Number Series Aptitude MCQ Questions with Answers Set 05

Answer: (d) 248

Explanation:
1. Differences: 7, 19, 39, 67.
2. Second differences: 12, 20, 28 (rising by 8), so the next is 36 and the next difference is 67 + 36 = 103.
3. ? = 145 + 103 = 248.

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) 725

Explanation:
1. Each term = previous × 2 + 11.
2. 12 × 2 + 11 = 35, 35 × 2 + 11 = 81, 81 × 2 + 11 = 173, 173 × 2 + 11 = 357.
3. ? = 357 × 2 + 11 = 725.

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: (e) None of these

Explanation:
1. Differences: 97, 197, 297, 397 - each 100 more than the last.
2. Next difference = 497, so ? = 991 + 497 = 1488.
3. 1488 is not in options (a) to (d).

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: (c) 287

Explanation:
1. Differences: 7, 21, 35, 49 = 7 × 1, 7 × 3, 7 × 5, 7 × 7.
2. Next difference = 7 × 9 = 63.
3. ? = 224 + 63 = 287.

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: (c) 61

Explanation:
1. Rule: multiply by 0.5, 1, 1.5, 2, 2.5, 3 and add the same number.
2. 9 × 0.5 + 0.5 = 5, 5 × 1 + 1 = 6, 6 × 1.5 + 1.5 = 10.5, 10.5 × 2 + 2 = 23.
3. 23 × 2.5 + 2.5 = 60 (not 61), and 60 × 3 + 3 = 183. So 61 is wrong.

Teacher's Note:
1. In a wrong-number question, find the rule using the terms at the start and the end of the series, then recompute each term to spot the odd one.
2. Only one term breaks the rule, so a rule that fails at two places is the wrong rule; try another pattern.

Answer: (b) 154

Explanation:
1. Read from the end: 125 + 1 = 126, + 2 = 128, + 4 = 132, + 8 = 140, + 16 = 156, + 32 = 188.
2. The differences should be powers of 2, so the 2nd term should be 156.
3. So 154 is wrong.

Teacher's Note:
1. In a wrong-number question, find the rule using the terms at the start and the end of the series, then recompute each term to spot the odd one.
2. Only one term breaks the rule, so a rule that fails at two places is the wrong rule; try another pattern.

Answer: (d) 151

Explanation:
1. Rule: multiply by n and add n + 1 (n = 1, 2, 3, ...).
2. 2 × 1 + 2 = 4, 4 × 2 + 3 = 11, 11 × 3 + 4 = 37, 37 × 4 + 5 = 153.
3. 153 × 5 + 6 = 771 and 771 × 6 + 7 = 4633, so 151 is wrong.

Teacher's Note:
1. In a wrong-number question, find the rule using the terms at the start and the end of the series, then recompute each term to spot the odd one.
2. Only one term breaks the rule, so a rule that fails at two places is the wrong rule; try another pattern.

Answer: (b) 394

Explanation:
1. Differences should be 1×2, 2×3, 3×4, 4×5, 5×6, 6×7 = 2, 6, 12, 20, 30, 42.
2. 391 + 2 = 393, 393 + 6 = 399, 399 + 12 = 411, 411 + 20 = 431, 431 + 30 = 461, 461 + 42 = 503.
3. The 2nd term should be 393, so 394 is wrong.

Teacher's Note:
1. In a wrong-number question, find the rule using the terms at the start and the end of the series, then recompute each term to spot the odd one.
2. Only one term breaks the rule, so a rule that fails at two places is the wrong rule; try another pattern.

Answer: (b) 8

Explanation:
1. Differences: 48, 32, 24, 20.
2. These fall by 16, 8, 4 (halving), so the next fall is 2 and the next difference is 18.
3. ? = 26 - 18 = 8.

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) 0.3

Explanation:
1. Divide by 5, 10, 15, 20, 25 in turn.
2. 4500 ÷ 5 = 900, 900 ÷ 10 = 90, 90 ÷ 15 = 6.
3. ? = 6 ÷ 20 = 0.3; check: 0.3 ÷ 25 = 0.012.

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: (d) 66.5

Explanation:
1. 24 × 0.5 - 1 = 11, 11 × 1 - 1 = 10, 10 × 1.5 - 1 = 14, 14 × 2 - 1 = 27.
2. The multiplier rises by 0.5 and 1 is always subtracted.
3. ? = 27 × 2.5 - 1 = 66.5.

