Which of the following numbers will replace the question marks (?) in the given series? 16, 36, 64, ?, ?, 196, 256, 324

Correct — D. Rule: the squares of consecutive even numbers, starting at 4².

4² = 16, 6² = 36, 8² = 64
10² = 100, 12² = 144

The terms printed after the gap confirm the chain: 14² = 196, 16² = 256, 18² = 324.

So the two blanks take 100 and 144 — option (d).

Why the others are wrong

• (a)
  81, 100 — 81 is 9², an odd base, and the chain is built from 4², 6², 8² and so on. The first blank is 10² = 100.
• (b)
  81, 121 — 81 = 9² and 121 = 11² are both odd squares. Between 8² and 14² the even chain needs 10² and 12², nothing else.
• (c)
  100, 121 — 100 is right, but 121 = 11² breaks the even run. The term after 10² is 12² = 144.

A series is a square series when its terms grow the way squares do, with gaps that widen by a fixed amount rather than staying equal.

Here 16, 36 and 64 are 4², 6² and 8², so the bases advance by 2 and the series is the even squares.

Read the terms on the far side of the gap before committing. 196, 256 and 324 are 14², 16² and 18², which pins the missing bases at 10 and 12. Working inwards from both ends is faster and safer than extending from the left and hoping.

Key facts

• 16, 36, 64, 100, 144, 196, 256 and 324 are the squares of 4, 6, 8, 10, 12, 14, 16 and 18.
• Successive even squares differ by 20, 28, 36, 44 and 52 — a rise of 8 each time.
• Every even square is divisible by 4, which rules out 81 and 121 at a glance.

Common traps

• Extending the series only from the left and never checking the terms printed after the gap
• Reading 16, 36, 64 as a doubling or addition pattern and missing that they are squares
• Getting the first blank right and taking an option whose second value is an odd square

No directly related past PYQ was found.