Number Series Questions and Answers

Answer: A

Correct answer: 13

Two series have been laid down alternately. The terms in the odd positions are 1, 5, 9, which rise steadily, and those in the even positions are 100, 90, 80, which fall. The missing term continues the first of these, giving 13. As a check, the answer differs from the term two places before it by 4, which is the step that strand has taken throughout. Separating the odd and even positions turns one confusing series into two simple ones.

Answer: B

Correct answer: 20

Two series have been laid down alternately. The terms in the odd positions are 5, 10, 15, which rise steadily, and those in the even positions are 80, 72, 64, which fall. The missing term continues the first of these, giving 20. As a check, the answer differs from the term two places before it by 5, which is the step that strand has taken throughout. The position of the missing term decides which strand supplies it, so the terms should be numbered before anything else is attempted.

Answer: C

Correct answer: 24

Two series have been laid down alternately. The terms in the odd positions are 3, 10, 17, which rise steadily, and those in the even positions are 60, 54, 48, which fall. The missing term continues the first of these, giving 24. As a check, the answer differs from the term two places before it by 7, which is the step that strand has taken throughout. Two strands moving in opposite directions will eventually cross, which limits how long such a series can be extended.

Answer: D

Correct answer: 41

Every gap is the same: the differences run 8, 8, 8, so the common difference is 8. Applying it once more to the final term, 33 + 8 gives 41. As a check, subtracting 8 from the answer returns 33, the term before it, and repeating that recovers the whole series. An answer that is close to the correct one but not exact usually means the rule was right and the arithmetic was not.

Answer: A

Correct answer: 63

Every gap is the same: the differences run 12, 12, 12, so the common difference is 12. Applying it once more to the final term, 51 + 12 gives 63. As a check, subtracting 12 from the answer returns 51, the term before it, and repeating that recovers the whole series. Checking the proposed answer against the rule from the first term forward is the cheapest way to catch an error.

Answer: B

Correct answer: 66

Every gap is the same: the differences run 16, 16, 16, so the common difference is 16. Applying it once more to the final term, 50 + 16 gives 66. As a check, subtracting 16 from the answer returns 50, the term before it, and repeating that recovers the whole series. Series questions reward writing the differences down; almost nothing in this topic is solved reliably by inspection alone.

Answer: C

Correct answer: 76

Every gap is the same: the differences run -11, -11, -11, so the common difference is -11. Applying it once more to the final term, 87 - 11 gives 76. As a check, subtracting -11 from the answer returns 87, the term before it, and repeating that recovers the whole series. Two candidate rules that agree on the early terms will diverge later, so the last pair is the one that discriminates.

Answer: D

Correct answer: 101

Every gap is the same: the differences run 15, 15, 15, so the common difference is 15. Applying it once more to the final term, 86 + 15 gives 101. As a check, subtracting 15 from the answer returns 86, the term before it, and repeating that recovers the whole series. When a rule fits every gap but one, the exception is usually the reader's arithmetic rather than the series.

Answer: A

Correct answer: 25

Every gap is the same: the differences run -7, -7, -7, -7, so the common difference is -7. Applying it once more to the final term, 32 - 7 gives 25. As a check, subtracting -7 from the answer returns 32, the term before it, and repeating that recovers the whole series. The number of terms shown is chosen so that the rule is determined; with one fewer, more than one answer would fit.

Answer: B

Correct answer: 105

Every gap is the same: the differences run 23, 23, 23, so the common difference is 23. Applying it once more to the final term, 82 + 23 gives 105. As a check, subtracting 23 from the answer returns 82, the term before it, and repeating that recovers the whole series. A series with only three terms shown can rarely be pinned down, which is why four or five are usually given.