Number Series Aptitude MCQ Questions with Answers Set 03

Answer: (d) 211

Explanation:
1. Each term is the sum of the two terms before it: 15 + 17 = 32, 17 + 32 = 49.
2. 32 + 49 = 81, 49 + 81 = 130.
3. Next term = 81 + 130 = 211.

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) 11011000

Explanation:
1. Read the terms as binary numbers: 1, 8, 27, 64, 125.
2. These are cubes 1³, 2³, 3³, 4³, 5³.
3. Next = 6³ = 216, which in binary is 11011000.

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) 52

Explanation:
1. Differences: +5, +7, +9, +11 (odd numbers).
2. Next difference = +13.
3. Next term = 39 + 13 = 52.

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) 56

Explanation:
1. Differences: +1, +4, +9, +16 = 1², 2², 3², 4².
2. Next difference = 5² = 25.
3. Next term = 31 + 25 = 56.

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: (a) 191

Explanation:
1. Each term = previous x 2 + 1: 5 x 2 + 1 = 11, 11 x 2 + 1 = 23.
2. Next term = 95 x 2 + 1 = 191.
3. Also the differences 6, 12, 24, 48 double, giving 95 + 96 = 191.

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: (a) 354

Explanation:
1. Differences: +11, +22, +44, +88 (doubling).
2. Next difference = +176.
3. Next term = 178 + 176 = 354 (also 178 x 2 - 2).

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: (c) 111

Explanation:
1. Differences: +1, +8, +27 = 1³, 2³, 3³.
2. Next difference = 4³ = 64.
3. Next term = 47 + 64 = 111.

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) 255

Explanation:
1. Each term = previous x 2 + 1: 7 x 2 + 1 = 15, 15 x 2 + 1 = 31.
2. Next term = 127 x 2 + 1 = 255.
3. The terms are also 2ⁿ - 1: 8 - 1, 16 - 1, ..., 256 - 1.

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) 837

Explanation:
1. Pattern: x 2 + prime numbers 2, 3, 5, 7, ...
2. 23 x 2 + 2 = 48, 48 x 2 + 3 = 99, 99 x 2 + 5 = 203, 203 x 2 + 7 = 413.
3. Next term = 413 x 2 + 11 = 837.

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) 235

Explanation:
1. 7 x 2 + 1 = 15, 15 x 2 - 1 = 29, 29 x 2 + 1 = 59, 59 x 2 - 1 = 117.
2. The pattern is x 2 with +1 and -1 alternately.
3. Next term = 117 x 2 + 1 = 235.

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) 4

Explanation:
1. Each term is the product of the digits of the previous term.
2. 9 x 8 = 72, 7 x 2 = 14.
3. Next term = 1 x 4 = 4.

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) 13

Explanation:
1. Odd positions: 1, 3, 7, ?, 21 with differences +2, +4, +6, +8.
2. Even positions: 3, 6, 9, 12 (multiples of 3).
3. Missing term = 7 + 6 = 13; check 13 + 8 = 21.

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) 34

Explanation:
1. Each term is the sum of the two before it: 2 + 3 = 5, 3 + 5 = 8, 5 + 8 = 13, 8 + 13 = 21.
2. Next term = 13 + 21 = 34.

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) 7

Explanation:
1. 840 / 5 = 168, 168 / 4 = 42, 42 / 3 = 14, 14 / 2 = 7.
2. The divisors are 5, 4, 3, 2, so the next divisor is 1.
3. Next term = 7 / 1 = 7.

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) 202

Explanation:
1. 11 x 2 + 1 = 23, 23 x 2 + 2 = 48, 48 x 2 + 3 = 99.
2. Missing term = 99 x 2 + 4 = 202.
3. Check: 202 x 2 + 5 = 409.

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) 381

Explanation:
1. Differences: +4, +16, +36, +64, +100 = 2², 4², 6², 8², 10².
2. Next difference = 12² = 144.
3. Next term = 237 + 144 = 381.

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) 497

Explanation:
1. 5 x 2 + 1 = 11, 11 x 2 + 3 = 25, 25 x 2 + 5 = 55.
2. 55 x 2 + 7 = 117, 117 x 2 + 9 = 243 - double and add odd numbers.
3. Next term = 243 x 2 + 11 = 497.

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) 597

Explanation:
1. 9 x 2 + 1 = 19, 19 x 2 - 1 = 37, 37 x 2 + 1 = 75, 75 x 2 - 1 = 149, 149 x 2 + 1 = 299.
2. The pattern is x 2 with +1 and -1 alternately.
3. Next term = 299 x 2 - 1 = 597.

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: (a) 1377

Explanation:
1. Differences: +4, +16, +64, +256 = 4¹, 4², 4³, 4⁴.
2. Next difference = 4⁵ = 1024.
3. Next term = 353 + 1024 = 1377.

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) 43

Explanation:
1. Differences: +4, +6, +8, +10 (even numbers).
2. Next difference = +12.
3. Next term = 31 + 12 = 43.

