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On a certain test, a grade of 50% or higher is considered a ‘pass’, an

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New post 07 Feb 2019, 07:02
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On a certain test, a grade of 50% or higher is considered a ‘pass’, and any grade under 50% is considered a ‘fail’. If 4 /5 of the students in a class of one hundred students received a grade of 80% or higher, and if the average grade for the entire class was 65%, what is the minimum possible percentage of the class which received a ‘fail’ on the test?

A) 15
B) 16
C) 17
D) 18
E) 19

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On a certain test, a grade of 50% or higher is considered a ‘pass’, an  [#permalink]

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New post Updated on: 08 Feb 2019, 00:57
gmatbusters wrote:
On a certain test, a grade of 50% or higher is considered a ‘pass’, and any grade under 50% is considered a ‘fail’. If 4 /5 of the students in a class of one hundred students received a grade of 80% or higher, and if the average grade for the entire class was 65%, what is the minimum possible percentage of the class which received a ‘fail’ on the test?

A) 15
B) 16
C) 17
D) 18
E) 19



let total max marks be 100
so >50 marks is pass and <50 marks is fail
given in a class of 100 students 4/5 ; 80 students have scored 80% or higher and rest 20 students we dont know..
also avg of class score is 65%
which means
supposedly let the each of 80 students has scored 80 marks so
class avg
80 * 80 + 20 * x/100 = 65
pr say
6400+20x=6500
20x=100
x=100/20 ; 5
so we can say that the avg score of marks scored by total 20 students has to be = 5
sum of score of 20 students /20 = 5

now seeing the answer options
option D 18 students
so if we assume that 18 students each scored 0 marks so total marks scored by 19th & 20th student = 50 each
and avg 18*0+2*50 = 100 marks and avg = 5
IMO D is the answer...

Originally posted by Archit3110 on 07 Feb 2019, 11:15.
Last edited by Archit3110 on 08 Feb 2019, 00:57, edited 2 times in total.
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Re: On a certain test, a grade of 50% or higher is considered a ‘pass’, an  [#permalink]

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New post 07 Feb 2019, 23:49
Archit3110 wrote:
gmatbusters wrote:
On a certain test, a grade of 50% or higher is considered a ‘pass’, and any grade under 50% is considered a ‘fail’. If 4 /5 of the students in a class of one hundred students received a grade of 80% or higher, and if the average grade for the entire class was 65%, what is the minimum possible percentage of the class which received a ‘fail’ on the test?

A) 15
B) 16
C) 17
D) 18
E) 19


I am not sure of the solution , have given a try to solve this question ..

let total max marks be 100
so >50 marks is pass and <50 marks is fail
given in a class of 100 students 4/5 ; 80 students have scored 80% or higher and rest 20 students we dont know..
also avg of class score is 65%
which means
supposedly let the each of 80 students has scored 80 marks so
class avg
80 * 80 + 20 * x/100 = 65
pr say
6400+20x=6500
20x=100
x=100/20 ; 5
so we can say that the avg score of marks scored by total 20 students has to be = 5
sum of score of 20 students /20 = 5

now seeing the answer options
option E 19 students
so if we assume that 19 students each scored 1 marks so total marks scored by 20th student = 81
and avg 19*1+1*81 = 100 marks and avg = 5
IMO E is the answer...

chetan2u
Hello could you please advise on solution for this question..


You are fine till the total score of 20 is 100 marks..
You have to find the MINIMUM failures, so distribute 100 so as to max out of 20 have passed..
50 marks is pass, so 100 can be divided in 2 of them , 50 each and remaining have got 0..
100=2*50+18*0, so 18 have failed
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On a certain test, a grade of 50% or higher is considered a ‘pass’, an  [#permalink]

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New post 07 Feb 2019, 23:58
chetan2u wrote:
Archit3110 wrote:
gmatbusters wrote:
On a certain test, a grade of 50% or higher is considered a ‘pass’, and any grade under 50% is considered a ‘fail’. If 4 /5 of the students in a class of one hundred students received a grade of 80% or higher, and if the average grade for the entire class was 65%, what is the minimum possible percentage of the class which received a ‘fail’ on the test?

A) 15
B) 16
C) 17
D) 18
E) 19


I am not sure of the solution , have given a try to solve this question ..

let total max marks be 100
so >50 marks is pass and <50 marks is fail
given in a class of 100 students 4/5 ; 80 students have scored 80% or higher and rest 20 students we dont know..
also avg of class score is 65%
which means
supposedly let the each of 80 students has scored 80 marks so
class avg
80 * 80 + 20 * x/100 = 65
pr say
6400+20x=6500
20x=100
x=100/20 ; 5
so we can say that the avg score of marks scored by total 20 students has to be = 5
sum of score of 20 students /20 = 5

now seeing the answer options
option E 19 students
so if we assume that 19 students each scored 1 marks so total marks scored by 20th student = 81
and avg 19*1+1*81 = 100 marks and avg = 5
IMO E is the answer...

chetan2u
Hello could you please advise on solution for this question..


You are fine till the total score of 20 is 100 marks..
You have to find the MINIMUM failures, so distribute 100 so as to max out of 20 have passed..
50 marks is pass, so 100 can be divided in 2 of them , 50 each and remaining have got 0..
100=2*50+18*0, so 18 have failed


chetan2u

Thanks.. , I really sometimes end up making silly errors.. god help me on D day...

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On a certain test, a grade of 50% or higher is considered a ‘pass’, an   [#permalink] 07 Feb 2019, 23:58
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