The figure below has exactly three intersecting line segments with a rectangular portion WXYZ missing. Which one of the following options $P, Q, R$, and $S$ is the missing portion WXYZ?

Real numbers $y, p$, and $n$ (all greater than 1 ) satisfy

$$ \left(\log _{p^{1 / n}} y\right)\left(\log _{y^{1 / n}} p\right)=16 $$

where the logarithms are taken to the bases $p^{1 / n}$ and $y^{1 / n}$ The value of $n$ is $\_\_\_\_$

The following observation is made about the scores obtained by 100 students in an exam: 'For each student, there exists another student in the class such that their scores are at most ten marks away.'

If the above statement is false, which one of the following statements is necessarily true?

Each one of the following clues contains a keyword that is partially filled.

Clue 1: Synonym of recognize (8 letters): _ D _ NT_ FY

Clue 2: A story long enough to fill a book (5 letters): $\_\_\_\_$

Clue 3: Two of something (6 letters): $\_\_\_\_$ PLE

Clue 4: A fraction of something, split equally into two parts (4 letters): $\_\_\_\_$ F

The first letter of each of the keywords can be rearranged to form a four-letter word. Which one of the options below is a possible choice for the four-letter word?