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In a class with 20 students, a test was administered and was
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29 Jul 2018, 04:29
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In a class with 20 students, a test was administered and was scored only in whole numbers from 0 to 10. At least one student got every possible score, and the average score was 7.
Quantity A
Quantity B
The lowest score that could have been received by more than one student
\(4\)
A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.
In a class with 20 students, a test was administered and was
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06 Apr 2020, 15:32
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sandy wrote:
In a class with 20 students, a test was administered and was scored only in whole numbers from 0 to 10. At least one student got every possible score, and the average score was 7.
Quantity A
Quantity B
The lowest score that could have been received by more than one student
\(4\)
A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.
In a class with 20 students, the average score was 7. We can write: (sum of all 20 scores)/20 = 7 Multiply both sides of the equation by 20 to get: sum of all 20 scores = 140
At least one student got every possible score Since every score from 0 to 10 has been achieved, the first 11 score in the class are as follows: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ?, ?, ?, ?, ?, ?, ?, ?, ?}
QUANTITY A: The lowest score that could have been received by more than one student So far, the sum of the first 11 scores = 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 140 - 55 = 85, which means the remaining (missing) 9 scores must add to 85
Our goal is to MINIMIZE one of the 9 remaining scores (keeping in mind that the SUM of those 9 scores must be 85) To MINIMIZE one of the remaining 9 scores, we'll MAXIMIZE the other eight scores. Since the maximum possible test score is 10, let's let eight of the remaining scores be 10. Since the some of those eight 10's is 80, and since the SUM of the remaining 9 scores must be 85, the last value must be 5 In other words, the test scores are: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 5}
So, 5 is The lowest score that could have been received by more than one student
Re: In a class with 20 students, a test was administered and was
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03 Aug 2018, 00:20
3
Since the avg of the class is 7, the total score of the class is 7*20 = 140
If there is a score of at least 0-10 inclusive we know that 9 people will score 85. This is because 0+1+....10 = 55 Remaining is 140-55 = 85 85 has to be distributed between 9 remaining students. Only when 1 of them gets 5 remaining 8 will get 80/8 =10 each. 10 is the maximum possible hence 5 is the least that two person can get.
Re: In a class with 20 students, a test was administered and was
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05 Aug 2018, 18:28
85 is to be distributed among 9 people and the marks that each person can score is between 0 and 10 inclusive.
Let us say someone among the 9 people scores 0. Then we have 8 people remaining and yet we have 85 marks to be distributed among those 8. 85/8 = 10.625 this is more than 10 hence the least repeating number is not 0. Only when the least repeating number is 5. 8 people can score 10 to fulfill the possible integer value and also add the value of 9 people to equal 85
Re: In a class with 20 students, a test was administered and was
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30 Mar 2020, 08:37
1
NickBass wrote:
Im sorry but I still don't get this
See there are 9 more people remaining and 85 is the score that needs to be divided. The score cannot be more than 10 as it is the whole number between 0-10.
Let us assume that the score is 10 for a person, then 75/9 = is not an integer Let us assume that the score is 9 for a person, then 76/9 = is not an integer Let us assume that the score is 8 for a person, then 77/9 = is not an integer Let us assume that the score is 7 for a person, then 78/9 = is not an integer Let us assume that the score is 6 for a person, then 79/9 = is not an integer Let us assume that the score is 5 for a person, then 80/9 = is an integer -> That's it!
Re: In a class with 20 students, a test was administered and was
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23 Aug 2020, 07:21
3
NickBass wrote:
Im sorry but I still don't get this
Total students : 20 Avg Score: 7 Since, Sum/total = avg we get sum=140 This means that 20 students scored a total of 140.
Now, the question mentions "atleast 1 student got every possible score". So, 11 students scored {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
We have 20 - 11 = 9 students left and 140 - 55 = 85 total score to be distributed among the 9 students. Now, we have to find ways to distribute the remaing 85 points. There are many ways to do this among 9 students For example: 1) 7 students score 10, 1 student scores 9, and 1 student scores 6 = 70 + 9 + 6 = 85 2) 8 students score 10, 1 student scores 5 = 80 + 5 = 85 etc
But the problem is that we need to find the lowest score possible for one of the 9 students, this forces us to allocate the maximum score for the remaining 8 students. So the maximum value we can give the remaining 8 students is 10, this would force us to choose 5 as the lowest for the other student, so that the total adds up to 85 Therefore, example 2) 8 students score 10, 1 student scores 5 = 80 + 5 = 85 works! It's the only answer because if we reduce the score of any one of the 8 students then we would have to choose a score more than 5 for the 9th student to add up to 85. It will not give us the lowest score. example 1) 7 students score 10, 1 student scores 9, and 1 student scores 6 = 70 + 9 + 6 = 85 does not work because 6 is not the lowest score possible.
Re: In a class with 20 students, a test was administered and was
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20 Oct 2023, 02:22
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