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: Find the position number of each letter.
In CAB, C is the 3rd letter of the alphabet, A is the 1st, and B is the 2nd.

Step 2: Work out the rule using C.
Square the position: \(3^2 = 9\). Cube that result: \(9^3 = 729\). Then subtract 6: \(729 - 6 = 723\), which matches the code given for C.

Step 3: Check the rule on B.
\(2^2 = 4\), \(4^3 = 64\), \(64 - 6 = 58\), which matches the code given for B. The rule, square the position, cube that answer, then subtract 6, is confirmed.

Step 4: Check the rule on A.
\(1^2 = 1\), \(1^3 = 1\), \(1 - 6 = -5\), which matches the -5 in the CAB code.

Step 5: Apply the rule to D, the new letter in DAD.
D is the 4th letter. \(4^2 = 16\), \(16^3 = 4096\), \(4096 - 6 = 4090\). A still codes to -5 as found in Step 4.

Step 6: Assemble the code for DAD.
D = 4090, A = -5, D = 4090, so DAD is coded as 4090 -5 4090.

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