Number Series Questions and Answers

Answer: B

The missing number is 182.

Each term is the product of two consecutive numbers:

\[ \begin{aligned} 132 &= 11 \times 12 \\ 156 &= 12 \times 13 \\ ? &= 13 \times 14 = 182 \\ 210 &= 14 \times 15 \end{aligned} \]

The pattern continues with \(240 = 15 \times 16\) and \(272 = 16 \times 17\). The differences 24, 26, 28, 30, 32 confirm it.

Answer: B

The missing number is 77.

In each row, the middle number is 7 times the difference between the left and right numbers:

\[ \begin{aligned} 7 \times (44 - 37) &= 49 \\ 7 \times (58 - 53) &= 35 \\ 7 \times (52 - 41) &= 77 \end{aligned} \]

The other options do not fit this rule for the second row.

Answer: D

The missing number is 204.

The series alternates subtraction and multiplication, with the step growing by one each time:

\[ \begin{aligned} 20 - 2 &= 18 \\ 18 \times 3 &= 54 \\ 54 - 3 &= 51 \\ 51 \times 4 &= 204 \\ 204 - 5 &= 199 \\ 199 \times 6 &= 1194 \end{aligned} \]

The last two terms confirm the rule. 48 would continue subtracting, 153 multiplies 51 by 3 rather than 4, and 194 fits neither step.

Answer: D

The next term is 4912. Each term is one less than the cube of a prime number. 7 = 2 cubed minus 1, 26 = 3 cubed minus 1, 124 = 5 cubed minus 1, 342 = 7 cubed minus 1, 1330 = 11 cubed minus 1, and 2196 = 13 cubed minus 1. The next prime after 13 is 17, and 17 cubed is 4913, so the term is 4913 - 1 = 4912. The options 2743, 3374 and 4095 are one less than 14 cubed (2744), 15 cubed (3375) and 16 cubed (4096), which are not primes, so they break the pattern.

Answer: B

The next number is 56. The series is two interleaved series: 35, 42, 49, ... goes up by 7 each time, and the second one is just the number 7 repeated. The terms are 35, 7, 42, 7, 49, 7 and then the series of sevens' multiples continues with \(49 + 7 = 56\). The number 63 would be the term after that, 14 and 21 are not terms of the increasing series, and the repeated 7 comes only at every second place, so the question mark, which falls at the odd place, takes 56.

Answer: D

The next number is 1280. Each term is four times the one before: \[ 5\times 4 = 20 \] \[ 20\times 4 = 80 \] \[ 80\times 4 = 320 \] \[ 320\times 4 = 1280 \] The other options 600, 900 and 1180 do not follow from multiplying by 4, and the ratio of consecutive terms in the printed part of the series is fixed at 4, so any answer not equal to 1280 breaks the pattern.

Answer: D

The next number is 27. The series is made up of two alternating series. The terms in the first, third and fifth places are 15, 19 and 23, which go up by 4, so the next in that series is 27. The terms in the second, fourth and sixth places are 8, 12 and 16, also up by 4. The question mark falls at the seventh place, which belongs to the first series, so it is \(23 + 4 = 27\). The options 35, 40 and 45 are far from the pattern, and 20 would be the next term of the second series.

Answer: D

The terms are cubes of consecutive numbers: \(2^3 = 8\), \(3^3 = 27\), \(4^3 = 64\) and \(5^3 = 125\). So the next term is the cube of 6.

\[ 6^3 = 216 \]

The values 236, 276 and 225 do not follow the pattern: 225 is the square of 15 and the other two are not cubes. The answer is 216, option D.

Answer: D

The terms are the cubes of 3, 4, 5 and 6: \(27 = 3^3\), \(64 = 4^3\), \(125 = 5^3\) and \(216 = 6^3\). The next term is the cube of 7.

\[ 7^3 = 343 \]

The values 340, 341 and 342 are close to 343 but are not cubes. The answer is 343, option D.

As a check, the gaps between terms are 37, 61 and 91, which increase by 24 and 30, so the next gap is 36 more than 91, that is 127, and 216 + 127 = 343, which agrees with the cube of 7.

Answer: B

The next term is 218. Each term is double the previous term plus a number that rises by one each time: 12 x 2 + 1 = 25, 25 x 2 + 2 = 52, 52 x 2 + 3 = 107. The next step is 107 x 2 + 4 = 218. The other options, 216, 219 and 220, would need an added number of 2, 5 or 6, which breaks the sequence of +1, +2, +3, +4. The differences between the terms are 13, 27, 55, and each one equals the previous difference doubled plus 1, since 13 x 2 + 1 = 27 and 27 x 2 + 1 = 55. Both the terms and the differences follow the same rule, so the next difference is 111 and the term is 107 + 111 = 218.