Understanding Alphabetic Coding Patterns

This question involves an alphabetic coding pattern where letters or words are assigned numerical values based on a specific rule. We are given two examples: N = 13 and GROUP = 58. We need to deduce the rule from these examples and apply it to find the value of MOBILE.

Decoding the Logic for N = 13

Let's consider the position of the letter 'N' in the English alphabet. The standard positions are A=1, B=2, ..., N=14, ..., Z=26. However, the given value for N is 13. This doesn't match the standard 1-based position (14) or a 0-based position (13). Let's think of other ways to assign numerical values to letters.

One common pattern is assigning values based on the position counting backward from Z. If we assign Z=1, Y=2, X=3, and so on, let's see what value N gets:

• Z = 1
• Y = 2
• ...
• N = ?

The position counting backward can be calculated as \(26 - (\text{standard position}) + 1\). The standard position of N is 14.

Value for N = \(26 - 14 + 1 = 12 + 1 = 13\).

This matches the given value N = 13. This suggests the coding pattern might be assigning a value to each letter based on its position when counting backward from Z, where Z=1.

Verifying the Pattern with GROUP = 58

Let's verify this pattern with the word GROUP. We will calculate the value for each letter in GROUP using the rule: Value = \(26 - (\text{standard position}) + 1\).

• G is the 7th letter. Value for G = \(26 - 7 + 1 = 19 + 1 = 20\).
• R is the 18th letter. Value for R = \(26 - 18 + 1 = 8 + 1 = 9\).
• O is the 15th letter. Value for O = \(26 - 15 + 1 = 11 + 1 = 12\).
• U is the 21st letter. Value for U = \(26 - 21 + 1 = 5 + 1 = 6\).
• P is the 16th letter. Value for P = \(26 - 16 + 1 = 10 + 1 = 11\).

Now, let's sum the values for the letters in GROUP:

Total value for GROUP = Value(G) + Value(R) + Value(O) + Value(U) + Value(P)

Total value for GROUP = \(20 + 9 + 12 + 6 + 11 = 58\).

This calculated value 58 matches the given value for GROUP. The pattern is confirmed: Each letter's value is its position counting backward from Z=1, and the word's value is the sum of its letters' values.

Calculating the Value for MOBILE

Now, we apply the same pattern to the word MOBILE. We will find the backward position value for each letter:

• M is the 13th letter. Value for M = \(26 - 13 + 1 = 13 + 1 = 14\).
• O is the 15th letter. Value for O = \(26 - 15 + 1 = 11 + 1 = 12\).
• B is the 2nd letter. Value for B = \(26 - 2 + 1 = 24 + 1 = 25\).
• I is the 9th letter. Value for I = \(26 - 9 + 1 = 17 + 1 = 18\).
• L is the 12th letter. Value for L = \(26 - 12 + 1 = 14 + 1 = 15\).
• E is the 5th letter. Value for E = \(26 - 5 + 1 = 21 + 1 = 22\).

Finally, we sum the values for the letters in MOBILE:

Total value for MOBILE = Value(M) + Value(O) + Value(B) + Value(I) + Value(L) + Value(E)

Total value for MOBILE = \(14 + 12 + 25 + 18 + 15 + 22\).

Let's add them up:

• \(14 + 12 = 26\)
• \(26 + 25 = 51\)
• \(51 + 18 = 69\)
• \(69 + 15 = 84\)
• \(84 + 22 = 106\)

The total value for MOBILE is 106.

Comparing with Options

The calculated value for MOBILE is 106. Let's check the given options:

1. 100
2. 51
3. 116
4. 106

Our calculated value matches option 4.

Conclusion on Alphabet Coding Pattern

The coding pattern used in this question assigns a value to each letter based on its reverse alphabetical order position (Z=1, Y=2, ... A=26). The value of a word is the sum of the values of its constituent letters.

Following this pattern:

• N = 13 (Backward position of N)
• GROUP = 58 (Sum of backward positions of G, R, O, U, P)
• MOBILE = 106 (Sum of backward positions of M, O, B, I, L, E)

Revision Table: Key Pattern Details

Additional Information on Coding Reasoning

Coding and decoding questions in reasoning tests often involve patterns related to alphabets and numbers. Here are some common types of patterns you might encounter:

• Letter to Number Coding: Assigning numerical values to letters based on standard position (A=1), reverse position (Z=1), sum of digits if position > 9, or other arithmetic operations.
• Letter to Letter Coding: Shifting letters by a certain number of positions (e.g., A codes to C, B to D), substituting letters based on a pattern, or reversing the order of letters.
• Word to Word Coding: Words are coded as other words based on logical relationships or phonetic similarities, though less common in number-based coding.
• Mixed Coding: A combination of letter and number coding rules.

Solving these questions requires careful observation of the given examples to identify the underlying rule or pattern. Practice with different types helps in quickly recognizing the logic.