Answer: Option B
:
B
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).
$\begin{array}{cccc}& \text{PRACTICAL - PASS}& \text{PRACTICAL - FAIL}& \text{TOTALS}\\ \text{WRITTEN - PASS}& .7x& .3x& x\\ \text{WRITTEN - FAIL}& & 0& \\ \text{TOTALS}& & .3x& \end{array}$
(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.
$\begin{array}{cccc}& \text{PRACTICAL - PASS}& \text{PRACTICAL - FAIL}& \text{TOTALS}\\ \text{WRITTEN - PASS}& .7x& .3x& x\\ \text{WRITTEN - FAIL}& & 0& \\ \text{TOTALS}& & .3x& 188\end{array}$
(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.
$\begin{array}{cccc}& \text{PRACTICAL - PASS}& \text{PRACTICAL - FAIL}& \text{TOTALS}\\ \text{WRITTEN - PASS}& .7x=.8y& .3x& x\\ \text{WRITTEN - FAIL}& .2y& 0& .2y\\ \text{TOTALS}& y& .3x& \end{array}$
(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;
$\begin{array}{cccc}& \text{PRACTICAL - PASS}& \text{PRACTICAL - FAIL}& \text{TOTALS}\\ \text{WRITTEN - PASS}& .7x=.8y& .3x& x\\ \text{WRITTEN - FAIL}& .2y& 0& .2y\\ \text{TOTALS}& y& .3x& 188\end{array}$
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.