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: (e) 635

Explanation:
1. 8 × 1 - 1 = 7, 7 × 2 - 2 = 12, 12 × 3 - 3 = 33, 33 × 4 - 4 = 128.
2. Multiply by n and subtract n.
3. ? = 128 × 5 - 5 = 635.

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: (c) 309

Explanation:
1. 7 × 1 - 2 = 5, 5 × 2 - 3 = 7, 7 × 3 - 4 = 17, 17 × 4 - 5 = 63.
2. The multiplier and the number subtracted both rise by 1.
3. ? = 63 × 5 - 6 = 309.

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: (a) 52

Explanation:
1. Differences should be n³ + 1: 2, 9, 28, 65, 126.
2. 50 + 2 = 52, 52 + 9 = 61, 61 + 28 = 89, 89 + 65 = 154, 154 + 126 = 280.
3. So ? = 52.

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.

Answer: (c) 57

Explanation:
1. Differences: 2, 6, 12 = 1×2, 2×3, 3×4.
2. Next difference = 4×5 = 20, so ? = 37 + 20 = 57.
3. Check: 57 + 5×6 = 57 + 30 = 87.

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: (e) 66

Explanation:
1. Differences: 3, 5, 9, 15.
2. Second differences: 2, 4, 6, so the next is 8 and the next difference is 23.
3. ? = 43 + 23 = 66.

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: (b) 1725

Explanation:
1. Differences should be squares of odd numbers: 23², 25², 27², 29², 31² = 529, 625, 729, 841, 961.
2. 560 + 529 = 1089, 1089 + 625 = 1714, 1714 + 729 = 2443, 2443 + 841 = 3284, 3284 + 961 = 4245.
3. The 3rd term should be 1714, so 1725 is wrong.

Teacher's Note:
1. In a wrong-number question, find the rule using the terms at the start and the end of the series, then recompute each term to spot the odd one.
2. Only one term breaks the rule, so a rule that fails at two places is the wrong rule; try another pattern.

Answer: (d) 3252

Explanation:
1. Read from the end: the differences should be 7² + 1, 9² + 1, 11² + 1, 13² + 1 = 50, 82, 122, 170.
2. 2826 + 50 = 2876, 2876 + 82 = 2958, 2958 + 122 = 3080, 3080 + 170 = 3250.
3. The first term should be 3250, so 3252 is wrong.

Teacher's Note:
1. In a wrong-number question, find the rule using the terms at the start and the end of the series, then recompute each term to spot the odd one.
2. Only one term breaks the rule, so a rule that fails at two places is the wrong rule; try another pattern.

Answer: (e) 1250

Explanation:
1. Differences from the 2nd term on: 130, 222, 350, 520 = 5³ + 5, 6³ + 6, 7³ + 7, 8³ + 8.
2. So the first difference should be 4³ + 4 = 68, and the first term should be 1322 - 68 = 1254.
3. So 1250 is wrong.

Teacher's Note:
1. In a wrong-number question, find the rule using the terms at the start and the end of the series, then recompute each term to spot the odd one.
2. Only one term breaks the rule, so a rule that fails at two places is the wrong rule; try another pattern.

Answer: (d) 59904

Explanation:
1. 81 × 1 + 6 = 87, 87 × 2 - 12 = 162, 162 × 3 + 18 = 504, 504 × 4 - 24 = 1992, 1992 × 5 + 30 = 9990.
2. Multiply by n and alternately add or subtract 6n.
3. ? = 9990 × 6 - 36 = 59904.

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: (c) 210

Explanation:
1. Differences: 23, 46 - each double the last.
2. 118 + 92 = 210, 210 + 184 = 394, 394 + 368 = 762, 762 + 736 = 1498.
3. So ? = 210.

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: (b) 658

Explanation:
1. Differences: 1, 13, 37, 79, 145.
2. These are 1³ + 0, 2³ + 5, 3³ + 10, 4³ + 15, 5³ + 20.
3. Next difference = 6³ + 25 = 241, so ? = 417 + 241 = 658.

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.

Answer: (c) 928

Explanation:
1. Differences: 4, 36, 48, 150, 180.
2. These are 2³ - 2², 3³ + 3², 4³ - 4², 5³ + 5², 6³ - 6².
3. Next difference = 7³ + 7² = 392, so ? = 536 + 392 = 928.

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.

Answer: (b) 62

Explanation:
1. Differences: 6, 6, 10, 10, 14.
2. Each difference appears twice and then rises by 4, so the next difference is 14.
3. ? = 48 + 14 = 62.

