AMC 12A 2025 (Problem 7)

In a certain alien world, the maximum running speed

v

of an organism is dependent on its number of toes

n

and number of eyes

m

. The relationship can be expressed as

v=kn^am^b

centimeters per hour, where

k

a

, and

b

are integer constants. In a population where all organisms have

5

toes,

\log v=4+2\log m

; and in a population where all organisms have

25

eyes,

\log v=4+4\log n

, where the logarithms are base

10

. What is

k+a+b

\text{(A)}\;20

\text{(B)}\;21

\text{(C)}\;22

\text{(D)}\;23

\text{(E)}\;24