Question

The sum of the any three distinct natural numbers arranged in ascending order is $200$ such that the second number is a perfect cube. How many possible values are there for this number.

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

The correct option is B

$3$

Finding the Possible Values :

$$\begin{gathered} \mathrm{The}\mathrm{perfect}\mathrm{cubes}\mathrm{upto}200\mathrm{are}1,8,27,64,125\left[\mathrm{Number}\mathrm{should}\mathrm{be}\mathrm{less}\mathrm{than}200\right] \\ \therefore 125\mathrm{cannot}\mathrm{be}\mathrm{second}\mathrm{number}.\left[\mathrm{Sum}\mathrm{should}\mathrm{be}\mathrm{less}\mathrm{than}200\right] \\ \therefore \mathrm{The}\mathrm{numbers}\mathrm{are}8,27,64. \\ \therefore \mathbf{}\mathbf{Possible}\mathbf{}\mathbf{values}\mathbf{}\mathbf{are}\mathbf{}\mathbf{3}\mathbf{.} \end{gathered}$$

Hence, correct option is B.