Question

$(8-1\frac{1}{2})+23+(256-73)+4.2-\frac{1}{2}-(3.2-2.3)$ equals

• A. 169.3
• B. 196.3
• C. 215.3
• D. 233.3

Answer 1

The correct option is C

215.3

$(8-1\frac{1}{2})+23+(256-73)+4.2-\frac{1}{2}-(3.2-2.3)$

=$(8-1\frac{1}{2})-\frac{1}{2}+(256-73)+23+4.2-(3.2-2.3)$

We know that $(x-y)-z=x-(y+z)$, for all numbers $x$, $y$, $z$.

So, $(8-1\frac{1}{2})-\frac{1}{2}=8-(1\frac{1}{2}+\frac{1}{2})=8-2=6$

Also, we know that $(x-y)+z=x-(y-z)$, for all numbers $x$, $y$, $z$ with $y>z$.

Since the above is true for all the numbers, it must be true for $x=256$, $y=73$ and $z=23$ also, as $y=73>23=z$

So, $(256-73)+23=256-(73-23)=256-50=206$

Also, we know that $x-(y-z)=(x-y)+z$, for all numbers $x$, $y$, $z$ with $y>z$.

Since the above is true for all the numbers, it must be true for $x=4.2$, $y=3.2$ and $z=2.3$ also, as $y=3.2>2.3=z$

So, $4.2-(3.2-2.3)=(4.2-3.2)+2.3=1.0+2.3=3.3$

Therefore,

$(8-1\frac{1}{2})-\frac{1}{2}+(256-73)+23+4.2-(3.2-2.3)$

= $6+206+3.3$

= $215.3$