Number Series Questions and Answers

Answer: C

Correct answer: 25

The gaps are 4, 4, 4, 4, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is four times its position plus one: position 1 gives 5 and position 5 gives 21. The next position is 6, which gives 25. As a check, the same rule applied to the earlier positions reproduces 5, 9, 13, 17, 21 exactly, so it accounts for every term shown and not merely the last. Doubling every square keeps the difference pattern intact but doubles it, which is a useful check.

Answer: D

Correct answer: 35

The gaps are 6, 6, 6, 6, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is six times its position less one: position 1 gives 5 and position 5 gives 29. The next position is 6, which gives 35. As a check, the same rule applied to the earlier positions reproduces 5, 11, 17, 23, 29 exactly, so it accounts for every term shown and not merely the last. Where a series mixes a power with a linear term, the power dominates and the linear part shows up in the small terms.

Answer: A

Correct answer: 37

Each term is the sum of the two before it. Testing this in the middle of the series, 1 plus 4 is 5, and 4 plus 5 is 9. Applying it to the last pair, 14 plus 23 is 37. As a check, subtracting 23 from the answer leaves 14, which is the term two places back, exactly as the rule requires. Testing the rule on the earliest pair guards against a rule invented to fit only the end of the series.

Answer: B

Correct answer: 37

Each term is the sum of the two before it. Testing this in the middle of the series, 4 plus 5 is 9, and 5 plus 9 is 14. Applying it to the last pair, 14 plus 23 is 37. As a check, subtracting 23 from the answer leaves 14, which is the term two places back, exactly as the rule requires. The gap pattern is often clearer when written as a separate row beneath the terms than when held in the head.

Answer: C

Correct answer: 41

Each term is the sum of the two before it. Testing this in the middle of the series, 2 plus 7 is 9, and 7 plus 9 is 16. Applying it to the last pair, 16 plus 25 is 41. As a check, subtracting 25 from the answer leaves 16, which is the term two places back, exactly as the rule requires. Two series in the same family differ only in their parameters, so the method transfers unchanged between them.

Answer: D

Correct answer: 53

Each term is the sum of the two before it. Testing this in the middle of the series, 6 plus 7 is 13, and 7 plus 13 is 20. Applying it to the last pair, 20 plus 33 is 53. As a check, subtracting 33 from the answer leaves 20, which is the term two places back, exactly as the rule requires. Where a series involves both a multiplication and an addition, the multiplication is usually applied first.

Answer: A

Correct answer: 45

Each term is the sum of the two before it. Testing this in the middle of the series, 1 plus 5 is 6, and 5 plus 6 is 11. Applying it to the last pair, 17 plus 28 is 45. As a check, subtracting 28 from the answer leaves 17, which is the term two places back, exactly as the rule requires. The size of the jump between the last two terms sets a rough expectation for the answer, which filters the options.

Answer: B

Correct answer: 44

Each term is the sum of the two before it. Testing this in the middle of the series, 3 plus 7 is 10, and 7 plus 10 is 17. Applying it to the last pair, 17 plus 27 is 44. As a check, subtracting 27 from the answer leaves 17, which is the term two places back, exactly as the rule requires. Recognising squares and cubes on sight saves more time in this topic than any other single piece of preparation.

Answer: C

Correct answer: 26

Each term is the sum of the two before it. Testing this in the middle of the series, 2 plus 2 is 4, and 2 plus 4 is 6. Applying it to the last pair, 10 plus 16 is 26. As a check, subtracting 16 from the answer leaves 10, which is the term two places back, exactly as the rule requires. A series whose differences are constant in the second row is quadratic and can be given a formula.

Answer: D

Correct answer: 59

The gaps are not equal: they run 3, 7, 11, 15, each 4 more than the last. The next gap must therefore be 19, and adding it to the final term, 40 plus 19 is 59. As a check, the gap between the answer and 40 is 19, which continues the run of gaps 3, 7, 11, 15 by a further 4. Every family in this topic can be identified from the terms alone; none requires information from outside the question.