Number Series Questions and Answers

Answer: C

The next term is 33600.

Each term is the previous one multiplied by a number that falls by 1 each time:

\[ \begin{aligned} 5 \times 8 &= 40,\quad 40 \times 7 = 280 \\ 280 \times 6 &= 1680,\quad 1680 \times 5 = 8400 \\ 8400 \times 4 &= 33600 \end{aligned} \]

The other options are close to 33,600 but are not 8400 times any whole number in the pattern.

Answer: B

The next term is 45.

The differences are squares with alternating signs:

\[ \begin{aligned} 30 + 1^{2} &= 31,\quad 31 - 2^{2} = 27 \\ 27 + 3^{2} &= 36,\quad 36 - 4^{2} = 20 \\ 20 + 5^{2} &= 45 \end{aligned} \]

Subtracting 25 (as if the sign did not alternate) gives -5, and the other options do not fit the square pattern.

Patterns built on alternating additions and subtractions of squares (or cubes) are common in number-series questions; checking the differences 1, -4, 9, -16 shows it at once.

Answer: A

Correct answer: 13

The terms are the prime numbers in order - 2, 3, 5, 7, 11 - each divisible only by itself and 1. The next prime after 11 is 13; 12, 14 and 15 all have smaller factors.

Answer: B

Correct answer: 196

Each term is a perfect square of consecutive whole numbers: \[ 11^2 = 121,\quad 12^2 = 144,\quad 13^2 = 169 \] so the next is \( 14^2 = \mathbf{196} \).

Answer: C

Correct answer: 125

Each term is a perfect cube of consecutive whole numbers: \[ 1^3 = 1,\quad 2^3 = 8,\quad 3^3 = 27,\quad 4^3 = 64 \] so the next is \( 5^3 = \mathbf{125} \).

Answer: D

Correct answer: -2

Each term is 3 less than the one before: \( 10 - 3 = 7 \), \( 7 - 3 = 4 \), \( 4 - 3 = 1 \). Continuing past zero gives \[ 1 - 3 = \mathbf{-2} \]

Answer: A

Correct answer: 33

Every gap is the same: the differences run 7, 7, 7, so the common difference is 7. Applying it once more to the final term, 26 + 7 gives 33. As a check, subtracting 7 from the answer returns 26, the term before it, and repeating that recovers the whole series. A constant difference is the first thing to test on any number series, because it is the commonest rule and takes only two subtractions to rule in or out.

Answer: B

Correct answer: 48

Every gap is the same: the differences run 9, 9, 9, so the common difference is 9. Applying it once more to the final term, 39 + 9 gives 48. As a check, subtracting 9 from the answer returns 39, the term before it, and repeating that recovers the whole series. Where the difference is constant the series is an arithmetic progression, and its nth term can be written down directly rather than reached step by step.

Answer: C

Correct answer: 51

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, 40 + 11 gives 51. As a check, subtracting 11 from the answer returns 40, the term before it, and repeating that recovers the whole series. Subtracting each term from the next is worth doing before anything else; a row of identical results settles the matter immediately.

Answer: D

Correct answer: 66

The differences themselves form a pattern: \[ 100 - 96 = 4,\quad 96 - 89 = 7,\quad 89 - 79 = 10 \] each gap being 3 more than the last. The next gap is therefore 13, giving \[ 79 - 13 = \mathbf{66} \]