Question

Help Linda choose the best answer for the missing number.
41 : 25 :: 145 : ?

• A. 36
• B. 121
• C. 81
• D. 100

Answer 1

The correct option is C 81

The given analogy is:
$41:25::145:\text{?}$

Let's try to find the pattern.

Considering first the left side:

$41:5^2$
$(16+25):5^2$
$4^2+5^2:5^2$

$\text{The right side is}{5}^2$.
$\text{The left side is}{4}^2+5^2$.

So, the square of the greater of the two left side terms is used as the right side term.

Let's try to apply the same logic and try to find the missing number.

$145:\text{?}$
$64+81:\text{?}$
$8^2+9^2:\text{?}$

So, out of 8 and 9 on the left term, the square of 9 will appear on the right side.

∴ We can write:
$8^2+9^2:9^2$
$8^2+9^2:81$

Hence, the correct analogy is
41 : 25 :: 145 : 81

So, the missing number is 81.