The mass of 1 cubic meter of a substance is 800 kg under

BTGmoderatorDC wrote:The mass of 1 cubic meter of a substance is 800 kg under certain conditions. What is the volume in cubic centimeters of 1 gram of this substance under these conditions? (1 kg =1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)

A. 0.8
B. 1.25
C. 8.0
D. 12.50
E. 80
Source: GMAT Prep

$$1\,{{\rm{m}}^3}\,\, \leftrightarrow \,\,800\,{\rm{kg}}\,\,\,\,\,\,\,\left( {1\,{\rm{kg}}\,\, = \,\,{{10}^3}\,{\rm{g}}\,\,\,\,\,{\rm{;}}\,\,\,\,1\,{{\rm{m}}^3}\,\, = \,\,{{10}^6}\,{\rm{c}}{{\rm{m}}^3}} \right)$$
$${\rm{1}}\,\,{\rm{g}}\,\,\, \leftrightarrow \,\,{\rm{?}}\,\,{\rm{c}}{{\rm{m}}^3}$$

PERFECT opportunity for the UNITS CONTROL, one of the most powerful tools in our method!
$$?\,\,\, = \,\,\,1\,\,{\rm{g}}\,\,\,\left( {{{1\,{\rm{kg}}\,} \over {{{10}^3}\,{\rm{g}}}}\matrix{
\nearrow \cr
\nearrow \cr

} } \right)\,\,\,\,\left( {{{1\,{{\rm{m}}^3}\,} \over {800\,{\rm{kg}}}}\matrix{
\nearrow \cr
\nearrow \cr

} } \right)\,\,\,\,\left( {{{{{10}^6}\,{\rm{c}}{{\rm{m}}^3}\,} \over {1\,{{\rm{m}}^3}}}\matrix{
\nearrow \cr
\nearrow \cr

} } \right)\,\,\,\,\,\, = \,\,\,\,{{{{10}^6}} \over {{{10}^3} \cdot 800}} = {{10} \over 8} = 1{1 \over 4}\,\,\,\,\,\,\,\,\left[ {{\rm{c}}{{\rm{m}}^3}} \right]$$
Obs.: arrows indicate licit converters.


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.