Question

(m+1)${}^2$ = 24n+ 2m +2. m is less than 100 and n is any whole number. How many values are possible for m?

• A. 10
• B. 32
• C. 18
• D. none of these

Answer 1

The correct option is D none of these

option d

m${}^2$ -1 =24n. This means that when m${}^2$ is divided by 24 it leaves a remainder -1.

m is of the form (6p+1)${}^2$ or (6p-1)${}^2$.

Therefore we have to find the possible values of (6p+1) and ( 6p-1) less than 100.

Answer is 33.