Number Series Aptitude MCQ Questions with Answers Set 02

Answer: (d) 33

Explanation:
1. Differences: 12 - 6 = 6, 21 - 12 = 9, next differences go up by 3.
2. So the differences are 6, 9, 12, 15.
3. Missing term = 21 + 12 = 33; check: 33 + 15 = 48.

Teacher's Note:
1. Always write the differences between consecutive terms first; most slow-growing series are solved at this step.
2. If the first differences are not constant, take the differences of the differences (second differences).

Answer: (d) 88

Explanation:
1. Differences: +8, +10, +12, +14, +16 (increase by 2).
2. Next difference = +18.
3. Next term = 70 + 18 = 88.

Teacher's Note:
1. Always write the differences between consecutive terms first; most slow-growing series are solved at this step.
2. If the first differences are not constant, take the differences of the differences (second differences).

Answer: (d) 28

Explanation:
1. Differences: +5, +9, then they increase by 4 each time.
2. Differences: 5, 9, 13, 17, 21, 25.
3. Missing term = 15 + 13 = 28; check 28 + 17 = 45.

Teacher's Note:
1. Always write the differences between consecutive terms first; most slow-growing series are solved at this step.
2. If the first differences are not constant, take the differences of the differences (second differences).

Answer: (b) 81

Explanation:
1. Differences: +5, +10, +15, +20 (multiples of 5).
2. Next difference = +25.
3. Next term = 56 + 25 = 81.

Teacher's Note:
1. Always write the differences between consecutive terms first; most slow-growing series are solved at this step.
2. If the first differences are not constant, take the differences of the differences (second differences).

Answer: (d) 24

Explanation:
1. Differences: +2, +6, +6, then +10, +10.
2. After the first step each difference is used twice and then increases by 4.
3. Missing term = 14 + 10 = 24; check 24 + 10 = 34.

Teacher's Note:
1. Always write the differences between consecutive terms first; most slow-growing series are solved at this step.
2. If the first differences are not constant, take the differences of the differences (second differences).

Answer: (d) 1

Explanation:
1. Differences: +0.05, +0.10, +0.15.
2. Next difference = +0.20.
3. Next term = 0.8 + 0.20 = 1.

Teacher's Note:
1. Always write the differences between consecutive terms first; most slow-growing series are solved at this step.
2. If the first differences are not constant, take the differences of the differences (second differences).

Answer: (b) 34

Explanation:
1. The pattern alternates: +5, -2, +5, -2, +5.
2. 28 + 5 = 33, 33 - 2 = 31, 31 + 5 = 36.
3. Missing term = 36 - 2 = 34; check 34 + 5 = 39.

Teacher's Note:
1. Always write the differences between consecutive terms first; most slow-growing series are solved at this step.
2. If the first differences are not constant, take the differences of the differences (second differences).

Answer: (d) 128

Explanation:
1. Differences: +11.5, +12.5, +13.5, +14.5 (each 1 more).
2. Next difference = +15.5.
3. Next term = 112.5 + 15.5 = 128.

Teacher's Note:
1. Always write the differences between consecutive terms first; most slow-growing series are solved at this step.
2. If the first differences are not constant, take the differences of the differences (second differences).

Answer: (d) 478

Explanation:
1. Differences: +14, +21, +28, +35, +42 (multiples of 7).
2. Next difference = +49.
3. Next term = 429 + 49 = 478.

Teacher's Note:
1. Always write the differences between consecutive terms first; most slow-growing series are solved at this step.
2. If the first differences are not constant, take the differences of the differences (second differences).

Answer: (b) 127

Explanation:
1. Differences: +5, +7, +11, +13, +17 - consecutive prime numbers.
2. Next prime = 19.
3. Next term = 108 + 19 = 127.

Teacher's Note:
1. Always write the differences between consecutive terms first; most slow-growing series are solved at this step.
2. If the first differences are not constant, take the differences of the differences (second differences).

