Number Series Questions and Answers

Answer: C

Correct answer: 56

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, 43 + 13 gives 56. As a check, subtracting 13 from the answer returns 43, the term before it, and repeating that recovers the whole series. The distractors here sit one step either side of the answer, which is what a miscount of a single term produces.

Answer: D

Correct answer: 94

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, 108 - 14 gives 94. As a check, subtracting -14 from the answer returns 108, the term before it, and repeating that recovers the whole series. Once the difference is known the series can be extended in either direction, and checking backwards to the first term is a quick way to confirm it.

Answer: A

Correct answer: 36

Each term is a perfect square of consecutive whole numbers: \[ 1^2 = 1,\quad 2^2 = 4,\quad 3^2 = 9,\quad 4^2 = 16,\quad 5^2 = 25 \] so the next is \( 6^2 = \mathbf{36} \).

Answer: B

Correct answer: 91

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, 74 + 17 gives 91. As a check, subtracting 17 from the answer returns 74, the term before it, and repeating that recovers the whole series. Large differences are easier to handle by adding in parts, taking the tens and the units separately.

Answer: C

Correct answer: -7

Every gap is the same: the differences run -3, -3, -3, -3, so the common difference is -3. Applying it once more to the final term, -4 - 3 gives -7. As a check, subtracting -3 from the answer returns -4, the term before it, and repeating that recovers the whole series. A series that decreases will eventually pass zero and continue into negative numbers, which is worth remembering when the terms are already small.

Answer: D

Correct answer: 107

Every gap is the same: the differences run 19, 19, 19, so the common difference is 19. Applying it once more to the final term, 88 + 19 gives 107. As a check, subtracting 19 from the answer returns 88, the term before it, and repeating that recovers the whole series. The gap between the first and last shown terms divided by the number of steps gives the common difference directly, which is a useful check.

Answer: A

Correct answer: 90

Every gap is the same: the differences run 21, 21, 21, so the common difference is 21. Applying it once more to the final term, 69 + 21 gives 90. As a check, subtracting 21 from the answer returns 69, the term before it, and repeating that recovers the whole series. Arithmetic progressions appear more often than any other family in this topic, so they are worth eliminating quickly before looking for anything subtler.

Answer: B

Correct answer: 768

The terms are multiplied rather than added to. Dividing each by its predecessor gives the same result throughout: 12 over 3 is 4, and 48 over 12 is 4, so the ratio is 4. Multiplying the last term, 192 times 4 is 768. As a check, dividing the answer by 4 returns 192, which is the last term shown. Where the terms grow quickly a ratio is more likely than a difference, and dividing adjacent terms is the test.

Answer: C

Correct answer: 405

The terms are multiplied rather than added to. Dividing each by its predecessor gives the same result throughout: 15 over 5 is 3, and 45 over 15 is 3, so the ratio is 3. Multiplying the last term, 135 times 3 is 405. As a check, dividing the answer by 3 returns 135, which is the last term shown. A single pair of terms is consistent with both an addition and a multiplication rule, so at least two pairs must agree before a ratio can be trusted.

Answer: D

Correct answer: 10

Each term is 2 more than the one before - the even numbers in order - so after 8 comes \( 8 + 2 = \mathbf{10} \).