Which of the following numbers will replace the question mark (?) in the given series? 12, 25, 49, ?, 197, 395

Correct — C.

Rule: double, then add 1 and subtract 1 alternately, starting with the addition.

12 × 2 + 1 = 25
25 × 2 − 1 = 49
49 × 2 + 1 = 99

Now test it forward against the terms the paper prints.

99 × 2 − 1 = 197 and 197 × 2 + 1 = 395. Both match, so the blank is 99 → option (c).

Why the others are wrong

• (a)
  100 — 100 fails at the very next step: 100 × 2 − 1 = 199, and the paper prints 197. Rounding 99 up to a neat hundred costs the whole item.
• (b)
  96 — 96 comes from 49 × 2 − 2, a rider the series never uses. Carried forward it gives 96 × 2 − 1 = 191, not 197.
• (d)
  121 — 121 overshoots the doubling: 49 × 2 is 98, so no rider of plus or minus 1 can reach 121. It is a square number placed there to tempt a different reading.

In a multiply-and-adjust series the multiplier stays put and the small rider changes. Test the multiplier first: 12 to 25, 25 to 49 and 99 to 197 are all close to doubling, which fixes × 2 immediately.

Then read the leftovers. They run +1, −1, +1, −1, +1, which is a rider that alternates rather than grows.

The differences are a useful cross-check: 13, 24, 50, 98, 198. Each is roughly twice the one before, which is the signature of a doubling series and rules out a series built on squares.

Key facts

• The rule is × 2 with +1 and −1 applied alternately, beginning with +1.
• 12, 25, 49, 99, 197, 395 satisfies that rule at every step.
• The differences run 13, 24, 50, 98, 198, each about double the one before.

Common traps

• Settling on × 2 + 1 alone, which happens to give 99 here but predicts 199 instead of 197.
• Rounding a near-hundred answer to 100 because it looks tidier.
• Chasing squares because 25 and 49 are square numbers while 12 is not.

No directly related past PYQ was found.