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All the students in an algebra class took a 100-point test. Five stude

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All the students in an algebra class took a 100-point test. Five stude  [#permalink]

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New post 22 Mar 2019, 00:24
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

42% (02:46) correct 58% (02:20) wrong based on 12 sessions

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Re: All the students in an algebra class took a 100-point test. Five stude  [#permalink]

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New post 22 Mar 2019, 00:45
There are two ways of approaching this problem... First is by answer choices...

Say if I have got 12(because it's the middle value) students in the class... The sum of their scores would be 12*76 = 912...
Out of 12 students 5 got 100... Now 912-500 = 412..
Each student scored atleast 60... Which means the minimum value of the sum of marks scored by remaining 7 students should be 7*60 = 420.. and 420>412.. which means our answer should be the next greatest value I.e 13...

Alternatively this can also be solved algebraically... Say there are "n" students in the class... The total or the sum of marks scored by n students is 76n..
5 students got 100 , their sum is 500... The remaining (n-5) atleast got 60...

(500+(n-5)60)= 76n
500 +60n -300 = 76n
500-300 = 76n-60n
200 = 16n
N= 12.5... rounding up to 13..

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Re: All the students in an algebra class took a 100-point test. Five stude  [#permalink]

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New post 22 Mar 2019, 02:38
Bunuel wrote:
All the students in an algebra class took a 100-point test. Five students scored 100, each student scored at least 60, and the mean score was 76. What is the smallest possible number of students in the class?

(A) 10
(B) 11
(C) 12
(D) 13
(E) 14


5*100+(x-5)*60 = 76x
solve for x = 12.5 ~ 13
IM D
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Re: All the students in an algebra class took a 100-point test. Five stude   [#permalink] 22 Mar 2019, 02:38
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