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Question

A sequence is given, of which one term is incorrect. Select the wrong term from the given alternatives.

PC81, SG130, VK179, YO228, BS277, EX326

The correct answer is

EX326

The given sequence is PC81, SG130, VK179, YO228, BS277, EX326.

Each term in the sequence consists of two letters followed by a number. To find the incorrect term, we need to analyze the pattern followed by the letters and the numbers separately.

Analyzing the Letter Patterns in the Sequence

Let's examine the pattern for the first letter and the second letter in each term.

First Letter Pattern

The first letters of the terms are P, S, V, Y, B, E.

Let's look at the position of these letters in the English alphabet (A=1, B=2, ..., Z=26):

LetterAlphabet Position
P16
S19
V22
Y25
B2 (which is 26 + 2 = 28 considering wrap-around)
E5 (which is 26 + 5 = 31 considering wrap-around)

Now, let's find the difference in the positions of consecutive first letters:

  • From P (16) to S (19): \(19 - 16 = 3\)
  • From S (19) to V (22): \(22 - 19 = 3\)
  • From V (22) to Y (25): \(25 - 22 = 3\)
  • From Y (25) to B (2 or 28): \(28 - 25 = 3\)
  • From B (2 or 28) to E (5 or 31): \(31 - 28 = 3\) or \(5 - 2 = 3\)

The first letter of each term consistently moves 3 positions forward in the alphabet (with wrap-around from Z to A).

Second Letter Pattern

The second letters of the terms are C, G, K, O, S, X.

Let's look at the position of these letters in the English alphabet:

LetterAlphabet Position
C3
G7
K11
O15
S19
X24

Now, let's find the difference in the positions of consecutive second letters:

  • From C (3) to G (7): \(7 - 3 = 4\)
  • From G (7) to K (11): \(11 - 7 = 4\)
  • From K (11) to O (15): \(15 - 11 = 4\)
  • From O (15) to S (19): \(19 - 15 = 4\)
  • From S (19) to X (24): \(24 - 19 = 5\)

The second letter of each term moves 4 positions forward in the alphabet for the first five steps, but moves 5 positions forward in the last step. This jump of 5 instead of 4 suggests that the pattern is broken at the last term.

Analyzing the Number Pattern in the Sequence

The numbers in the terms are 81, 130, 179, 228, 277, 326.

Let's find the difference between consecutive numbers:

  • From 81 to 130: \(130 - 81 = 49\)
  • From 130 to 179: \(179 - 130 = 49\)
  • From 179 to 228: \(228 - 179 = 49\)
  • From 228 to 277: \(277 - 228 = 49\)
  • From 277 to 326: \(326 - 277 = 49\)

The number in each term consistently increases by 49 from the previous term.

Identifying the Incorrect Term

We found that:

  • The first letter sequence follows a consistent pattern of +3 positions.
  • The number sequence follows a consistent pattern of +49.
  • The second letter sequence follows a pattern of +4 positions, except for the last step, which is +5.

The inconsistency lies in the second letter of the last term, EX326. If the pattern for the second letter were consistently +4, the second letter after 'S' (19th position) should be the 19 + 4 = 23rd letter, which is 'W'.

Therefore, the term after BS277 should have been BW326 to follow all established patterns.

The term that does not fit the established pattern is EX326.

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Important Questions from Mixed Series

  1. Find the missing term in the following series:

    2A11, 4D13, 12G17, 48J23, _______

  2. A series is given, with one missing term. Choose the correct option from the given ones that will complete the sequence.

    T9, V13, X17, Z21, B25, ?

  3. Select the number from among the given options that can replace the question mark (?) in the following series.

    6Q9, ____, 20Y23, 27C30

  4. Which option will fill in the blanks and complete the series correctly?
    KSH22, MVI26, PZK31, ______

  5. A sequence is given, one of which is incorrect. Choose the wrong term from the given alternatives.

    48, 73, 122, 243, 412, 637

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