Question

Which letter from the options given will replace the "?" in the table given below?

Word 1	Number	Word 2
CAT	389376	DOG
RAT	1758276	MAT
CAB	15876	FAN
CAN	571536	?

• A. MAN
• B. GIFT
• C. PAN
• D. SOFT

Hint:

Add up the alphabet position of each letter, square it, and the two squares multiply to the given number.

Answer 1

The Correct Option is B

Step 1: Turn CAT into a number using A = 1, B = 2, and so on.
C = 3, A = 1, T = 20, so CAT adds up to 24. Square that value: \( 24^2 = 576 \).

Step 2: Do the same for DOG.
D = 4, O = 15, G = 7, so DOG adds up to 26. Square that value: \( 26^2 = 676 \).

Step 3: Multiply the two squares and check against the table.
\( 576 \times 676 = 389376 \), which matches the number next to CAT and DOG exactly. So the rule is: square each word's letter sum, then multiply the two squares together to get the table number.

Step 4: Apply the rule to CAN.
C = 3, A = 1, N = 14, so CAN adds up to 18. Square it: \( 18^2 = 324 \).

Step 5: Work backward to the missing word's square.
Divide the given number by 324: \( 571536 \div 324 = 1764 \). Take the square root: \( \sqrt{1764} = 42 \). So the missing word's letters must add up to 42.

Step 6: Check the answer word.
GIFT: G = 7, I = 9, F = 6, T = 20, which adds up to \( 7+9+6+20 = 42 \), exactly the value needed.

Final Answer:
GIFT is the missing word. \[ \boxed{\text{GIFT}} \]