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The average of marks obtained by 120 candidates was 35. If the average

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Bunuel
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The average of marks obtained by 120 candidates was 35. If the average [#permalink] New post   20 Feb 2019, 04:55
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The average of marks obtained by 120 candidates was 35. If the average of passed candidates was 39 and that of failed candidates was 15, the number of candidates who passed the examination, is

A. 100
B. 120
C. 150
D. 160
E. 170
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Re: The average of marks obtained by 120 candidates was 35. If the average [#permalink] New post   20 Feb 2019, 05:05
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Answer is A .

Total marks = 120*35
PASSEd student = x
failed ones = 120- x

now by the given condition
x*39+ (120-x)*15 = 120*35

we can solve it to find x= 100

Answer A.

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Re: The average of marks obtained by 120 candidates was 35. If the average [#permalink] New post   20 Feb 2019, 09:08
Bunuel wrote:
The average of marks obtained by 120 candidates was 35. If the average of passed candidates was 39 and that of failed candidates was 15, the number of candidates who passed the examination, is

A. 100
B. 120
C. 150
D. 160
E. 170


total sum of height of students ; 120 * 35 = 4200
let pass students =x and fail will be 120-x
so
x*39 + ( 120-x)*15 = 4200
solve for x
x= 100
IMO A
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Re: The average of marks obtained by 120 candidates was 35. If the average [#permalink] New post   20 Feb 2019, 13:08
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Total Student = 120
Avg score = 35
Total score = 120*35

Lets say passed student = x
Avg score of passed student = 39
total score of passed student =39x

So failed student = (120-x)
Avg score of failed student =15
Total score of failed student = (120-x)*15

Now ,
120 *35 = 39*x+ (120-x)*15
120*35 - 120* 15 = 39x-15 x
120*20 = 24x
After solving this linear equation ,

we get x= 100

So Answer is A
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Re: The average of marks obtained by 120 candidates was 35. If the average [#permalink] New post   20 Feb 2019, 13:30
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The above explainations are correct the right answer is A but there is a problem with the options.

If total students are 120 then how can the numbers of students who passed the exams be greater than 120 so C,D, and E are out. Is total average = average of students who passed in that case the number of students who passed can be equal to 120, clearly this is not the case, so Answer is A. This is the only valid option. There is no need of any math here.

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Re: The average of marks obtained by 120 candidates was 35. If the average [#permalink] New post   20 Feb 2019, 14:02
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I wont say the wrong options are incorrect. Though i agree that having out of boundaries options degrades the level of question :)
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Re: The average of marks obtained by 120 candidates was 35. If the average [#permalink] New post   20 Feb 2019, 14:06
Yes my point is that only, the options could have been anything less than 60 which can be eliminated based on weighed average but they are supposed to be valid option, right.

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Re: The average of marks obtained by 120 candidates was 35. If the average [#permalink] New post   20 Feb 2019, 17:19
Well, I think you got too deep under the skin of options :).. though cant deny you... :)
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Re: The average of marks obtained by 120 candidates was 35. If the average [#permalink] New post   28 Feb 2020, 14:50
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Solution



Given
    • The average of marks obtained by 120 candidates was 35.
    • The average of passed candidates was 39.
    • The average of failed candidates was 15.

To find
    • The number of candidates who passed the examination


Approach and Working out
Let’s assume x students passed the exam. Then, 120-x students failed the exam.
    • 35= x*39 +(120-x)15/120
    • 120*35 = 39x +120*15 -15x
    • 120 *35 -120 *15 =24x
    • 120*20 = 24x
    • 20*5 =x
    • x= 100


Hence, option A is the correct answer.

Correct Answer: Option A
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Re: The average of marks obtained by 120 candidates was 35. If the average [#permalink] New post   28 Feb 2020, 15:00
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Alternate Solution



Approach and Working out

This can also be solved by applying the Allegation Method.

39_____15
____35
x_______y
x : y = (35-15):(39 -35)= 20:4= 5:1
x:y = 5:1
• Hence, x=5y

x + y = 120
6y= 120
y= 20 and x= 100

Hence, option A is the correct answer.

Correct Answer: Option A
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Re: The average of marks obtained by 120 candidates was 35. If the average [#permalink] New post   01 Mar 2020, 13:33
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Bunuel wrote:
The average of marks obtained by 120 candidates was 35. If the average of passed candidates was 39 and that of failed candidates was 15, the number of candidates who passed the examination, is

A. 100
B. 120
C. 150
D. 160
E. 170


We can let n = the number of candidates who passed the examination and create the equation:

[39n + 15(120 - n)] / 120 = 35

39n + 1800 - 15n = 4200

24n = 2400

n = 100

Answer: A
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Re: The average of marks obtained by 120 candidates was 35. If the average [#permalink] New post   06 Jan 2022, 11:42
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Re: The average of marks obtained by 120 candidates was 35. If the average [#permalink]
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