Number Series Practice Test Questions for Logical Reasoning

This is a simple alternating subtraction series, which subtracts 4, then 7: 48 - 4 = 44.

This is a simple addition series with a random number, 4, interpolated as every other number. In the series, 5 is added to each number except 4, to arrive at the next number: 12, 17, 22.

This alternating addition series begins with 5; then 2 is added to give 7; then 5 is added to give 12; then 2 is added, and so on: 21 + 5 = 26.

This is a simple subtraction series. Each number is 8 less than the previous number: 63 - 8 = 55.

In this alternating repetition series, the number 17 is interpolated every other number into an otherwise simple addition series that increases by 3, beginning with the number 4: 4, 7, 10, 13.

In this series, each number is repeated, then 12 is subtracted to arrive at the next number: 66 - 12 = 54.

In this alternating subtraction and addition series, 2 is subtracted, then 3 is added, and so on: 30 + 3 = 33.

This is an alternating number subtraction series. First, 3 is subtracted, then 6, then 3, and so on: 32 - 3 = 29.

This is a simple alternating addition and subtraction series. In the first pattern, 4 is added; in the second, 2 is subtracted: 5, 9, 7, 11, 9, 13, 11.

This is a simple division series; each number is one-third of the previous number: (1/9) / 3 = (1/27).

This is an alternating series. The first series begins with 6 and adds 4 (6, 10, 14, 18); the second begins with 50 and subtracts 3 (50, 47, 44). The blank is 14.

In this series, 4 is added to the previous number; the number 40 is inserted as every third number: 51, 55, 59, 63, 67. The blank is 63.

This is a simple addition series of Roman numerals; each number is 4 more than the previous number: 3, 7, 11, 15, 19, 23. The blank is XIX.

This is an alternating division and addition series: first divide by 2, then add 10. 372 / 2 = 186, 186 + 10 = 196, 196 / 2 = 98.

The letters decrease by 1 and the numbers are multiplied by 2: H5, G10, F20, E40, D80.

Each term is multiplied by 2.5, then 3.5, then 4.5: 7 × 2.5 = 17.5, 17.5 × 3.5 = 61.25 and 61.25 × 4.5 = 275.625.

An 8 qualifies only if it is exactly divisible by both its neighbours. Checking each 8: 3-8-6 no, 6-8-8 no, 8-8-7 no, 6-8-3 no, 4-8-2 yes, 2-8-2 yes, 4-8-6 no, 4-8-4 yes, 5-8-4 no.
So 3 eights qualify, which is fewer than 4.

A 7 qualifies only when both neighbours are perfect squares (0, 1, 4 or 9). Checking each 7 by its neighbours: 3-7-9 no, 9-7-4 yes, 9-7-2 no, 1-7-4 yes, 4-7-9 yes, 9-7-1 yes, 4-7-1 yes.
So 5 sevens qualify.

The 9s that are preceded by 5 are followed by 6, 7, 4, 4 and 3 in turn (5 in all).
Excluding the one followed by 7 leaves 4.

The differences are 76, 108 and 140, which increase by 32 each time. The next difference is 172.
So the next term = 380 + 172 = 552.

The series follows an alternating pattern of +4, +2:
7 (+4) 11 (+2) 13 (+4) 17 (+2) 19 (+4) 23 (+2) 25 (+4) 29 (+2) ?
Following the pattern, the next difference is +2: 29 + 2 = 31

The series alternates between ×2+1 and ×2-1:
6 ×2+1→ 13 ×2-1→ 25 ×2+1→ 51 ×2-1→ 101 ×2+1→ ?
101 × 2 + 1 = 203

The series alternates between +5 and -2:
28 (+5) 33 (-2) 31 (+5) 36 (-2) 34 (+5) 39 (-2) ?
39 - 2 = 37

The series is a sequence of consecutive prime numbers: 23, 29, 31, 37, 41, 43 are all prime.
The next prime number after 43 is 47.

The series alternates between +6 and -3:
18 (+6) 24 (-3) 21 (+6) 27 (-3) ? (+6) 30 (-3) 27
Missing term = 27 - 3 = 24

The differences between consecutive terms double each time:
7-5=2, 11-7=4, next difference=8, 35-?=16, 67-35=32
Missing term = 11 + 8 = 19 (and indeed 35-19=16, 67-35=32, confirming the doubling pattern)

The series is consecutive perfect squares: 2², 3², 4², 5², 6², 7²
Next term = 8² = 64

Each term is the sum of the previous three terms (a tribonacci-style pattern):
1 + 3 + 4 = 8 ✓
3 + 4 + 8 = 15 ✓
4 + 8 + 15 = 27 ✓
Next term = 8 + 15 + 27 = 50

Each term is a cumulative sum of squares: 1², 1²+2², 1²+2²+3², and so on:
1, 1+4=5, 5+9=14, 14+16=30, 30+25=55, 55+36=91
Next term = 91 + 7² = 91 + 49 = 140

