The statements (S1), (S2), and (S3) pertain to the scores obtained by students in an exam. The maximum possible marks in the exam is 150.

(S1) The highest score is 100.

(S2) The fourth highest score is 76.

(S3) There are at least four students whose scores are within 25 of each other.

Which one of the following options is necessarily correct?

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?