Question

Mark the correct alternative in the following question:

The sum of two consecutive odd numbers is 36. The larger number is

(a) 17 (b) 15 (c) 19 (d) 21

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{two}\mathrm{consecutive}\mathrm{odd}\mathrm{numbers}\mathrm{be}x\mathrm{and}x+2. \\ \mathrm{As},\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{the}\mathrm{two}\mathrm{consecutive}\mathrm{odd}\mathrm{numbers}\mathrm{is}36. \\ \Rightarrow x+\left(x+2\right)=36 \\ \Rightarrow 2x+2=36 \\ \Rightarrow 2x=36-2 \\ \Rightarrow 2x=34 \\ \Rightarrow x=\frac{34}{2} \\ \Rightarrow x=17 \\ \therefore x+2=17+2=19 \end{gathered}$$

So, the larger number is 19.

Hence, the correct alternative is option (c).