The series increases by 22 each time: 121, 143, 165, 187, 209
186 does not fit this pattern; the correct term should be 187

Each term follows n³ - 1: 2³ - 1 = 7, 3³ - 1 = 26, 4³ - 1 = 63, 5³ - 1 = 124, 6³ - 1 = 215, 7³ - 1 = 342
Next term = 8³ - 1 = 511

Each term follows the pattern ×2 + 1: 2 × 2 + 1 = 5, 5 × 2 + 1 = 11, 11 × 2 + 1 = 23, 23 × 2 + 1 = 47
Next term = 47 × 2 + 1 = 95

Each term follows (2n-1)(2n+1) for n = 1, 2, 3...: 1×3 = 3, 3×5 = 15, 5×7 = 35, 7×9 = 63, 9×11 = 99, 11×13 = 143
Missing (3rd) term = 35

Each term follows the pattern ×2 + 1: 3 × 2 + 1 = 7, 7 × 2 + 1 = 15, 15 × 2 + 1 = 31, 31 × 2 + 1 = 63, 63 × 2 + 1 = 127
Missing term = 31

This is two interleaved series. The 1st, 3rd, 5th, 7th and 9th terms (4, 10, 22, 46, ?) have differences that double each time: +6, +12, +24, so the next difference is +48, giving 46 + 48 = 94. The 2nd, 4th, 6th and 8th terms (7, 11, 17, 25) separately increase by +4, +6, +8.

This is two interleaved series. The 1st, 3rd, 5th and 7th terms (7, 16, 25, ?) increase by +9 each time, giving 25 + 9 = 34. The 2nd, 4th and 6th terms (11, 23, 35) separately increase by +12 each time.

This is the series of consecutive odd numbers, each increasing by 2. The next term after 17 is 19.

The differences between consecutive terms increase by 4 each time: +9, +13, +17, +21. The next difference is +25, giving 65 + 25 = 90.

Each term follows the pattern n x (n+1): 1x2=2, 2x3=6, 3x4=12, 4x5=20, 5x6=30. The next term is 6x7=42.

The differences between consecutive terms are powers of 3: 6-5=1(3⁰), 9-6=3(3¹), 18-9=9(3²), 45-18=27(3³). The next difference is 3⁴=81, giving 45 + 81 = 126.

Each term is obtained from the previous term using the rule: multiply by 4 and subtract the term's position minus 1. 1x4-1=3, 3x4-2=10, 10x4-3=37. Continuing the pattern, the next term is 37x4-4=144.

The differences between consecutive terms are consecutive odd numbers: +3, +5, +7. The next difference is +9, giving 19 + 9 = 28.

This is two interleaved series. The 1st, 3rd, 5th and 7th terms are squares of consecutive odd numbers: 1²=1, 3²=9, 5²=25, 7²=49. The 2nd, 4th, 6th and 8th terms are cubes of consecutive even numbers: 2³=8, 4³=64, 6³=216, 8³=512. So the two missing terms are 49 and 512.

This is the factorial series: 0!=1, 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720.

Two interleaved series: odd positions divide by 5 each time (625,125,25,5); even positions multiply by 5 each time (5,25,125). The missing (6th) term is 125.

The multipliers are 3, 3, 5, 5. 5 × 3 = 15, 15 × 3 = 45, 45 × 5 = 225, so the next term is 225 × 5 = 1125.

The terms at the odd places are 28, 31, 34, which increase by 3. The terms at the even places are 33, ?, 39, which also increase by 3. So the missing term = 33 + 3 = 36.

The differences between the terms are 66, 55, 44, 33, 22, 11, decreasing by 11 each time. So the missing term = 127 - 22 = 105, and 105 - 11 = 94 fits the last term.

The differences are 3, 4, 5, 6, 7, increasing by 1. So the missing term = 13 + 6 = 19, and 19 + 7 = 26 fits the last term.

The differences are 22 each time (143 - 121 = 22). So the next term = 187 + 22 = 209.

The series follows the operations +1, ×1, +2, ×2, +3, ×3, +4, ×4, +5: 2 + 1 = 3, 3 × 1 = 3, 3 + 2 = 5, 5 × 2 = 10, 10 + 3 = 13, 13 × 3 = 39, 39 + 4 = 43, 43 × 4 = 172, 172 + 5 = 177. The missing term is 43.

The terms are 3 + 1, 9 + 1, 27 + 1, 81 + 1, 243 + 1, 729 + 1, that is 3ⁿ + 1. The missing term is 81 + 1 = 82.

The odd places carry cubes (1³, 3³, 5³, 7³ = 1, 27, 125, 343) and the even places carry squares (2², 4², 6² = 4, 16, 36). So the missing term is 6² = 36.

