Question

On the set $\mathrm{Z}$ of all integers $*$ is defined by$\mathrm{a}*\mathrm{b}=\mathrm{a}+\mathrm{b}-5$. If $2*(\mathrm{x}*3)=5$, then $\mathrm{x}$ is equal to

• A. $0$
• B. $3$
• C. $5$
• D. $10$

Answer 1

The correct option is D

$10$

Explanation for the correct option:

Find $X$:

Given : $\mathrm{a}*\mathrm{b}=\mathrm{a}+\mathrm{b}-5$

$$\begin{gathered} 2*(\mathrm{x}*3)=5 \\ R.H.S=5 \end{gathered}$$

Find $L.H.S$

$$\begin{gathered} 2*\left(\mathrm{x}*3\right)=2*\left(\mathrm{x}+3-5\right)\left[\because \mathrm{a}*\mathrm{b}=\mathrm{a}+\mathrm{b}-5\right] \\ =2*\left(\mathrm{x}-2\right) \\ =2+\mathrm{x}-2-5\left[\because \mathrm{a}*\mathrm{b}=\mathrm{a}+\mathrm{b}-5\right] \\ =\mathrm{x}-5 \end{gathered}$$

Equating $L.H.S$ and $R.H.S$

$$\begin{gathered} x-5=5 \\ x=10 \end{gathered}$$

Hence, option (D) is the correct answer.