This problem involves a coding pattern where words are converted into numbers. We need to figure out the rule used to code 'DOLBY' as '53' and 'STUDENT' as '96' and then apply this rule to find the code for 'GENEVA'.
Let's find the sum of the alphabetical positions of the letters in 'DOLBY'. We assign numbers to letters based on their position in the alphabet (A=1, B=2, C=3, ...).
Calculating the sum:
$$ \text{Sum} = 4 + 15 + 12 + 2 + 25 = 58 $$
The coded value is '53'. Notice that the number of letters in 'DOLBY' is 5.
Let's see if subtracting the number of letters from the sum gives the coded value:
$$ 58 - 5 = 53 $$
This matches the given code for 'DOLBY'.
Now, let's apply the same potential rule to the word 'STUDENT'.
First, find the sum of the alphabetical positions of the letters in 'STUDENT':
Calculating the sum:
$$ \text{Sum} = 19 + 20 + 21 + 4 + 5 + 14 + 20 = 103 $$
The number of letters in 'STUDENT' is 7.
Applying the rule (Sum - Number of letters):
$$ 103 - 7 = 96 $$
This matches the given code for 'STUDENT'. The pattern is confirmed.
Finally, let's use the confirmed pattern to find the code for 'GENEVA'.
Find the sum of the alphabetical positions of the letters in 'GENEVA':
Calculating the sum:
$$ \text{Sum} = 7 + 5 + 14 + 5 + 22 + 1 = 54 $$
The number of letters in 'GENEVA' is 6.
Apply the rule (Sum - Number of letters):
$$ 54 - 6 = 48 $$
Therefore, 'GENEVA' will be coded as '48' in this language.
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