Answer: (b) 728

Explanation:
1. Terms are powers of 3 with +1 and -1 alternately.
2. 3¹ + 1 = 4, 3² - 1 = 8, 3³ + 1 = 28, 3⁴ - 1 = 80, 3⁵ + 1 = 244.
3. Next term = 3⁶ - 1 = 729 - 1 = 728.

Teacher's Note:
1. Memorise squares up to 25 and cubes up to 20; series built on them become instant to spot.
2. When numbers sit close to a square or cube, check whether a fixed amount is being added or subtracted.

Answer: (b) 247

Explanation:
1. Differences: -1, +8, -27, +64, -125 = -1³, +2³, -3³, +4³, -5³.
2. Next difference = +6³ = +216.
3. Next term = 31 + 216 = 247.

Teacher's Note:
1. Memorise squares up to 25 and cubes up to 20; series built on them become instant to spot.
2. When numbers sit close to a square or cube, check whether a fixed amount is being added or subtracted.

Answer: (b) 823543

Explanation:
1. Each term is nⁿ: 1¹, 2², 3³, 4⁴, 5⁵, 6⁶.
2. Next term = 7⁷ = 823543.

Teacher's Note:
1. Memorise squares up to 25 and cubes up to 20; series built on them become instant to spot.
2. When numbers sit close to a square or cube, check whether a fixed amount is being added or subtracted.

Answer: (d) None of these

Explanation:
1. Differences: +49, +36, +25 = +7², +6², +5².
2. Next difference = +4² = +16.
3. Next term = 214 + 16 = 230, which is not among options a to c.

Teacher's Note:
1. Memorise squares up to 25 and cubes up to 20; series built on them become instant to spot.
2. When numbers sit close to a square or cube, check whether a fixed amount is being added or subtracted.

Answer: (d) None of these

Explanation:
1. Differences: +4, +27, +16, +125, +36.
2. These are 2², 3³, 4², 5³, 6² - square and cube alternately.
3. Next difference = 7³ = 343, so next term = 210 + 343 = 553, which is not listed.

Teacher's Note:
1. Memorise squares up to 25 and cubes up to 20; series built on them become instant to spot.
2. When numbers sit close to a square or cube, check whether a fixed amount is being added or subtracted.

Answer: (b) 122

Explanation:
1. 6 x 2 + 1 = 13, 13 x 2 + 2 = 28, 28 x 2 + 3 = 59.
2. The pattern is x 2 and then add 1, 2, 3, 4, ...
3. Next term = 59 x 2 + 4 = 122.

Teacher's Note:
1. When terms grow roughly two or three times each step, divide each term by the previous one to find the multiplier.
2. Check patterns of the form (term x n) + k, where n or k changes in a regular way.

Answer: (b) 12285

Explanation:
1. Multipliers: x 1, x 1.5, x 2.5, x 4, x 6.5.
2. Each multiplier is the sum of the two before it (1 + 1.5 = 2.5, 1.5 + 2.5 = 4, 2.5 + 4 = 6.5), so the next is 4 + 6.5 = 10.5.
3. Next term = 1170 x 10.5 = 12285.

Teacher's Note:
1. When terms grow roughly two or three times each step, divide each term by the previous one to find the multiplier.
2. Check patterns of the form (term x n) + k, where n or k changes in a regular way.

Answer: (c) 354

Explanation:
1. Each term is one-third of the previous term: 2916 / 3 = 972.
2. 972 / 3 = 324, not 354; and 324 / 3 = 108 continues correctly.
3. So 354 is the wrong term.

Teacher's Note:
1. To find the wrong term, first identify the rule using the majority of terms, then test each term against it.
2. Once a term fails, recompute what it should be; this confirms you have the right rule.

Answer: (b) 19753

Explanation:
1. 23 x 1 + 2 = 25, 25 x 2 + 3 = 53, 53 x 3 + 4 = 163.
2. 163 x 4 + 5 = 657, 657 x 5 + 6 = 3291.
3. Next term = 3291 x 6 + 7 = 19753.