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) 72

Explanation:
1. Differences: +2, +4, +8, +16 (doubling).
2. Next difference = +32.
3. Next term = 40 + 32 = 72.

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: (c) 215

Explanation:
1. Terms are cubes with +1 and -1 alternately: 1³ + 1 = 2, 2³ - 1 = 7, 3³ + 1 = 28.
2. 4³ - 1 = 63, 5³ + 1 = 126.
3. Next term = 6³ - 1 = 215.

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) 126

Explanation:
1. 999 = 10³ - 1, 730 = 9³ + 1, 511 = 8³ - 1, 344 = 7³ + 1, 215 = 6³ - 1.
2. Cubes of 10, 9, 8, ... with -1 and +1 alternately.
3. Next term = 5³ + 1 = 126.

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) 168

Explanation:
1. Differences: +16, +24, +32, +40 (multiples of 8).
2. Next difference = +48.
3. Next term = 120 + 48 = 168 (terms are also 3² - 1, 5² - 1, 7² - 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) 243

Explanation:
1. Differences: +4, +16, +36, +64 = 2², 4², 6², 8².
2. Next difference = 10² = 100.
3. Next term = 143 + 100 = 243.

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) 96

Explanation:
1. Each term is double the previous term.
2. After 64 the next term should be 128, not 96.
3. So 96 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: (c) 24

Explanation:
1. Terms are n² + 1: 2² + 1 = 5, 3² + 1 = 10, 4² + 1 = 17.
2. The fourth term should be 5² + 1 = 26 (differences +5, +7, +9, +11, ...).
3. So 24 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: (d) 64

Explanation:
1. Terms are n² + 1: 1 + 1, 4 + 1, 9 + 1, 16 + 1, ...
2. The last term should be 8² + 1 = 65.
3. So 64 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: (c) 27

Explanation:
1. The series lists consecutive prime numbers: 13, 17, 19, 23, ..., 31.
2. 27 = 3 x 9 is not prime; the prime after 23 is 29.
3. So 27 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: (d) 46

Explanation:
1. Differences should be squares: +1, +4, +9, +16, +25.
2. 31 + 16 = 47, and 47 + 25 = 72.
3. So 46 is the wrong term; it should be 47.

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: (c) 69

Explanation:
1. Pattern: x 2 + 1, x 2 + 3, x 2 + 5, x 2 + 7, ...
2. 7 x 2 + 1 = 15, 15 x 2 + 3 = 33, 33 x 2 + 5 = 71, 71 x 2 + 7 = 149, 149 x 2 + 9 = 307.
3. The fourth term should be 71, so 69 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: (c) 154

Explanation:
1. Sum of digits: 1 + 2 + 6 = 9, 1 + 3 + 5 = 9, 1 + 4 + 4 = 9, 2 + 1 + 6 = 9, 8 + 0 + 1 = 9.
2. For 154 the digit sum is 1 + 5 + 4 = 10.
3. So 154 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: (d) 489

Explanation:
1. Differences: +13, +26, +52, +104 (doubling).
2. Next difference should be +208: 271 + 208 = 479.
3. So 489 is the wrong term; it should be 479.

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: (d) 114

Explanation:
1. Each term = square + multiple of 13: 3² + 13 = 22, 4² + 26 = 42, 5² + 39 = 64, 6² + 52 = 88.
2. So ? = 7² + 65 = 49 + 65 = 114.
3. Check: the differences are 20, 22, 24, 26, so 88 + 26 = 114.

Teacher's Note:
1. First write the differences between consecutive terms; if they are not constant, take differences again or compare them with squares, cubes or powers of 2 and 3.
2. When a series grows by roughly the same factor each time, test multiply-and-add rules such as x × 2 + 1 before trying differences.

Answer: (a) 3559

Explanation:
1. 11 × 6 - 5 = 61, 61 × 5 - 6 = 299, 299 × 4 - 7 = 1189.
2. The multiplier falls by 1 and the number subtracted rises by 1.
3. ? = 1189 × 3 - 8 = 3567 - 8 = 3559.

Teacher's Note:
1. If each term is roughly a fixed multiple of the previous one, divide neighbouring terms to find the multiplier, then check what is added or subtracted.
2. Multipliers that rise by 1 (×1, ×2, ×3 ...) or halve/double each step are very common in bank and SSC exam series.

Answer: (b) 127

Explanation:
1. 215 - 196 (14²) = 19, 19 + 144 (12²) = 163, 163 - 100 (10²) = 63.
2. The squares of 14, 12, 10, 8 are subtracted and added alternately.
3. ? = 63 + 64 (8²) = 127.

Teacher's Note:
1. Learn squares up to 30 and cubes up to 15 by heart; many series are just n², n³ or n⁴ with a small change.
2. If the terms are large and do not grow evenly, check whether they are powers such as 7², 6³, 5⁴.