Understanding the Coding Language Logic

The question asks us to decipher a coding language where 'DXF' is coded as '102' and 'URO' is coded as '162'. We need to find the code for 'LNZ' using the same rule.

Let's analyze the given examples by looking at the alphabetical positions of the letters:

Analyzing the Code for 'DXF'

Let's find the positions of the letters in 'DXF':

• D is the 4th letter.
• X is the 24th letter.
• F is the 6th letter.

The sum of the positions is: $4 + 24 + 6 = 34$.

The given code for 'DXF' is 102. How can we get 102 from 34? Let's try multiplying the sum by a number. If we multiply 34 by 3, we get $34 \times 3 = 102$. This matches the code for 'DXF'.

Analyzing the Code for 'URO'

Let's test this potential rule with the second example, 'URO'. The positions of the letters are:

• U is the 21st letter.
• R is the 18th letter.
• O is the 15th letter.

The sum of the positions is: $21 + 18 + 15 = 54$.

Now, let's apply the rule (sum multiplied by 3): $54 \times 3 = 162$. This matches the given code for 'URO'.

The rule seems consistent: calculate the sum of the alphabetical positions of the letters and then multiply the sum by 3.

Applying the Logic to Decode 'LNZ'

Now, let's apply the same logic to find the code for 'LNZ'. We need to find the alphabetical positions of these letters:

• L is the 12th letter.
• N is the 14th letter.
• Z is the 26th letter.

Calculate the sum of their positions:

Sum $= 12 + 14 + 26$

Sum $= 52$

Now, apply the rule: multiply the sum by 3.

Code for 'LNZ' $= 52 \times 3$

Code for 'LNZ' $= 156$

So, in this code language, 'LNZ' is written as '156'.

Conclusion

By analyzing the pattern in the given coded words, we found that the code is generated by summing the alphabetical positions of the letters and multiplying the result by 3. Applying this logic to 'LNZ' gives us the code 156.

Revision Table: Coding Language Patterns

Additional Information: Logical Reasoning in Coding-Decoding

Coding-decoding questions are common in logical reasoning sections of competitive exams. They test your ability to identify patterns and rules in how words, letters, or numbers are transformed into a coded form. Common patterns include:

• Shifting letters (e.g., A becomes B, B becomes C)
• Using alphabetical positions (as seen in this problem)
• Using reverse alphabetical positions
• Mixing position values with arithmetic operations
• Substituting letters with other letters based on a rule
• Substituting letters with numbers or symbols

Practicing various types of coding-decoding problems helps improve analytical skills and speed in identifying the underlying logic.