GMAT Official Guide 2019 Last semester, Professor K taught

[BTGmoderatorDC]

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.

[Jay@ManhattanReview]

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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[Scott@TargetTestPrep]

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.

Solution:

We need to determine the number of students in class A.
Statement One Alone:

Even though we know a total of 85 assignments were handed in by the students in the two classes, we still can’t determine the number of students in class A (or class B). It’s possible that class A has 5 students and class B has 10 students (notice that 5 x 7 + 10 x 5 = 85). However, it’s also possible that class A has 10 students and class B has 3 students (notice that 10 x 7 + 3 x 5 = 85). Therefore, statement one alone is not sufficient.

Statement Two Alone:

Knowing only the number of students in class B does not allow us to determine the number of students in class A. We know that the 10 students in class B handed in a total of 10 x 5 = 50 assignments, but without knowing the combined number of assignments for both classes, we can’t determine the number of students in class A. Statement two alone is not sufficient.

Statements One and Two Together:

From statement two, we know that the students in class B handed in a total of 10 x 5 = 50 assignments. Since we are told in statement one that the two classes handed in a total of 85 assignments, we see that the students in class A handed in a total of 85 - 50 = 35 assignments. Since each student in class A handed in 7 assignments, there must be 35/7 = 5 students in class A.

Answer: C