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: (c) 70

Explanation:
1. Each term = sum of the two previous terms + an increasing number.
2. 3 + 8 + 2 = 13, 8 + 13 + 3 = 24, 13 + 24 + 4 = 41.
3. ? = 24 + 41 + 5 = 70.

Teacher's Note:
1. If no difference or ratio pattern works, check whether each term is built from the two terms before it (sum, product or difference).
2. Fibonacci-type rules (add the previous two terms) often appear with a small extra number added each step.

Answer: (d) 32

Explanation:
1. Split the series into two: odd places 2, 4, 16, 256 and even places 4, 8, 16, ?.
2. In the odd places each term is the square of the previous one; in the even places each term doubles.
3. ? = 16 × 2 = 32.

Teacher's Note:
1. When the terms go up and down alternately, split the series into odd-position and even-position terms and study each part separately.
2. Two interleaved simple series (one adding, one multiplying, for example) are a favourite trick in reasoning papers.

Answer: (b) 13

Explanation:
1. Each term is the sum of the two terms before it (Fibonacci series).
2. 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8.
3. ? = 5 + 8 = 13.

Teacher's Note:
1. If no difference or ratio pattern works, check whether each term is built from the two terms before it (sum, product or difference).
2. Fibonacci-type rules (add the previous two terms) often appear with a small extra number added each step.

Answer: (d) 23

Explanation:
1. Each term is 23 less than the previous one.
2. ? = 46 - 23 = 23.

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: (d) 2048

Explanation:
1. Each term is the product of the two terms before it.
2. 4 × 2 = 8, 2 × 8 = 16, 8 × 16 = 128.
3. ? = 16 × 128 = 2048.

Teacher's Note:
1. If no difference or ratio pattern works, check whether each term is built from the two terms before it (sum, product or difference).
2. Fibonacci-type rules (add the previous two terms) often appear with a small extra number added each step.

Answer: (b) 17

Explanation:
1. Each term = difference of the two terms before it.
2. 186 - 115 = 71, 115 - 71 = 44, 71 - 44 = 27.
3. ? = 44 - 27 = 17.

Teacher's Note:
1. If no difference or ratio pattern works, check whether each term is built from the two terms before it (sum, product or difference).
2. Fibonacci-type rules (add the previous two terms) often appear with a small extra number added each step.

Answer: (b) 8

Explanation:
1. Each term is half the previous one.
2. ? = 16 ÷ 2 = 8; check: 8 ÷ 2 = 4.

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: (c) 64

Explanation:
1. Each term doubles: powers of 2.
2. ? = 32 × 2 = 64.

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: (a) 4450

Explanation:
1. The operations alternate: ×10, then -5.
2. 5 × 10 = 50, 50 - 5 = 45, 45 × 10 = 450, 450 - 5 = 445.
3. ? = 445 × 10 = 4450; check: 4450 - 5 = 4445.

Teacher's Note:
1. When the terms go up and down alternately, split the series into odd-position and even-position terms and study each part separately.
2. Two interleaved simple series (one adding, one multiplying, for example) are a favourite trick in reasoning papers.

Answer: (c) 135

Explanation:
1. Odd places: 243, 81, 27, 9 - each divided by 3.
2. Even places: 5, 15, 45 - each multiplied by 3.
3. ? = 45 × 3 = 135.

Teacher's Note:
1. When the terms go up and down alternately, split the series into odd-position and even-position terms and study each part separately.
2. Two interleaved simple series (one adding, one multiplying, for example) are a favourite trick in reasoning papers.

Answer: (b) 4

Explanation:
1. Odd places: 1, 2, 3 - natural numbers.
2. Even places: 2, 5, 10 = n² + 1.
3. The missing term is in an odd place, so ? = 4.

Teacher's Note:
1. When the terms go up and down alternately, split the series into odd-position and even-position terms and study each part separately.
2. Two interleaved simple series (one adding, one multiplying, for example) are a favourite trick in reasoning papers.

Answer: (a) -44

Explanation:
1. Ignoring signs: 4, 8, 14, 22, 32 with differences 4, 6, 8, 10; next difference 12 gives 44.
2. The signs alternate +, -, +, -, +, so the next term is negative.
3. ? = -44.

Teacher's Note:
1. When the terms go up and down alternately, split the series into odd-position and even-position terms and study each part separately.
2. Two interleaved simple series (one adding, one multiplying, for example) are a favourite trick in reasoning papers.