend who paid the most, we want to keep A and B as close together as we possible can ———> because C has to pay at the very least $1 dollar more than B (because they all pay different integers amounts)
For instance, if we had A pay 1 dollar ——-> B would have to pay 45 dollars ——-> and C would have to pay at least 46 dollars
If instead, we apportioned 10 to A ——-> B would have to pay 36 ———> and C would have to pay at least 37.
As the amounts A and B pay come closer to being equal, we MINIMIZE the amount that we can apportion to C.
In other words, If we put A and B’s payments as close as possible, this will result in the smallest value we can apportion to C.
We can apportion 22 to A and 24 to B —-> this is the closest we can make the values, have them be Different Integral Values, and add up to $46.
And since C must pay a different integral amount, we can minimize C’s contribution by making it just $1 more than B’s ——>$25
(A = 22) < (B = 24) < (C= 25) < (D = 124) < (E = ?) ——-> amounts must SUM to $320
By apportioning the amounts above, we have fulfilled the conditions of the question and Maximized the highest possible payment that could have been made by friend E
MAX E = (320) - (22 + 24 + 25 + 124)
MAX E = (320) - (195)
MAX -E = $125
(A)
The highest amount a friend can pay is $125
Posted from my mobile device
