To pass to the next level (Batch A) in aschool's sports team, students in the in

Question

To pass to the next level (Batch A) in a
school's sports team, students in the intermediate batch (Batch B) at Premier
High School have to pass both a written and a practical test. Everyone has to
take the tests, and no one failed both tests. If 30% of the students of Batch B
who passed the written test did not pass the practical, how many Batch B
students at Premier High School go to Batch A?

(1) There are 188 Batch B students at Premier
High School.

(2) 20% of the Batch B students who passed
the practical test failed the written test.

Options:

A . if the question can be answered by using any of the statements alone but not by using the other statement alone.

B . if the question can be answered by using either of the statements alone.

C . if the question can be answered only by using both the statements together.

D . if the question cannot be answered

Answer: Option C
:
C
For an overlapping set question, we can use a
double-set matrix to organize the information and solve. The two sets in this
question are the practical test (pass/fail) and the written test (pass/fail).

(1)
INSUFFICIENT: If we add the total number of students to the information from
the question, we do not have enough to solve for
.7x.

(2) INSUFFICIENT: If we add the fact that 20%
of the Batch
B who passed the practical
test failed the written test to the original
matrix from the question, we can come up with the relationship .7x = .8y. However, that is not enough to solve for .7x.