BTGmoderatorDC wrote:Last semester, Professor K taught two classes, A and B. Each student in class A handed in 7 assignments, and each student in class B handed in 5 assignments. How many students were in class A ?
(1) The students in both classes combined handed in a total of 85 assignments.
(2) There were 10 students in class B.
Given: Each student in class A handed in 7 assignments, and each student in class B handed in 5 assignments
To find out: Number of students in class A
Let's take each statement one by one.
(1) The students in both classes combined handed in a total of 85 assignments.
Say there are a number of students in class A and b number of students in class B
Thus, 7a + 5b = 85;
Though we can straight away discard the linear equation as we see that we do not have any information about b to get the value of a; however, seeing the prime co-efficient for a and b, we must analyze the equation.
We have 7a + 5b = 85 => a = (85 - 5b)/7 = 5(17 - b)/7. Since a is a positive integer, (17 - b) must be a multiple of 7, or (17 - b) should be either 7 or 14.
At (17 - b) = 7, we have a = 5
At (17 - b) = 14, we have a = 10
We can't get the unique value of a. Insufficient.
(2) There were 10 students in class B.
Can't get the number of students in class A. Insufficient.
(1) and (2) together
From (2), we have b = 10 and from (1), we have 7a + 5b = 85; thus, 7a + 5*10 = 85 => a = 5. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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