In a certain code, the letter Z is written as 52 and the word ACT is written as 48. Using the same coding rule, what will be the numeric code for the word BAT?

Introduction / Context:
This coding and decoding question combines letters of the alphabet with numbers. You are given the codes Z = 52 and ACT = 48, and you have to find the code for BAT. The pattern involves positions of letters in the alphabet and a simple arithmetic operation. Such questions measure how quickly you can connect alphabet positions to numeric expressions.

Given Data / Assumptions:
Single letter code: Z corresponds to 52.
Three letter word code: ACT corresponds to 48.
You must determine the rule that connects letters to these numbers.
Then you must apply that rule to the word BAT to find its code.
We use the standard English alphabet where A is 1, B is 2, C is 3 and so on up to Z which is 26.

Concept / Approach:
Usually, such questions involve summing the alphabet positions of the letters and then applying multiplication or another simple operation. The given value Z = 52 suggests that Z might be mapped by doubling its alphabet position because 26 multiplied by 2 equals 52. If that guess is correct, then for a word like ACT, you can add the positions of A, C and T and then double the total. You must then verify that this gives the value 48 for ACT. If it does, the same rule can be safely used for BAT.

Step-by-Step Solution:
Step 1: Determine the alphabet position of Z. Z is the 26th letter of the alphabet. Step 2: If the pattern is to double the position, compute 26 multiplied by 2, which equals 52. This matches the given code for Z, so the rule is plausible. Step 3: For ACT, find the positions of its letters: A is 1, C is 3 and T is 20. Step 4: Add these positions: 1 plus 3 plus 20 equals 24. Step 5: Apply the same doubling rule: 24 multiplied by 2 equals 48, which matches the given code for ACT. So the rule is confirmed: the code is twice the sum of the alphabet positions of the letters in the word. Step 6: Now apply this rule to BAT. Find the alphabet positions: B is 2, A is 1 and T is 20. Step 7: Add these positions: 2 plus 1 plus 20 equals 23. Step 8: Double the sum: 23 multiplied by 2 equals 46. Step 9: Therefore, the code for BAT must be 46.

Verification / Alternative check:
You can quickly recheck each step. The positions 2, 1 and 20 are correct for B, A and T respectively. Their sum is 23, and doubling gives 46. This matches one of the answer options and is consistent with the pattern established by both Z and ACT. No other simple interpretation of the given examples produces the correct codes for both Z and ACT, so the rule is unique and reliable.

Why Other Options Are Wrong:
39: This would correspond to a sum of 19.5 before doubling, which is not an integer sum of letter positions, so it cannot be correct.
41: This would lead to a non integer sum when halved, so it does not match the pattern of doubling the sum of positions.
44: This would imply a sum of 22, but the actual sum of positions for BAT is 23, so 44 does not follow the rule used for Z and ACT.

Common Pitfalls:
A common error is to guess that each letter is coded separately with a multiplication factor and then combined in an inconsistent way, or to try products instead of sums. Remember that the presence of both a single letter example and a multi letter example is a strong hint that you should work with letter positions and simple sums. Always verify that the same rule works for all given examples before applying it to the target word.

Final Answer:
Using the rule “twice the sum of alphabet positions”, the correct code for BAT is 46.