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

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Joined: 07 Jun 2014
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Kudos [?]: 1910 [0], given: 397

In a class with 20 students, a test was administered and was [#permalink]  29 Jul 2018, 04:29
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Question Stats:

60% (01:23) correct 40% (01:11) wrong based on 10 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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Director
Joined: 07 Jan 2018
Posts: 648
Followers: 7

Kudos [?]: 606 [2] , given: 88

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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Manager
Joined: 27 Feb 2017
Posts: 189
Followers: 1

Kudos [?]: 53 [0], given: 15

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
Director
Joined: 07 Jan 2018
Posts: 648
Followers: 7

Kudos [?]: 606 [0], given: 88

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] 05 Aug 2018, 18:28
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