Understanding Word Coding and Decoding

This question asks us to decipher a specific coding rule applied to the word "TOUCH" and then use that same rule to find the code for the word "ERROR". These types of questions test our ability to find patterns and apply logical reasoning.

Analyzing the Code for TOUCH

We are given that the word TOUCH is coded as 68. Let's examine the letters in TOUCH (T, O, U, C, H) and try to find a numerical relationship that results in 68.

A common method in word coding is to assign numerical values to letters based on their position in the alphabet (A=1, B=2, ..., Z=26). Let's try this first:

• T is the 20th letter.
• O is the 15th letter.
• U is the 21st letter.
• C is the 3rd letter.
• H is the 8th letter.

Summing these values gives: $20 + 15 + 21 + 3 + 8 = 67$.

The sum 67 is very close to 68, but not exactly 68. This suggests that either a small adjustment is made to the sum, or a different numerical assignment method is used.

Exploring Reverse Alphabetical Positions

Another common method in word coding is using the reverse alphabetical position, where Z=1, Y=2, ..., A=26. Let's try this for the letters in TOUCH:

• The position of T is 20. Its reverse position is $26 - 20 + 1 = 7$.
• The position of O is 15. Its reverse position is $26 - 15 + 1 = 12$.
• The position of U is 21. Its reverse position is $26 - 21 + 1 = 6$.
• The position of C is 3. Its reverse position is $26 - 3 + 1 = 24$.
• The position of H is 8. Its reverse position is $26 - 8 + 1 = 19$.

Now, let's sum these reverse alphabetical positions:

$7 + 12 + 6 + 24 + 19 = 68$.

This sum matches the given code for TOUCH (68) exactly. So, the rule for coding the word is the sum of the reverse alphabetical positions of its letters.

Applying the Logic to ERROR

Now that we have found the coding rule, we will apply the same rule to the word ERROR. The rule is the sum of the reverse alphabetical positions of the letters in ERROR (E, R, R, O, R).

Let's find the reverse alphabetical position for each letter:

• The position of E is 5. Its reverse position is $26 - 5 + 1 = 22$.
• The position of R is 18. Its reverse position is $26 - 18 + 1 = 9$.
• The position of R is 18. Its reverse position is $26 - 18 + 1 = 9$.
• The position of O is 15. Its reverse position is $26 - 15 + 1 = 12$.
• The position of R is 18. Its reverse position is $26 - 18 + 1 = 9$.

Next, we sum these reverse alphabetical positions:

$22 + 9 + 9 + 12 + 9 = 61$.

Therefore, according to the established coding rule, the word ERROR will be written as 61.

Conclusion

Based on the coding logic derived from TOUCH = 68, which is the sum of the reverse alphabetical values of the letters, the code for ERROR is 61.

Looking at the given options, 61 is present as option 1.

Revision Table: Word Coding Concepts

Additional Information: Logical Reasoning in Coding

Coding and decoding questions are a common part of logical reasoning tests. They require careful observation and systematic analysis to identify the pattern or rule used to transform one set of information (like a word) into another (like a number or another word). Here are some tips:

• Always look at the given examples first (like TOUCH to 68). This is the key to finding the rule.
• Consider different types of numerical values for letters (alphabetical position, reverse position, vowel/consonant grouping, etc.).
• Think about mathematical operations: addition, subtraction, multiplication, division, squaring, etc., applied to individual letter values or the sum/product of values.
• Look for patterns related to the number of letters, vowels, or consonants in the word.
• Test the suspected rule on the given example to confirm it before applying it to the word you need to code.
• Check all options once you have a result to see which one matches.

Practicing different types of coding and decoding problems helps improve your ability to quickly spot the underlying logic.