Question

Let $D_{70}=\{1,2,5,7,10,14,35,70\}$ . Define ${}^{\prime }{+}^{\prime },$ $.,$ and ${}^{\prime }{.}^{\prime }$ by $a+b=1cm(a,b),a.b=\gcd (a,b)$ and $a^{\prime }=\frac{70}{a}$ for all $a,b\in D_{70}$ .The value of $(2+7)$ $(14.10{)}^{\prime }$ is:

• A. 7
• B. 14
• C. 35
• D. 5
• E. 1

Answer 1

Answer: (A)

$(2+7)=1cm\text{ (}2,7)=14$
and $(14-10)=gcd\text{ (}14,10)=2$
$\therefore$ $(14.10)=\frac{70}{2}=35$
$\therefore$ $(2+7)(14.10)$
$=14.35=\gcd (14,35)=7$