The rule alternates ×2 + 1 and ×2 - 1: 2 × 2 + 1 = 5, 5 × 2 - 1 = 9, 9 × 2 + 1 = 19, 19 × 2 - 1 = 37, so the next term is 37 × 2 + 1 = 75.

Separate the alternate terms. The odd places give 3, 8, 13, 18, 23 (+5 each). The even places give 2, 12, ?, 32, 42, which should increase by 10 each time: 2, 12, 22, 32, 42. So the term 24 should be 22, and 24 is the wrong term.

The terms at the even places are 126, 127, 128 (+1 each). The terms at the odd places should be 125, 124, 123 (-1 each). So 122 is the wrong term and should be 123.

The pattern alternates ×2 + 1 and ×3 + 1: 1 × 2 + 1 = 3, 3 × 3 + 1 = 10, 10 × 2 + 1 = 21, 21 × 3 + 1 = 64, 64 × 2 + 1 = 129. So 63 is the wrong term and should be 64.

The differences should be 1, 4, 9, 16, 25 (squares). 15 + 1 = 16, 16 + 4 = 20, 20 + 9 = 29, 29 + 16 = 45, 45 + 25 = 70. So 30 is the wrong term and should be 29.

The series follows +4, ×2 alternately: 10 + 4 = 14, 14 × 2 = 28, 28 + 4 = 32, 32 × 2 = 64, 64 + 4 = 68, 68 × 2 = 136. So 34 is the wrong term and should be 32.

The differences follow the pattern +3, +2, +1 repeated: 4, 7, 9, 10, 13, 15, 16, then +3 gives 19. So 20 is the wrong term and should be 19.

The differences are 4, 6, 8, 10, 12 and then 14. So the last term should be 41 + 14 = 55, and 56 is the wrong term.

The series is the Fibonacci pattern, where each term is the sum of the previous two: 2, 3, 5, 8, 13, 21, 34. So 20 is the wrong term and should be 21.

The terms are the squares of 14, 13, 12, 11, 10 and then 9, that is 196, 169, 144, 121, 100, 81. So 80 is the wrong term and should be 81.

The terms are n² - 1: 2² - 1 = 3, 3² - 1 = 8, 4² - 1 = 15, 5² - 1 = 24, 6² - 1 = 35, 7² - 1 = 48, 8² - 1 = 63. So 49 is the wrong term and should be 48.

The differences are 8, 8, 16, 16, 24, 24.
So the next term = 135 + 24 = 159.

This is a simple addition series: each number increases by 0.7. So 4.5 + 0.7 = 5.2.

This is a simple addition series: each number increases by 0.9. So 3.3 + 0.9 = 4.2.

This series alternates between multiplying by 3 and subtracting 7: 9 × 3 = 27, 27 − 7 = 20, 20 × 3 = 60, 60 − 7 = 53. The next step is a multiplication: 53 × 3 = 159.

This series alternates between multiplying by 2 and subtracting 5: 12 × 2 = 24, 24 − 5 = 19, 19 × 2 = 38, 38 − 5 = 33. The next step is a multiplication: 33 × 2 = 66.

This is a simple addition series: each number increases by 3. So 15 + 3 = 18.

This is a simple addition series: each number increases by 5. So 27 + 5 = 32.

The amount added goes up by 1 each time: 105 + 1 = 106, 106 + 2 = 108, 108 + 3 = 111, 111 + 4 = 115. Next, 5 is added: 115 + 5 = 120.

The amount added goes up by 2 each time: +2, +4, +6, +8. Next, 10 is added: 70 + 10 = 80.

This is a simple subtraction series: each number is 47 less than the one before. So 791 − 47 = 744.

This is a simple subtraction series: each number is 27 less than the one before. So 534 − 27 = 507.

Two series alternate. The 1st, 3rd and 5th numbers fall by 9 (90, 81, 72), and the 2nd and 4th numbers rise by 5 (12, 17). The 6th number belongs to the second series: 17 + 5 = 22.

Two series alternate. The 1st, 3rd and 5th numbers fall by 8 (64, 56, 48), and the 2nd and 4th numbers rise by 4 (5, 9). The 6th number belongs to the second series: 9 + 4 = 13.

This is a simple multiplication series: each number is 4 times the one before. So 192 × 4 = 768.

This is a simple multiplication series: each number is 2 times the one before. So 80 × 2 = 160.

This is a simple subtraction series: each number decreases by 0.7. So 7.0 − 0.7 = 6.3.

This is a simple subtraction series: each number decreases by 0.3. So 5.6 − 0.3 = 5.3.

Each number is multiplied by 1, 2, 3, ... and then the same number is added:
3 × 1 + 1 = 4
4 × 2 + 2 = 10
10 × 3 + 3 = 33
33 × 4 + 4 = 136

Each number is multiplied by 1, 2, 3, ... and then the same number is subtracted:
5 × 1 − 1 = 4
4 × 2 − 2 = 6
6 × 3 − 3 = 15
15 × 4 − 4 = 56