Which of the following numbers will replace the question marks (?) in the given series? 88, 78, 70, 64, 60, ?, ?

Correct — C. Work the gaps, not the terms.

Rule: the differences run −10, −8, −6, −4, shrinking by 2 each time.

88 → 78 is −10
78 → 70 is −8
70 → 64 is −6
64 → 60 is −4

The next two gaps are therefore −2 and 0.
60 − 2 = 58, then 58 − 0 = 58, which is option (c).

Why the others are wrong

• (a)
  56, 56 — Option (a) skips the −2 step. It takes −4 from 60, a gap already spent between 64 and 60, and then 0, dropping the −2 that belongs between them.
• (b)
  56, 54 — Option (b) applies the gap sequence one place late. It takes −4 and then −2 from 60, when the −4 step was already used to get from 64 to 60.
• (d)
  58, 56 — The first term is right, the second is not. Option (d) reaches 58 correctly with −2, then subtracts 2 again, where the shrinking gap has already run down to 0.

When a series falls but not evenly, write the first differences before anything else. They turn an irregular-looking list into a short, obvious pattern.

Here the differences are −10, −8, −6, −4 — an arithmetic sequence in their own right, rising by 2 towards zero.

A gap sequence that reaches 0 makes the series repeat a term. That is why two identical numbers can be a legitimate answer rather than a misprint.

Key facts

• The first differences of 88, 78, 70, 64, 60 are −10, −8, −6 and −4.
• Those differences form their own arithmetic sequence with a common difference of +2.
• The sixth and seventh gaps are therefore −2 and 0, giving 58 and 58.

Common traps

• Assuming a series must keep falling, and rejecting 58, 58 because the numbers repeat.
• Applying the gaps one place late, which lands on 56 instead of 58.
• Working on the terms directly instead of writing the differences down first.

No directly related past PYQ was found.