Select the number from among the given options that can replace the question mark (?) in the following series. 35, 46, 68, 101, 145, ?

Correct — B. Subtract each term from the one after it.

46 - 35 = 11
68 - 46 = 22
101 - 68 = 33
145 - 101 = 44

Rule: the gaps run 11, 22, 33, 44 — each one 11 larger than the last, so the next gap is 55.

145 + 55 = 200 — option (b).

Why the others are wrong

• (a)
  212 — 212 asks for a gap of 67. The gaps climb by a fixed 11, so the fifth gap is 44 + 11 = 55, and 67 belongs to no rung of that ladder.
• (c)
  214 — 214 sits 14 above 200 and would need a gap of 69. Every gap in this series is a multiple of 11 and 69 is not one.
• (d)
  210 — 210 needs a gap of 65, which again is no multiple of 11. Its round shape is the only thing recommending it, and roundness is not a rule.

When a number series climbs unevenly, subtract neighbours before anything else and look at the gaps.

Here the gaps form a series of their own — 11, 22, 33, 44 — so the series is second-order: the second differences are a constant 11.

That constant is what you extend. Add 11 to the last gap to reach 55, then add 55 to the last term. Once the gap ladder is clean there is no need to test the terms for squares, primes or digit sums.

Key facts

• The differences of 35, 46, 68, 101 and 145 are 11, 22, 33 and 44.
• The second differences are a constant 11, which makes the next gap 55.
• 145 + 55 = 200, the keyed term.

Common traps

• Hunting the terms for squares or cubes instead of subtracting neighbours first
• Adding the last gap again, giving 145 + 44 = 189, instead of the next gap
• Choosing the roundest option before the arithmetic is finished

No directly related past PYQ was found.