Number Series Questions and Answers

Answer: A

Correct answer: 231

The steps run 10, 8, 46, 8, which grow and then fall back, so a single operation cannot account for them. Two operations are applied in turn, and continuing the alternation from 77 gives 231. As a check, the step from 77 to the answer is 154, which breaks the run of preceding gaps exactly as an alternating rule demands. The difference between the two largest options is often the clue to which arithmetic slip they represent.

Answer: B

Correct answer: 98

The steps run 4, 11, 19, 11, which grow and then fall back, so a single operation cannot account for them. Two operations are applied in turn, and continuing the alternation from 49 gives 98. As a check, the step from 49 to the answer is 49, which breaks the run of preceding gaps exactly as an alternating rule demands. Reading the series aloud sometimes reveals a rhythm that the written form conceals.

Answer: C

Correct answer: 22

Two series have been laid down alternately. The terms in the odd positions are 4, 10, 16, which rise steadily, and those in the even positions are 90, 81, 72, which fall. The missing term continues the first of these, giving 22. As a check, the answer differs from the term two places before it by 6, which is the step that strand has taken throughout. Each strand here is an ordinary arithmetic progression; only the interleaving makes the series look difficult.

Answer: D

Correct answer: 26

Two series have been laid down alternately. The terms in the odd positions are 2, 10, 18, which rise steadily, and those in the even positions are 70, 63, 56, which fall. The missing term continues the first of these, giving 26. As a check, the answer differs from the term two places before it by 8, which is the step that strand has taken throughout. Any series can be checked by generating it afresh from the identified rule and comparing term by term.

Answer: A

Correct answer: 19

Two series have been laid down alternately. The terms in the odd positions are 7, 11, 15, which rise steadily, and those in the even positions are 45, 41, 37, which fall. The missing term continues the first of these, giving 19. As a check, the answer differs from the term two places before it by 4, which is the step that strand has taken throughout. The rule is confirmed only when it reproduces every term shown, which is a stricter test than fitting the last pair.

Answer: B

Correct answer: 28

Two series have been laid down alternately. The terms in the odd positions are 1, 10, 19, which rise steadily, and those in the even positions are 64, 56, 48, which fall. The missing term continues the first of these, giving 28. As a check, the answer differs from the term two places before it by 9, which is the step that strand has taken throughout. Options that are not of the right order of magnitude can be discarded before the rule is even settled.

Answer: C

Correct answer: 15

Two series have been laid down alternately. The terms in the odd positions are 6, 9, 12, which rise steadily, and those in the even positions are 55, 50, 45, which fall. The missing term continues the first of these, giving 15. As a check, the answer differs from the term two places before it by 3, which is the step that strand has taken throughout. Where two adjacent terms share a factor, that factor often appears in the rule itself.

Answer: D

Correct answer: 36

Two series have been laid down alternately. The terms in the odd positions are 3, 14, 25, which rise steadily, and those in the even positions are 88, 77, 66, which fall. The missing term continues the first of these, giving 36. As a check, the answer differs from the term two places before it by 11, which is the step that strand has taken throughout. The simplest rule that fits all the terms is the intended one, and further sophistication is rarely rewarded.

Answer: A

Correct answer: 29

The gaps run 2, 4, 2, 4 and settle into no pattern at all, so no arithmetic step will fit. The terms are the prime numbers in order, each having no divisor but itself and one. The next prime after 23 is 29. As a check, every number between 23 and the answer has a divisor other than itself and one, so none of them could be the next term. Where the differences settle into no pattern at all, the terms usually share a property rather than a relationship.

Answer: B

Correct answer: 43

The gaps run 6, 2, 6, 4 and settle into no pattern at all, so no arithmetic step will fit. The terms are the prime numbers in order, each having no divisor but itself and one. The next prime after 41 is 43. As a check, every number between 41 and the answer has a divisor other than itself and one, so none of them could be the next term. Prime numbers are the most frequent non-arithmetic family in series questions, and their irregular gaps are the giveaway.