Question

If the word "GIFT" is coded using A=1, B=2, ..., Z=26, and each letter’s value is squared, what is the sum of the coded values?

• A. \( 566 \)
• B. \( 216 \)
• C. \( 234 \)
• D. 252

Hint:

In coding problems, ensure the operation (e.g., squaring) is applied correctly to each letter’s value.

Answer 1

The Correct Option is A

To solve the problem of coding the word "GIFT," we begin by translating each letter into its corresponding numerical value according to the rule: A=1, B=2, ..., Z=26.

Let's break it down:

• G is the 7th letter of the alphabet, so G = 7.
• I is the 9th letter, so I = 9.
• F is the 6th letter, so F = 6.
• T is the 20th letter, so T = 20.

Next, compute the square of each value:

• \( G^2 = 7^2 = 49 \)
• \( I^2 = 9^2 = 81 \)
• \( F^2 = 6^2 = 36 \)
• \( T^2 = 20^2 = 400 \)

Now, add these squared values together to find the sum:

\( 49 + 81 + 36 + 400 = 566 \)

Therefore, the sum of the coded values is 566.

Answer 2

To solve the problem of finding the sum of the coded values for the word "GIFT" using the code A=1, B=2, ..., Z=26, and squaring each letter's value, follow these steps:

• Calculate the numerical value for each letter:
  • G = 7
  • I = 9
  • F = 6
  • T = 20
• Square each numerical value:
  • G: \(7^2 = 49\)
  • I: \(9^2 = 81\)
  • F: \(6^2 = 36\)
  • T: \(20^2 = 400\)
• Add the squared values together: \(49 + 81 + 36 + 400 = 566\)

Thus, the sum of the coded values is 566.