Understanding the Coding-Decoding Problem

This question is an example of a letter coding or word coding problem. We are given a rule applied to two words, "AT" and "BEG", which converts them into numerical values, 20 and 70 respectively. Our task is to identify the underlying pattern or rule and then apply it to the word "BANK" to find its corresponding numerical value.

Analyzing the Given Examples: AT and BEG

Let's look at the numerical values assigned to the letters in the English alphabet. A=1, B=2, C=3, ..., Z=26. We need to see how the letters in "AT" and "BEG" might be combined to get 20 and 70.

Example 1: AT = 20

• The letter A is the 1st letter of the alphabet.
• The letter T is the 20th letter of the alphabet.

Let's consider possible operations on their alphabetical positions (1 and 20):

• Sum: $1 + 20 = 21$ (Not 20)
• Difference: $|1 - 20| = 19$ (Not 20)
• Product: $1 \times 20 = 20$ (This matches the given value!)

Example 2: BEG = 70

Let's test if the product pattern works for "BEG" as well.

• The letter B is the 2nd letter.
• The letter E is the 5th letter.
• The letter G is the 7th letter.

Their alphabetical positions are 2, 5, and 7. Let's find their product:

Product: $2 \times 5 \times 7 = 10 \times 7 = 70$ (This also matches the given value!)

Identifying the Letter Coding Pattern

From the analysis of "AT" and "BEG", the pattern appears to be consistent: The numerical value assigned to a word is the product of the alphabetical positions of its letters.

Applying the Pattern to BANK

Now, let's apply this pattern to the word "BANK" to find its numerical value.

• The letter B is the 2nd letter.
• The letter A is the 1st letter.
• The letter N is the 14th letter.
• The letter K is the 11th letter.

The alphabetical positions of the letters in "BANK" are 2, 1, 14, and 11.

According to the pattern, the value of BANK is the product of these positions:

Value of BANK $= 2 \times 1 \times 14 \times 11$

Let's calculate the product:

$2 \times 1 = 2$

$2 \times 14 = 28$

$28 \times 11$

To calculate $28 \times 11$:

$28 \times 11 = 28 \times (10 + 1) = (28 \times 10) + (28 \times 1) = 280 + 28 = 308$

Thus, the numerical value for BANK is 308.

Summary of the Solution Steps

1. Assign alphabetical positions to the letters (A=1, B=2, ...).
2. Analyze the given examples (AT=20, BEG=70) to find the pattern.
3. Determine that the pattern is the product of the alphabetical positions.
4. Apply the product pattern to the letters in "BANK".
5. Calculate the final product for BANK.

Revision Table: Letter Coding Practice

Understanding the pattern is key in coding-decoding questions. Practicing different types helps.

Additional Information: Importance of Alphabetical Positions

Alphabetical positions are fundamental to many coding-decoding problems. It's helpful to know the positions of letters or have a quick way to figure them out. Some people use mnemonics like E J O T Y (5, 10, 15, 20, 25) or C F I L O R U X (3, 6, 9, 12, 15, 18, 21, 24) to quickly recall positions.

These types of questions test your logical reasoning and pattern recognition skills, which are important for many competitive exams.