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# In a class with 20 students, a test was administered and was

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In a class with 20 students, a test was administered and was [#permalink]  29 Jul 2018, 04:29
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33% (01:24) correct 66% (01:10) wrong based on 53 sessions
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.
[Reveal] Spoiler: OA

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Re: In a class with 20 students, a test was administered and was [#permalink]  03 Aug 2018, 00:20
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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.

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Re: In a class with 20 students, a test was administered and was [#permalink]  05 Aug 2018, 13:49
I understand till the part where 9, out of 20, students can get a total of 85. I do not understand how do we get to the answer after that
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Re: In a class with 20 students, a test was administered and was [#permalink]  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

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Re: In a class with 20 students, a test was administered and was [#permalink]  29 Mar 2020, 01:03
Im sorry but I still don't get this
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Re: In a class with 20 students, a test was administered and was [#permalink]  30 Mar 2020, 08:37
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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!
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Re: In a class with 20 students, a test was administered and was [#permalink]  06 Apr 2020, 13:07
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Re: In a class with 20 students, a test was administered and was [#permalink]  06 Apr 2020, 15:32
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Expert's post
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

We have:
QUANTITY A: 5
QUANTITY B: 4

Cheers,
Brent
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Re: In a class with 20 students, a test was administered and was   [#permalink] 06 Apr 2020, 15:32
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