Odd Man Out and Series: Formulas, Shortcuts and Solved Examples — MCQs with Answers (Set 1)

This is a geometric series where each term is 4 times the previous term. Check the ratio between each pair of consecutive terms: 2 to 8 is x4.00 (OK), 8 to 16 is x2.00 (should be x4), 16 to 128 is x8.00 (should be x4), 128 to 512 is x4.00 (OK), 512 to 2048 is x4.00 (OK). One or more steps near 16 do not match this x4 pattern. So 16 breaks the pattern and is the wrong number.

This is a geometric series where each term is 3 times the previous term. Check the ratio between each pair of consecutive terms: 3 to 15 is x5.00 (should be x3), 15 to 27 is x1.80 (should be x3), 27 to 81 is x3.00 (OK), 81 to 243 is x3.00 (OK), 243 to 729 is x3.00 (OK). One or more steps near 15 do not match this x3 pattern. So 15 breaks the pattern and is the wrong number.

This is a geometric series where each term is 3 times the previous term. Check the ratio between each pair of consecutive terms: 5 to 15 is x3.00 (OK), 15 to 45 is x3.00 (OK), 45 to 270 is x6.00 (should be x3), 270 to 405 is x1.50 (should be x3), 405 to 1215 is x3.00 (OK). One or more steps near 270 do not match this x3 pattern. So 270 breaks the pattern and is the wrong number.

This is a geometric series where each term is 2 times the previous term. Check the ratio between each pair of consecutive terms: 4 to 20 is x5.00 (should be x2), 20 to 16 is x0.80 (should be x2), 16 to 32 is x2.00 (OK), 32 to 64 is x2.00 (OK), 64 to 128 is x2.00 (OK). One or more steps near 20 do not match this x2 pattern. So 20 breaks the pattern and is the wrong number.

This is a geometric series where each term is 2 times the previous term. Check the ratio between each pair of consecutive terms: 2 to 4 is x2.00 (OK), 4 to 8 is x2.00 (OK), 8 to 16 is x2.00 (OK), 16 to 80 is x5.00 (should be x2), 80 to 64 is x0.80 (should be x2). One or more steps near 80 do not match this x2 pattern. So 80 breaks the pattern and is the wrong number.

This is a geometric series where each term is 3 times the previous term. Check the ratio between each pair of consecutive terms: 4 to 12 is x3.00 (OK), 12 to 36 is x3.00 (OK), 36 to 180 is x5.00 (should be x3), 180 to 324 is x1.80 (should be x3), 324 to 972 is x3.00 (OK). One or more steps near 180 do not match this x3 pattern. So 180 breaks the pattern and is the wrong number.

This is an arithmetic series with a common difference of 3. Check the gap between each pair of consecutive terms: 27 to 30 is +3 (OK), 30 to 34 is +4 (should be +3), 34 to 36 is +2 (should be +3), 36 to 39 is +3 (OK), 39 to 42 is +3 (OK), 42 to 45 is +3 (OK). One or more gaps near 34 do not equal 3. So 34 breaks the pattern and is the wrong number.

This is an arithmetic series with a common difference of 8. Check the gap between each pair of consecutive terms: 1 to 9 is +8 (OK), 9 to 17 is +8 (OK), 17 to 23 is +6 (should be +8), 23 to 33 is +10 (should be +8), 33 to 41 is +8 (OK), 41 to 49 is +8 (OK). One or more gaps near 23 do not equal 8. So 23 breaks the pattern and is the wrong number.

This is an arithmetic series with a common difference of 8. Check the gap between each pair of consecutive terms: 17 to 26 is +9 (should be +8), 26 to 33 is +7 (should be +8), 33 to 41 is +8 (OK), 41 to 49 is +8 (OK), 49 to 57 is +8 (OK), 57 to 65 is +8 (OK). One or more gaps near 26 do not equal 8. So 26 breaks the pattern and is the wrong number.

This is an arithmetic series with a common difference of 7. Check the gap between each pair of consecutive terms: 6 to 13 is +7 (OK), 13 to 20 is +7 (OK), 20 to 27 is +7 (OK), 27 to 33 is +6 (should be +7), 33 to 41 is +8 (should be +7), 41 to 48 is +7 (OK). One or more gaps near 33 do not equal 7. So 33 breaks the pattern and is the wrong number.

This is an arithmetic series with a common difference of 2. Check the gap between each pair of consecutive terms: 25 to 27 is +2 (OK), 27 to 29 is +2 (OK), 29 to 31 is +2 (OK), 31 to 33 is +2 (OK), 33 to 38 is +5 (should be +2), 38 to 37 is -1 (should be +2). One or more gaps near 38 do not equal 2. So 38 breaks the pattern and is the wrong number.

