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In a certain class, some students donated cans of food to a local food

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In a certain class, some students donated cans of food to a local food  [#permalink]

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New post 24 Jun 2018, 20:55
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In a certain class, some students donated cans of food to a local food bank. What was the average (arithmetic mean) number of cans donated per student in the class?

(1) The students donated a total of 56 cans of food.
(2) The total number of cans donated was 40 greater than the total number of students in the class.



NEW question from GMAT® Official Guide 2019


(DS03138)

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Re: In a certain class, some students donated cans of food to a local food  [#permalink]

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New post 24 Jun 2018, 22:13
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Bunuel wrote:
In a certain class, some students donated cans of food to a local food bank. What was the average (arithmetic mean) number of cans donated per student in the class?

(1) The students donated a total of 56 cans of food.
(2) The total number of cans donated was 40 greater than the total number of students in the class.



NEW question from GMAT® Official Guide 2019


(DS03138)


average (arithmetic mean) number of cans donated per student = \(\frac{Number of cans donated (C)}{Number of Students (X)}\)

1) As we are not given number of students who donated, hence Not Suff

2) Cans = total students + 40, so the equation becomes \(\frac{(X+40)}{X}\),Not Suff

1) + 2) from 1) we have C=56, from 2) C=40+X ==> 56=40+X ==> X= 16,
now we can find \(\frac{C}{X}\) = \(\frac{56}{16}\) = 3.5

Hence , C
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Re: In a certain class, some students donated cans of food to a local food  [#permalink]

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New post 25 Jun 2018, 02:41
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Solution



Given:
    • In a certain class, some students donated cans of food to a local food bank

To find:
    • The average (arithmetic mean) number of cans donated per student in the class

Analysing Statement 1
    • As per the information given in statement 1, the students donated a total of 56 cans of food
    • To find the average, we also need to know the number of students in the class
      o As this information is not given, we cannot find out the average contribution

Hence, statement 1 is not sufficient to answer

Analysing Statement 2
    • As per the information given in statement 2, the total number of cans donated was 40 greater than the total number of students in the class
      o If we assume the total number of students to be n, then the number of cans donated will be (n + 40)
      o The average contribution per student = \(\frac{n + 40}{n}\) = \(1 + \frac{40}{n}\)
    • As we don’t know the value of n, we can’t find out the average

Hence, statement 2 is not sufficient to answer

Combining Both Statements
Combining both the statements, we can say:
    • If there are n students, total number of cans donated will be n + 40, which is equal to 56
      o Therefore, n = 16
    • As we know the total number of students and the total number of cans donated, we can find out the average donation per student.

Hence, the correct answer is option C.

Answer: C
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Re: In a certain class, some students donated cans of food to a local food  [#permalink]

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New post 25 Jun 2018, 02:55
Bunuel wrote:
In a certain class, some students donated cans of food to a local food bank. What was the average (arithmetic mean) number of cans donated per student in the class?

(1) The students donated a total of 56 cans of food.
(2) The total number of cans donated was 40 greater than the total number of students in the class.



NEW question from GMAT® Official Guide 2019


(DS03138)



We are to just find info is enough to answer..

What do we require for average
1) total cans - C
2) total students- S

Let's what info each equation gives..
(1) The students donated a total of 56 cans of food.
C=56
Gives us C, but S NOT known
Insufficient
(2) The total number of cans donated was 40 greater than the total number of students in the class.
C=40+S
Only a linear equation in two variables
Insufficient

Combined
Two linear equation with 2 unknowns
Sufficient

C
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Re: In a certain class, some students donated cans of food to a local food   [#permalink] 25 Jun 2018, 02:55
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