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.
For an overlapping set question, we can use a double-set matrix to organize theinformation and solve. The two sets in this question are the practical test (pass/fail)and the written test (pass/fail).
PRACTICAL - PASSPRACTICAL - FAILTOTALSWRITTEN - PASS.7x.3xxWRITTEN - FAIL0TOTALS.3x
(1) INSUFFICIENT 1) INSUFFICIENT: If we add the total number of students to the information from thequestion, we do not have enough to solve for .7x.
PRACTICAL - PASSPRACTICAL - FAILTOTALSWRITTEN - PASS.7x.3xxWRITTEN - FAIL0TOTALS.3x188
(2) INSUFFICIENT: If we add the fact that 20% of the Batch B who passed thepractical test failed the written test to the original matrix from the question, we cancome up with the relationship .7x = .8y. However, that is not enough to solve for .7x.
PRACTICAL - PASSPRACTICAL - FAILTOTALSWRITTEN - PASS.7x=.8y.3xxWRITTEN - FAIL.2y0.2yTOTALSy.3x
(1) AND (2) SUFFICIENT: If we combine the two statements we get a matrix that can be used to form two relationships between x and y;
PRACTICAL - PASSPRACTICAL - FAILTOTALSWRITTEN - PASS.7x=.8y.3xxWRITTEN - FAIL.2y0.2yTOTALSy.3x188
This would allow us to solve for x and in turn find the value of .7x, the number Batch B students who went to Batch A.
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