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: Get CAN's letter sum and square it.
C = 3, A = 1, N = 14 gives a sum of 18, and $18^2 = 324$.

Step 2: Set up what the missing word's square must multiply out to.
From the CAT and DOG row, the rule is clear, (word 1 sum) squared times (word 2 sum) squared equals the table number. So here, 324 times the missing word's squared sum must equal 571536.

Step 3: Test each option by adding its letters.
MAN: M = 13, A = 1, N = 14, sum = 28, squared = 784. Check $324 \times 784 = 254016$, which does not match 571536. GIFT: G = 7, I = 9, F = 6, T = 20, sum = 42, squared = 1764. Check $324 \times 1764 = 571536$, an exact match. PAN: sum = 31, squared = 961, giving $324 \times 961 = 311364$, no match. SOFT: sum = 60, squared = 3600, giving $324 \times 3600 = 1166400$, no match.

Final Answer:
Only GIFT gives the exact product the table needs. \[ \boxed{\text{GIFT}} \]