Select the number from among the given options that can replace the question mark (?) in the following series. 96,77,60,47,36, ?

Correct — C.
Rule: subtract the primes in descending order — 19, 17, 13, 11, then 7.

96 − 19 = 77
77 − 17 = 60
60 − 13 = 47

47 − 11 = 36
36 − 7 = 29

The missing term is 29, which is option (c).

Why the others are wrong

• (a)
  32 — 32 needs a last drop of 4. Four is not prime, and every gap so far has been.
• (b)
  30 — 30 needs a last drop of 6. Six is composite — 2 × 3 — and every gap in this series is prime, so the one after 11 is 7.
• (d)
  28 — 28 needs a drop of 8, an even number. The next prime below 11 is 7, which lands on 29.

Write the first differences before trying anything else. Here they are 19, 17, 13 and 11 — falling, but not by a constant amount.

That unevenness is the signal. The gaps shrink by 2, then 4, then 2, which rules out an arithmetic progression and points at a named sequence instead. Read downwards, 19, 17, 13, 11 is simply the primes in reverse.

Series built on primes, squares, cubes or factorials all announce themselves this way: the differences look almost regular and then refuse to be.

Key facts

• The first differences are 19, 17, 13, 11 and then 7 — consecutive primes taken downwards.
• Those gaps shrink by 2, then 4, then 2, then 4, which is why no constant second difference fits.
• The primes below 11 run 7, 5, 3, 2, so the next gap after 11 is 7.

Common traps

• Forcing the gaps to fall by a constant 2, which makes the next gap 9 and gives 36 − 9 = 27 — not even on the option list
• Writing the first differences and not noticing that all of them are prime

No directly related past PYQ was found.