Number Series Questions and Answers

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.

Answer: C

Correct answer: 23

Every gap is the same: the differences run -13, -13, -13, so the common difference is -13. Applying it once more to the final term, 36 - 13 gives 23. As a check, subtracting -13 from the answer returns 36, the term before it, and repeating that recovers the whole series. Reading a series backwards sometimes turns an awkward rule into a familiar one.

Answer: D

Correct answer: 67

Every gap is the same: the differences run 14, 14, 14, so the common difference is 14. Applying it once more to the final term, 53 + 14 gives 67. As a check, subtracting 14 from the answer returns 53, the term before it, and repeating that recovers the whole series. The last term is the one most often misread, and re-checking it costs nothing.

Answer: A

Correct answer: 103

Every gap is the same: the differences run 25, 25, 25, so the common difference is 25. Applying it once more to the final term, 78 + 25 gives 103. As a check, subtracting 25 from the answer returns 78, the term before it, and repeating that recovers the whole series. Odd and even terms behaving differently is the first sign of an interleaved rather than a single series.

Answer: B

Correct answer: 106

Every gap is the same: the differences run 22, 22, 22, so the common difference is 22. Applying it once more to the final term, 84 + 22 gives 106. As a check, subtracting 22 from the answer returns 84, the term before it, and repeating that recovers the whole series. A large jump between two terms usually means multiplication rather than addition.

Answer: C

Correct answer: 132

Every gap is the same: the differences run -17, -17, -17, so the common difference is -17. Applying it once more to the final term, 149 - 17 gives 132. As a check, subtracting -17 from the answer returns 149, the term before it, and repeating that recovers the whole series. Where every term is even, the rule usually involves a factor of two somewhere.

Answer: D

Correct answer: 79

Every gap is the same: the differences run 13, 13, 13, so the common difference is 13. Applying it once more to the final term, 66 + 13 gives 79. As a check, subtracting 13 from the answer returns 66, the term before it, and repeating that recovers the whole series. Units digits often follow a short cycle, which can confirm an answer without the full arithmetic.

Answer: A

Correct answer: 0

Every gap is the same: the differences run -9, -9, -9, -9, so the common difference is -9. Applying it once more to the final term, 9 - 9 gives 0. As a check, subtracting -9 from the answer returns 9, the term before it, and repeating that recovers the whole series. A quick estimate of the expected size of the answer eliminates at least one option in most questions of this kind.

Answer: B

Correct answer: 80

Every gap is the same: the differences run 18, 18, 18, so the common difference is 18. Applying it once more to the final term, 62 + 18 gives 80. As a check, subtracting 18 from the answer returns 62, the term before it, and repeating that recovers the whole series. The options are constructed so that each corresponds to a specific misreading, which makes guessing unprofitable.