Question

Last year $\frac{4}{5}$ of the applicants for a job on a police force passed the physical examination. If $\frac{3}{4}$of the applicants who passed the physical examination also passed the written examination, how the applicants passed both examinations?
I. The number of applicants who did not either examination was equal to the number who passed the physical examination only.
II. There were a total of 100 applicants.
Decide whether the data in the statements are sufficient to answer the question.

• A. if Statement I alone is sufficient but Statement II alone is not sufficient to answer the question
• B. if Statement II alone is sufficient but Statement I alone is not sufficient to answer the question
• C. if both statements taken together are sufficient to answer the question but neither Statement alone is sufficient
• D. if Statements I and II together are not sufficient, and additional data is needed to answer the question

Answer 1

Answer: (B)

if Statement II alone is sufficient but Statement I alone is not sufficient to answer the question

Answer 2

I. The number of applicants who did not either examination was equal to the number who passed the physical examination only.
II. There were a total of 100 applicants.
Let total applicants that apply = x
passed physical exam = $\frac{4}{5} x$
Written exam pass = $\frac{3}{4} \cdot \frac{4}{5} x = \frac{3}{5} x$
The applicants passed both examinations are $\frac{3}{5} x$ .
We need only x i.e. total number of applicants.
From Statement 2, we can get that, so alone Statement 2 is sufficient.
So, the correct option is (B).