Direction : Series I: 8, 9, 15, 25, 42, 68, 105 Series II: 60, 180, 450, 900,…

Concept

A wrong-number series follows ONE fixed generating rule; the wrong term is the single value that breaks that rule. For a multiplicative series the test is the ratio of each term to the one before it — in a clean series these ratios form their own regular pattern. Once the wrong term N is found, evaluate the requested expression and then test each given statement as an independent true/false claim.

Application — find the wrong term

Series II: 60, 180, 450, 900, 1350, 1380, 675. Take successive ratios (each term ÷ previous term):

1. 180 ÷ 60 = 3

2. 450 ÷ 180 = 2.5

3. 900 ÷ 450 = 2

4. 1350 ÷ 900 = 1.5

5. the multipliers are decreasing by 0.5 each step (3, 2.5, 2, 1.5, …), so the next multiplier must be 1, giving 1350 × 1 = 1350

6. the value printed in that slot is 1380, not 1350 — this is the term that breaks the rule

Check the rule still holds afterward: the final multiplier should be 0.5, and 1350 × 0.5 = 675, which matches the last printed term. So the corrected sequence is 60, 180, 450, 900, 1350, 1350, 675, and the wrong term is N = 1380.

Application — evaluate the expression

Substitute N = 1380 into (N / 30 + 1):

1. 1380 ÷ 30 = 46

2. 46 + 1 = 47

Cross-check — test each statement about 47

• Statement (i), primality — 47 is a prime number: its only divisors are 1 and 47, so this claim is true.

• Statement (ii), digit total below 9 — the digits of 47 add to 4 + 7 = 11, and 11 is not below 9, so this claim is false.

• Statement (iii), remainder 4 on division by 5 — the exam wording "nearest multiple of 5 and its remainder is 4" is read as the division test: 47 ÷ 5 gives quotient 9 and remainder 2, not 4, and 47 is not itself a multiple of 5 either, so this claim is false on both readings.

Result

Only the primality claim, statement (i), is true of the evaluated value, so the selection that names primality alone is the one that follows.