Discussion
30, 31, 27, 36, 20, ?
Answer: B
The next term is 45.
The differences are squares with alternating signs:
\[ \begin{aligned} 30 + 1^{2} &= 31,\quad 31 - 2^{2} = 27 \\ 27 + 3^{2} &= 36,\quad 36 - 4^{2} = 20 \\ 20 + 5^{2} &= 45 \end{aligned} \]
Subtracting 25 (as if the sign did not alternate) gives -5, and the other options do not fit the square pattern.
Patterns built on alternating additions and subtractions of squares (or cubes) are common in number-series questions; checking the differences 1, -4, 9, -16 shows it at once.
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