Teacher's Note:
1. When terms grow roughly two or three times each step, divide each term by the previous one to find the multiplier.
2. Check patterns of the form (term x n) + k, where n or k changes in a regular way.

Answer: (d) 5.12

Explanation:
1. Each term is 2/5 of the previous: 1250 x 2/5 = 500, 500 x 2/5 = 200, and so on.
2. Next term = 12.8 x 2/5 = 5.12.

Teacher's Note:
1. For decreasing series, divide each term by the next one to find the dividing factor.
2. Factors may alternate (like 5, 2.5, 5) or decrease steadily (like 5, 4, 3, 2).

Answer: (b) 114.24

Explanation:
1. 89250 / 5 = 17850, 17850 / 2.5 = 7140.
2. 7140 / 5 = 1428, 1428 / 2.5 = 571.2 - divisors alternate 5 and 2.5.
3. Next term = 571.2 / 5 = 114.24.

Teacher's Note:
1. For decreasing series, divide each term by the next one to find the dividing factor.
2. Factors may alternate (like 5, 2.5, 5) or decrease steadily (like 5, 4, 3, 2).

Answer: (b) 308

Explanation:
1. 3 x 3 + 1 = 10, 10 x 3 + 2 = 32, 32 x 3 + 4 = 100.
2. The added number doubles each time: 1, 2, 4, 8.
3. Next term = 100 x 3 + 8 = 308.

Teacher's Note:
1. When terms grow roughly two or three times each step, divide each term by the previous one to find the multiplier.
2. Check patterns of the form (term x n) + k, where n or k changes in a regular way.

Answer: (b) 16.5

Explanation:
1. 17 x 0.5 + 0.5 = 9, 9 x 1 + 1 = 10.
2. The multiplier and the number added both increase by 0.5 each step.
3. Missing term = 10 x 1.5 + 1.5 = 16.5; check 16.5 x 2 + 2 = 35 and 35 x 2.5 + 2.5 = 90.

Teacher's Note:
1. When terms grow roughly two or three times each step, divide each term by the previous one to find the multiplier.
2. Check patterns of the form (term x n) + k, where n or k changes in a regular way.

Answer: (b) 405

Explanation:
1. 13 x 2 - 1 = 25, 25 x 2 + 1 = 51, 51 x 2 - 1 = 101, 101 x 2 + 1 = 203.
2. The pattern is x 2 with -1 and +1 alternately.
3. Next term = 203 x 2 - 1 = 405.

Teacher's Note:
1. When terms grow roughly two or three times each step, divide each term by the previous one to find the multiplier.
2. Check patterns of the form (term x n) + k, where n or k changes in a regular way.

Answer: (d) None of these

Explanation:
1. Differences: +23, +46, +69, +92, +115 = 23 x 1, 23 x 2, ..., 23 x 5.
2. Next difference = 23 x 6 = 138.
3. Next term = 1050 + 138 = 1188, which is not listed.

Teacher's Note:
1. Always write the differences between consecutive terms first; most slow-growing series are solved at this step.
2. If the first differences are not constant, take the differences of the differences (second differences).

Answer: (b) 141

Explanation:
1. Differences: +2, +4, +8, +16, +32 (doubling).
2. Next difference = +64.
3. Next term = 77 + 64 = 141.

Teacher's Note:
1. Always write the differences between consecutive terms first; most slow-growing series are solved at this step.
2. If the first differences are not constant, take the differences of the differences (second differences).

Answer: (b) 26

Explanation:
1. Odd positions: 10, 8, 6 (decrease by 2).
2. Even positions: 22, 24, ? (increase by 2).
3. Missing term = 24 + 2 = 26.

Teacher's Note:
1. If the terms rise and fall irregularly, split the series into alternate terms and study each part separately.
2. Each hidden sub-series is usually a simple one: constant difference, constant ratio or squares.

Answer: (d) 10, 10

Explanation:
1. Odd positions: 20, 19, 17, 14, ? with differences -1, -2, -3, -4, giving 10.
2. Even positions: 20, 16, 13, 11, ? with differences -4, -3, -2, -1, giving 10.
3. The two missing terms are 10 and 10.