This is an arithmetic series with a common difference of 8. Check the gap between each pair of consecutive terms: 6 to 14 is +8 (OK), 14 to 22 is +8 (OK), 22 to 32 is +10 (should be +8), 32 to 38 is +6 (should be +8), 38 to 46 is +8 (OK), 46 to 54 is +8 (OK). One or more gaps near 32 do not equal 8. So 32 breaks the pattern and is the wrong number.

Check each number against its cube root. 8=2^3, 27=3^3, 64=4^3, 125=5^3. Every number here is a perfect cube. So this series consists of consecutive perfect cubes.

Check each number against its square root. 4=2^2, 9=3^2, 16=4^2, 25=5^2, 36=6^2. Every number here is a perfect square. So this series consists of consecutive perfect squares.

A geometric series has a fixed ratio between consecutive terms. Each term equals the previous term multiplied by this fixed ratio. For example, in 2, 6, 18, 54, the ratio is always 3: 6/2=3, 18/6=3, 54/18=3. So the quantity that stays constant is the ratio.

An arithmetic series has a fixed difference between consecutive terms. Each term equals the previous term plus this fixed difference. For example, in 2, 5, 8, 11, the difference is always 3: 5-2=3, 8-5=3, 11-8=3. So the quantity that stays constant is the difference.

This series alternates: add 4, then subtract 10, and repeat. Check each step: 30 to 34 is +4 (OK), 34 to 24 is -10 (OK), 24 to 26 is +2 (should be +4), 26 to 18 is -8 (should be -10), 18 to 22 is +4 (OK), 22 to 12 is -10 (OK). One or more steps near 26 break this pattern. So 26 is the wrong number.

This series alternates: add 5, then subtract 6, and repeat. Check each step: 31 to 36 is +5 (OK), 36 to 30 is -6 (OK), 30 to 35 is +5 (OK), 35 to 27 is -8 (should be -6), 27 to 34 is +7 (should be +5), 34 to 28 is -6 (OK). One or more steps near 27 break this pattern. So 27 is the wrong number.

This series alternates: add 5, then subtract 8, and repeat. Check each step: 29 to 34 is +5 (OK), 34 to 26 is -8 (OK), 26 to 30 is +4 (should be +5), 30 to 23 is -7 (should be -8), 23 to 28 is +5 (OK), 28 to 20 is -8 (OK). One or more steps near 30 break this pattern. So 30 is the wrong number.

This series alternates: add 3, then subtract 8, and repeat. Check each step: 19 to 22 is +3 (OK), 22 to 14 is -8 (OK), 14 to 17 is +3 (OK), 17 to 9 is -8 (OK), 9 to 10 is +1 (should be +3), 10 to 4 is -6 (should be -8). One or more steps near 10 break this pattern. So 10 is the wrong number.

This series alternates: add 7, then subtract 8, and repeat. Check each step: 5 to 12 is +7 (OK), 12 to 6 is -6 (should be -8), 6 to 11 is +5 (should be +7), 11 to 3 is -8 (OK), 3 to 10 is +7 (OK), 10 to 2 is -8 (OK). One or more steps near 6 break this pattern. So 6 is the wrong number.

This series alternates: add 9, then subtract 6, and repeat. Check each step: 20 to 29 is +9 (OK), 29 to 23 is -6 (OK), 23 to 33 is +10 (should be +9), 33 to 26 is -7 (should be -6), 26 to 35 is +9 (OK), 35 to 29 is -6 (OK). One or more steps near 33 break this pattern. So 33 is the wrong number.

This series alternates: add 6, then subtract 4, and repeat. Check each step: 13 to 18 is +5 (should be +6), 18 to 15 is -3 (should be -4), 15 to 21 is +6 (OK), 21 to 17 is -4 (OK), 17 to 23 is +6 (OK), 23 to 19 is -4 (OK). One or more steps near 18 break this pattern. So 18 is the wrong number.

This series alternates: add 10, then subtract 3, and repeat. Check each step: 20 to 30 is +10 (OK), 30 to 27 is -3 (OK), 27 to 38 is +11 (should be +10), 38 to 34 is -4 (should be -3), 34 to 44 is +10 (OK), 44 to 41 is -3 (OK). One or more steps near 38 break this pattern. So 38 is the wrong number.

This series alternates: add 9, then subtract 10, and repeat. Check each step: 39 to 49 is +10 (should be +9), 49 to 38 is -11 (should be -10), 38 to 47 is +9 (OK), 47 to 37 is -10 (OK), 37 to 46 is +9 (OK), 46 to 36 is -10 (OK). One or more steps near 49 break this pattern. So 49 is the wrong number.