Question

If the word "BITS" is coded using \( A=1, B=2, \ldots, Z=26 \), and the code is the sum of the squares of each letter's value, what is the code for the word?

• A. \( 846 \)
• B. \( 854 \)
• C. \( 864 \)
• D. \( 874 \)

Hint:

When coding words using letter values, squaring values and summing is a common pattern.

Answer 1

The Correct Option is A

To solve this problem, we need to code the word "BITS" by using the values of the letters according to their position in the alphabet, specifically using \( A=1, B=2, \ldots, Z=26 \). The code for the word is calculated as the sum of the squares of the values of each letter.

Let's find the value of each letter and then compute the sum of their squares:

• B: \(B=2\).
• I: \(I=9\).
• T: \(T=20\).
• S: \(S=19\).

Now, calculate the sum of the squares of each letter's value:

Code = \(2^2 + 9^2 + 20^2 + 19^2\).

Calculate each square:

• \(2^2 = 4\).
• \(9^2 = 81\).
• \(20^2 = 400\).
• \(19^2 = 361\).

Sum them up:

Code = \(4 + 81 + 400 + 361\).

Code = \(846\).

The code for the word "BITS" is therefore \(846\). 
The correct answer is option \(846\).