What should come at the place of question mark? 100, 97, 91, 82, ?, 55

Correct — B.
Rule: the drops are consecutive multiples of 3: −3, −6, −9, −12, −15.

100 − 3 = 97
97 − 6 = 91
91 − 9 = 82
82 − 12 = 70

Check: 70 − 15 = 55, the last term → option (b).

Why the others are wrong

• (a)
  68 — 68 makes the drop from 82 equal 14 and the next drop 13. The drops must keep growing by 3, so after 9 comes 12.
• (c)
  64 — 64 gives a drop of 18 from 82 and then 9 to reach 55. The drop after 9 is 12, which gives 70.
• (d)
  60 — 60 gives a drop of 22 from 82 and then only 5 to reach 55. The drops grow by 3 every step, so they never shrink.

When a series falls by uneven amounts, write the differences under it. Here they are 3, 6, 9, 12, the 3-times table.

Differences that grow by a fixed step mean a constant second difference (here 3). Once you see it, the missing term and the one after it are both fixed.

Use the last given term as a check: the gap you predict must land exactly on 55.

Key facts

• The drops are 3 × 1, 3 × 2, 3 × 3, 3 × 4 and 3 × 5.
• The nth term after 100 is 100 − 3 × (1 + 2 + … + n): n = 4 gives 100 − 30 = 70.

Common traps

• Filling the gap from the left and never checking that 70 − 15 lands on 55.

No directly related past PYQ was found.