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
OA B
Source: GMAT Prep
The mass of 1 cubic meter of a substance is 800 kg under
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GIVEN: 1 cubic METER of the substance weighs 800 KILOGRAMSBTGmoderatorDC 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
1 kg =1,000 grams, so we can write: 1 cubic METER of the substance weighs 800,000 GRAMS
1 cubic meter = 1,000,000, so we can write: 1,000,000 cubic CENTIMETERS of the substance weighs 800,000 GRAMS
What is the volume in cubic centimeters of 1 gram of this substance under these conditions?
Take last line and divide both values by 800,000 to get: 1,000,000/800,000 cubic CENTIMETERS of the substance weighs 800,000/800,000 GRAMS
Simplify to get: 1.25 cubic CENTIMETERS of the substance weighs 1 GRAM
Answer: B
Cheers,
Brent
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$$1\,{{\rm{m}}^3}\,\, \leftrightarrow \,\,800\,{\rm{kg}}\,\,\,\,\,\,\,\left( {1\,{\rm{kg}}\,\, = \,\,{{10}^3}\,{\rm{g}}\,\,\,\,\,{\rm{;}}\,\,\,\,1\,{{\rm{m}}^3}\,\, = \,\,{{10}^6}\,{\rm{c}}{{\rm{m}}^3}} \right)$$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
$${\rm{1}}\,\,{\rm{g}}\,\,\, \leftrightarrow \,\,{\rm{?}}\,\,{\rm{c}}{{\rm{m}}^3}$$
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.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Since 800 kg = 800 x 1000 = 800,000 grams and 1 m^3 = 1,000,000 cm^3, we can create the ratio, where x is the number of cubic centimeters of 1 gram of the substance: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
800,000/1,000,000 = 1/x
8/10 = 1/x
8x = 10
x = 1.25
Answer: B
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