Teacher's Note:
1. If the terms rise and fall irregularly, split the series into alternate terms and study each part separately.
2. Each hidden sub-series is usually a simple one: constant difference, constant ratio or squares.

Answer: (d) 456

Explanation:
1. Even positions 2, 3, 4 are the multipliers.
2. 19 x 2 = 38, 38 x 3 = 114.
3. Next term = 114 x 4 = 456.

Teacher's Note:
1. If the terms rise and fall irregularly, split the series into alternate terms and study each part separately.
2. Each hidden sub-series is usually a simple one: constant difference, constant ratio or squares.

Answer: (b) 26

Explanation:
1. Odd positions: 23, 24, 25, ? (increase by 1).
2. Even positions: 26, 27, 28 (increase by 1).
3. Missing term = 25 + 1 = 26.

Teacher's Note:
1. If the terms rise and fall irregularly, split the series into alternate terms and study each part separately.
2. Each hidden sub-series is usually a simple one: constant difference, constant ratio or squares.

Answer: (d) 252

Explanation:
1. Each term is n³ + n²: 1 + 1 = 2, 8 + 4 = 12, 27 + 9 = 36, 64 + 16 = 80, 125 + 25 = 150.
2. Next term = 6³ + 6² = 216 + 36 = 252.
3. Equivalently, second differences 14, 20, 26 rise by 6: next first difference 70 + 32 = 102, and 150 + 102 = 252.

Teacher's Note:
1. Memorise squares up to 25 and cubes up to 20; series built on them become instant to spot.
2. When numbers sit close to a square or cube, check whether a fixed amount is being added or subtracted.

Answer: (b) 65

Explanation:
1. Each term is n³ + 1: 1 + 1 = 2, 8 + 1 = 9, 27 + 1 = 28.
2. Missing term = 4³ + 1 = 65.
3. Check: 5³ + 1 = 126, 6³ + 1 = 217, 7³ + 1 = 344.

Teacher's Note:
1. Memorise squares up to 25 and cubes up to 20; series built on them become instant to spot.
2. When numbers sit close to a square or cube, check whether a fixed amount is being added or subtracted.

Answer: (d) 468

Explanation:
1. First differences: 17, 43, 81, 131; second differences: 26, 38, 50; third differences: 12, 12.
2. Next second difference = 50 + 12 = 62, next first difference = 131 + 62 = 193.
3. Next term = 275 + 193 = 468 (also equals 6² x 13).

Teacher's Note:
1. Always write the differences between consecutive terms first; most slow-growing series are solved at this step.
2. If the first differences are not constant, take the differences of the differences (second differences).

Answer: (b) 48

Explanation:
1. Each term is the product of the two terms before it: 3 x 4 = 12.
2. Missing term = 4 x 12 = 48.
3. Check: 12 x 48 = 576 and 48 x 576 = 27648.

Teacher's Note:
1. If no arithmetic pattern appears, try digit operations, sums of previous terms or a different number base.
2. Test your rule on every given term, not just the first two or three, before choosing an option.

Answer: (b) 194

Explanation:
1. Number in brackets = product of the two outer numbers - 1.
2. 13 x 13 - 1 = 168, 14 x 13 - 1 = 181.
3. Missing number = 15 x 13 - 1 = 194.

Teacher's Note:
1. If no arithmetic pattern appears, try digit operations, sums of previous terms or a different number base.
2. Test your rule on every given term, not just the first two or three, before choosing an option.

Answer: (d) None of these

Explanation:
1. Pattern: x 1 + 1², x 2 + 2², x 3 + 3², x 4 + 4².
2. 5 x 1 + 1 = 6, 6 x 2 + 4 = 16.
3. Check: 16 x 3 + 9 = 57, 57 x 4 + 16 = 244. The missing term 16 is not listed.

Teacher's Note:
1. When terms grow roughly two or three times each step, divide each term by the previous one to find the multiplier.
2. Check patterns of the form (term x n) + k, where n or k changes in a regular way.