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

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Math Expert
Joined: 02 Sep 2009
Posts: 55272
In a certain class, some students donated cans of food to a local food  [#permalink]

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24 Jun 2018, 20:55
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91% (00:53) correct 9% (01:03) wrong based on 502 sessions

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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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Location: India
Schools: ISB '20, GMBA '20
Re: In a certain class, some students donated cans of food to a local food  [#permalink]

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24 Jun 2018, 22:13
2
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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25 Jun 2018, 02:41
1

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.

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Joined: 02 Aug 2009
Posts: 7686
Re: In a certain class, some students donated cans of food to a local food  [#permalink]

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

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