Question

If CAB is coded as 723 -5 58 in a coded language, then how will DAD be coded?

• A. 4023 -5 4023
• B. 4090 -5 4090
• C. 1024 -5 1024
• D. 1246 -5 1189

Hint:

Find the position of each letter in the alphabet, then square it, cube that answer, and subtract 6.

Answer 1

The Correct Option is B

Step 1: Write the rule as one formula instead of three separate steps.
Squaring a number and then cubing that square is the same as raising the original number to the power 6, because $(n^2)^3 = n^6$. So the code for a letter in position $n$ is $n^6 - 6$.

Step 2: Test the formula on the given code.
For C, $n = 3$, so $3^6 - 6 = 729 - 6 = 723$, matching the given code. For B, $n = 2$, so $2^6 - 6 = 64 - 6 = 58$, also matching. For A, $n = 1$, so $1^6 - 6 = 1 - 6 = -5$, matching the -5 term. The formula $n^6 - 6$ checks out.

Step 3: Find the position number of each letter in DAD.
D is the 4th letter, A is the 1st letter, D repeats as the 4th letter.

Step 4: Plug each position into the formula.
For D, $n = 4$: $4^6 - 6 = 4096 - 6 = 4090$. For A, $n = 1$: $1^6 - 6 = -5$, as already found.

Step 5: Put the codes in order.
DAD becomes 4090, -5, 4090 in the same D, A, D order.

Final Answer:
\[ \boxed{4090\ {-5}\ 4090} \]