Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given sets? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) 9 – 27 – 31 – 36; 10 – 30 – 34 – 39

Correct — A. Read each given set as three steps, name the operation at each, then test the options in the same order.

9 × 3 = 27, 27 + 4 = 31, 31 + 5 = 36
10 × 3 = 30, 30 + 4 = 34, 34 + 5 = 39

Rule: × 3, then + 4, then + 5.

5 × 3 = 15
15 + 4 = 19
19 + 5 = 24 → option (a)

Why the others are wrong

• (b)
  8 – 24 – 28 – 35 — 8 – 24 – 28 – 35 clears × 3 and + 4, then adds 7. The last step must be + 5, which would give 33.
• (c)
  11 – 33 – 38 – 44 — 11 – 33 – 38 – 44 breaks at the second step: 33 + 4 = 37, not 38. Its two additions are + 5 then + 6.
• (d)
  15 – 45 – 50 – 55 — 15 – 45 – 50 – 55 breaks at the same place: 45 + 4 = 49, not 50. Its two additions are + 5 then + 5.

These items hand you two worked sets so the operations can be pinned down instead of guessed. A rule that fits one set may be an accident, and a rule that fits both is the rule.

Work left to right and name the operation at each step. Both 9 → 27 and 10 → 30 are × 3, and after that the numbers only creep, so the remaining steps have to be additions: + 4 then + 5.

Then run the options through the same three steps and abandon each at its first mismatch. You rarely need all three.

Key facts

• The chain is × 3, then + 4, then + 5, applied to whole numbers only.
• 5 × 3 = 15, 15 + 4 = 19, 19 + 5 = 24.
• Both given sets follow the chain, which is why it can be trusted on the options.

Common traps

• Testing only the first step — all four options multiply by 3 correctly.
• Assuming the last two additions are equal, which makes 15 – 45 – 50 – 55 look right.
• Breaking 27 into 2 and 7, which the printed note bars.

No directly related past PYQ was found.