Decoding the Coding Logic

This question is about figuring out a secret code used to represent words with numbers. We are given two examples: 'BUS' is coded as 42, and 'COT' is coded as 38. We need to use this pattern to find the code for 'DRUM'.

Analyzing the Examples

Let's look at the word 'BUS' and its code 42.

• The letters in 'BUS' are B, U, and S.
• A common way to code words is by using the position of each letter in the alphabet (A=1, B=2, C=3, ... Z=26).
• Let's find the positions for the letters in 'BUS':
  • B is the 2nd letter.
  • U is the 21st letter.
  • S is the 19th letter.
• Now, let's add these numbers together: $2 + 21 + 19 = 42$.

This matches the given code for 'BUS'! It seems the code is the sum of the alphabetical positions of the letters in the word.

Verifying with the Second Example

Let's check if this logic works for 'COT' coded as 38.

• The letters are C, O, T.
• Their positions in the alphabet are:
  • C = 3
  • O = 15
  • T = 20
• Adding these positions: $3 + 15 + 20 = 38$.

This also matches the given code. Our logic is confirmed: the code for a word is the sum of the alphabetical positions of its letters.

Calculating the Code for 'DRUM'

Now we can apply the same logic to find the code for 'DRUM'.

• The letters are D, R, U, M.
• Find their alphabetical positions:
  • D = 4
  • R = 18
  • U = 21
  • M = 13
• Add these positions together: $$ 4 + 18 + 21 + 13 $$
• Performing the addition: $$ 4 + 18 = 22 $$ $$ 22 + 21 = 43 $$ $$ 43 + 13 = 56 $$

So, the code for 'DRUM' is 56.

Final Answer Check

Comparing our result with the options provided:

• 1. 57
• 2. 65
• 3. 83
• 4. 56

Our calculated code, 56, matches option 4.