GMAT Official Guide 2019 In a certain class, some

[BTGmoderatorDC]

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.

[Jay@ManhattanReview]

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.

"The average (arithmetic mean) number of cans donated per student in the class" is given by

Number of cans / Number of students in the class

Say, the number of cans = C and the number of students in the class = S

Thus, we have to get the value of C/S.

Let's take each statement one by one.

(1) The students donated a total of 56 cans of food.

We have C = 56 but don't have S. Insufficient

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

=> C = 40 + S

Thus, the average = C/S = (40 + S) / S = 40/S + 1. We don't have S. Insufficient

(1) and (2) together

From (1), we have C = 56 and from (2), we have. C = 40 + S . Thus, S = 56 - 40 = 16

Thus, the average = C/S = 56/16. A unique value. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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[Scott@TargetTestPrep]

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.

Solution:


Question Stem Analysis:

We need to determine the average number of cans of food donated per student in the class.

Statement One Alone:

Although we know the total number of cans of food donated, we don’t know the number of students in the class, and thus we can’t determine the average number of cans of food donated per student in the class. Statement one alone is not sufficient.

Statement Two Alone:

Although we know that the total number of cans donated was 40 greater than the total number of students in the class, we know neither the total number of cans donated nor the number of students in the class. Thus, we can’t determine the average number of cans of food donated per student in the class. Statement two alone is not sufficient.

Statements One and Two Together:

With the two statements, we see that a total of 56 cans were donated, and the number of students in the class was 56 - 40 = 16. Thus, the average number of cans donated was 56/40 = 7/5 = 1.4. The two statements together are sufficient to answer the question.


Answer: C