Directions : There is a wrong number in these series. Find the wrong number &…

2022

Directions : There is a wrong number in these series. Find the wrong number & pattern of the given series and answer the questions given below.

Series A: 24, 31.5, 46.5, 69, 98, 136.5, 181.5
Series B: 5926, 886, 166, 46, 22, 18, 14
Series C: 11, 18, 44, 107, 231, 445, 788

X, Y & Z are the wrong number of the series A, B & C respectively. Find the relation between X, Y & Z.

  1. A.

    X > Y < Z

  2. B.

    X > Y > Z

  3. C.

    X ≤ Y < Z

  4. D.

    X > Y ≥ Z

  5. E.

    X = Y < Z

Attempted by 1 students.

Show answer & explanation

Correct answer: A

Concept

In a 'find the wrong number' series, every term is produced by ONE fixed rule applied to its neighbour, so the wrong number is the single term that breaks that rule. A reliable method: compute consecutive differences (or ratios), find the regular law they should follow, and the term that forces an irregularity is the wrong one. Replace it with the value the rule predicts and confirm the whole series becomes consistent.

Series A

Take first differences of 24, 31.5, 46.5, 69, 98, 136.5, 181.5. They should form an arithmetic progression rising by 7.5 each step (7.5, 15, 22.5, 30, 37.5, 45):

  1. 24 to 31.5 gives +7.5

  2. 31.5 to 46.5 gives +15

  3. 46.5 to 69 gives +22.5

  4. 69 + 30 should give 99, but the series shows 98

  5. with 99: 99 + 37.5 = 136.5 and 136.5 + 45 = 181.5, which match the rest

So in Series A the rule predicts 99 where 98 appears; hence X = 98.

Series B

The terms 5926, 886, 166, 46, 22, 18, 14 decrease by successive factorials (7!, 6!, 5!, 4!, 3!, 2!):

  1. 5926 - 5040 (7!) = 886

  2. 886 - 720 (6!) = 166

  3. 166 - 120 (5!) = 46

  4. 46 - 24 (4!) = 22

  5. 22 - 6 (3!) should give 16, but the series shows 18

  6. with 16: 16 - 2 (2!) = 14, which matches the last term

So in Series B the rule predicts 16 where 18 appears; hence Y = 18.

Series C

The terms 11, 18, 44, 107, 231, 445, 788 increase by (n3 - 1) for n = 2, 3, 4, ...:

  1. 11 + 7 (23 - 1) = 18

  2. 18 + 26 (33 - 1) = 44

  3. 44 + 63 (43 - 1) = 107

  4. 107 + 124 (53 - 1) = 231

  5. 231 + 215 (63 - 1) should give 446, but the series shows 445

  6. with 446: 446 + 342 (73 - 1) = 788, which matches the last term

So in Series C the rule predicts 446 where 445 appears; hence Z = 445.

Comparing X, Y, Z

We have X = 98, Y = 18, Z = 445. Compare them: 98 is greater than 18, and 18 is less than 445.

Therefore X > Y < Z is the relation that holds.

Cross-check

X = 98 > Y = 18 is true and Y = 18 < Z = 445 is true. The competing relations fail: X > Y > Z needs 18 > 445 (false); X = Y needs 98 = 18 (false); X <= Y needs 98 <= 18 (false). Only X > Y < Z survives.

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