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Each of the five friends contributed a different amount in a restauran
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01 Aug 2023, 03:49
01 Aug 2023, 03:49
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Each of the five friends contributed a different amount in a restaurant bill. The average payment made by all five of them was $64. The person who paid the 2nd highest paid $124 and the average amount paid by two of those who paid the minimum was $23. What is the maximum possible highest amount paid by one of them, if amount paid by all are integers?
A. 125
B. 127
C. 128
D. 130
E. More then 130
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A. 125
B. 127
C. 128
D. 130
E. More then 130
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
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\(\Longrightarrow\) Best GRE Test Books of 2023
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Re: Each of the five friends contributed a different amount in a restauran
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02 Aug 2023, 10:22
02 Aug 2023, 10:22
1
Expert Reply
Let's break down the information given:
The average payment made by all five friends was $64.
The person who paid the 2nd highest amount paid $124.
The average amount paid by two of those who paid the minimum was $23.
Let's represent the amounts paid by the five friends as A, B, C, D, and E. We are looking for the maximum possible highest amount (max value) among these payments.
We know that the average payment made by all five friends is $64, so we can write the equation:
(A + B + C + D + E) / 5 = 64
From this, we can get the sum of all five amounts:
A + B + C + D + E = 5 * 64
Next, we are told that the person who paid the 2nd highest amount paid $124. This means that out of the five payments, one of them is $124. Let's assume that person is A:
A = 124
Now we have:
B + C + D + E = 5 * 64 - 124
The average amount paid by two of those who paid the minimum was $23. This means that two of the payments are $23 each. Let's assume these are C and D:
C = 23
D = 23
Now we have:
B + E = 5 * 64 - 124 - 23 - 23
B + E = 320 - 124 - 46
B + E = 150
To maximize the highest amount (max value) paid by one of the friends, we want to minimize the sum of B and E. The minimum value of B is 1 (since all amounts are integers and must be greater than zero). So, to maximize the highest amount, we set B = 1:
1 + E = 150
E = 150 - 1
E = 149
Now, to get the maximum possible highest amount, we set A as the highest:
Max value = A = 124
So, the maximum possible highest amount paid by one of the friends is $124.
Therefore, the correct answer is option A. 125
The average payment made by all five friends was $64.
The person who paid the 2nd highest amount paid $124.
The average amount paid by two of those who paid the minimum was $23.
Let's represent the amounts paid by the five friends as A, B, C, D, and E. We are looking for the maximum possible highest amount (max value) among these payments.
We know that the average payment made by all five friends is $64, so we can write the equation:
(A + B + C + D + E) / 5 = 64
From this, we can get the sum of all five amounts:
A + B + C + D + E = 5 * 64
Next, we are told that the person who paid the 2nd highest amount paid $124. This means that out of the five payments, one of them is $124. Let's assume that person is A:
A = 124
Now we have:
B + C + D + E = 5 * 64 - 124
The average amount paid by two of those who paid the minimum was $23. This means that two of the payments are $23 each. Let's assume these are C and D:
C = 23
D = 23
Now we have:
B + E = 5 * 64 - 124 - 23 - 23
B + E = 320 - 124 - 46
B + E = 150
To maximize the highest amount (max value) paid by one of the friends, we want to minimize the sum of B and E. The minimum value of B is 1 (since all amounts are integers and must be greater than zero). So, to maximize the highest amount, we set B = 1:
1 + E = 150
E = 150 - 1
E = 149
Now, to get the maximum possible highest amount, we set A as the highest:
Max value = A = 124
So, the maximum possible highest amount paid by one of the friends is $124.
Therefore, the correct answer is option A. 125
Re: Each of the five friends contributed a different amount in a restauran
[#permalink]
09 Oct 2023, 08:43
09 Oct 2023, 08:43
GeminiHeat wrote:
Let's break down the information given:
The average payment made by all five friends was $64.
The person who paid the 2nd highest amount paid $124.
The average amount paid by two of those who paid the minimum was $23.
Let's represent the amounts paid by the five friends as A, B, C, D, and E. We are looking for the maximum possible highest amount (max value) among these payments.
We know that the average payment made by all five friends is $64, so we can write the equation:
(A + B + C + D + E) / 5 = 64
From this, we can get the sum of all five amounts:
A + B + C + D + E = 5 * 64
Next, we are told that the person who paid the 2nd highest amount paid $124. This means that out of the five payments, one of them is $124. Let's assume that person is A:
A = 124
Now we have:
B + C + D + E = 5 * 64 - 124
The average amount paid by two of those who paid the minimum was $23. This means that two of the payments are $23 each. Let's assume these are C and D:
C = 23
D = 23
Now we have:
B + E = 5 * 64 - 124 - 23 - 23
B + E = 320 - 124 - 46
B + E = 150
To maximize the highest amount (max value) paid by one of the friends, we want to minimize the sum of B and E. The minimum value of B is 1 (since all amounts are integers and must be greater than zero). So, to maximize the highest amount, we set B = 1:
1 + E = 150
E = 150 - 1
E = 149
Now, to get the maximum possible highest amount, we set A as the highest:
Max value = A = 124
So, the maximum possible highest amount paid by one of the friends is $124.
Therefore, the correct answer is option A. 125
The average payment made by all five friends was $64.
The person who paid the 2nd highest amount paid $124.
The average amount paid by two of those who paid the minimum was $23.
Let's represent the amounts paid by the five friends as A, B, C, D, and E. We are looking for the maximum possible highest amount (max value) among these payments.
We know that the average payment made by all five friends is $64, so we can write the equation:
(A + B + C + D + E) / 5 = 64
From this, we can get the sum of all five amounts:
A + B + C + D + E = 5 * 64
Next, we are told that the person who paid the 2nd highest amount paid $124. This means that out of the five payments, one of them is $124. Let's assume that person is A:
A = 124
Now we have:
B + C + D + E = 5 * 64 - 124
The average amount paid by two of those who paid the minimum was $23. This means that two of the payments are $23 each. Let's assume these are C and D:
C = 23
D = 23
Now we have:
B + E = 5 * 64 - 124 - 23 - 23
B + E = 320 - 124 - 46
B + E = 150
To maximize the highest amount (max value) paid by one of the friends, we want to minimize the sum of B and E. The minimum value of B is 1 (since all amounts are integers and must be greater than zero). So, to maximize the highest amount, we set B = 1:
1 + E = 150
E = 150 - 1
E = 149
Now, to get the maximum possible highest amount, we set A as the highest:
Max value = A = 124
So, the maximum possible highest amount paid by one of the friends is $124.
Therefore, the correct answer is option A. 125
Sir, I didn't understand the step of taking 1 -- because we cannot consider min = 1 since the problem clearly states that the minimum is 23. So, B+E = 150 and to maximise B, we must minimise E. Since the sum states that the mis is 23, let E =23. Then, B = 150-23 = 127. Still I don't know why my answer is wrong. Please guide.
