Number Series Questions and Answers

Answer: C

Correct answer: 67

The gaps are not equal: they run 5, 9, 13, 17, each 4 more than the last. The next gap must therefore be 21, and adding it to the final term, 46 plus 21 is 67. As a check, the gap between the answer and 46 is 21, which continues the run of gaps 5, 9, 13, 17 by a further 4. Writing the gaps under the terms converts an irregular series into a regular one, which is the standard technique for this family.

Answer: D

Correct answer: 67

The gaps are not equal: they run 2, 7, 12, 17, each 5 more than the last. The next gap must therefore be 22, and adding it to the final term, 45 plus 22 is 67. As a check, the gap between the answer and 45 is 22, which continues the run of gaps 2, 7, 12, 17 by a further 5. The gaps growing by a constant amount means the terms follow a quadratic rule, so they can also be produced by a formula in the position number.

Answer: A

Correct answer: 58

The gaps are not equal: they run 3, 5, 7, 9, 11, each 2 more than the last. The next gap must therefore be 13, and adding it to the final term, 45 plus 13 is 58. As a check, the gap between the answer and 45 is 13, which continues the run of gaps 3, 5, 7, 9, 11 by a further 2. Extending the row of differences by one entry and adding it to the last term is all that this family requires.

Answer: B

Correct answer: 91

The gaps are not equal: they run 6, 12, 18, 24, each 6 more than the last. The next gap must therefore be 30, and adding it to the final term, 61 plus 30 is 91. As a check, the gap between the answer and 61 is 30, which continues the run of gaps 6, 12, 18, 24 by a further 6. The commonest error here is to repeat the last gap rather than to extend the pattern the gaps themselves follow.

Answer: C

Correct answer: 50

The gaps are not equal: they run 1, 5, 9, 13, each 4 more than the last. The next gap must therefore be 17, and adding it to the final term, 33 plus 17 is 50. As a check, the gap between the answer and 33 is 17, which continues the run of gaps 1, 5, 9, 13 by a further 4. A second row of differences that is constant confirms the reading, and it is worth writing out before committing to an answer.

Answer: D

Correct answer: 54

The steps run 3, 5, 11, 5, 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 27 gives 54. As a check, the step from 27 to the answer is 27, which breaks the run of preceding gaps exactly as an alternating rule demands. Two operations applied in turn produce differences that grow and then fall back, which is the signature of this family.

Answer: A

Correct answer: 102

The steps run 4, 4, 20, 4, 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 34 gives 102. As a check, the step from 34 to the answer is 68, which breaks the run of preceding gaps exactly as an alternating rule demands. Reading the steps in pairs rather than singly is what makes an alternating rule visible.

Answer: B

Correct answer: 82

The steps run 5, 7, 17, 7, 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 41 gives 82. As a check, the step from 41 to the answer is 41, which breaks the run of preceding gaps exactly as an alternating rule demands. An alternating series needs the position counted carefully, since the operation due next depends on how many steps have already been taken.

Answer: C

Correct answer: 180

The steps run 8, 6, 36, 6, 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 60 gives 180. As a check, the step from 60 to the answer is 120, which breaks the run of preceding gaps exactly as an alternating rule demands. The distractor formed by applying the wrong operation is always among the options in questions of this shape.

Answer: D

Correct answer: 11

Two series have been laid down alternately. The terms in the odd positions are 2, 5, 8, which rise steadily, and those in the even positions are 50, 45, 40, which fall. The missing term continues the first of these, giving 11. As a check, the answer differs from the term two places before it by 3, which is the step that strand has taken throughout. Interleaved series are recognised by terms that jump between two quite different ranges rather than moving steadily.