The mass of 1 cubic meter of a substance is 800 kilograms under certai

Question

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

(A) 0.80
(B) 1.25
(C) 8.00
(D) 12.50
(E) 80.00

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Is there an easy way to do these types of problems? I spent a lot of time trying to figure out the correct conversions and then still got the wrong answer (correct digits, just was off by a power of 10)

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Official Answer

B

Bunuel · Accepted Answer

800 kg - 1 cubic meter; 800,000 g - 1 cubic meter; 800,000 g - 1,000,000 cubic centimeters; 1 g - 1,000,000/800,000 = 10/8 = 1.25 cubic centimeters. Answer: B. Please read and follow: how-to-improve-the-forum-search-function-for-others-99451.html Provide answer choices for PS questions

Yalephd · Answer

Thanks, Bunuel. Sorry about posting in the wrong forum. 
I am confused, because isn't 1,000,000 cubic centimeters / 800,000 g the density of the substance. That is 1.25 cubic cubic centimeters per gram of the substance. The question asked for volume, not density.

Bunuel · Answer

Density is mass divided by volume. So density of the given substance will be mass/volume=800kg/1m^3=800 kg/m^3 or 1g/1.25cm^3=0.8 g/cm^3.

Next, ask yourself if 800,000 g is equivalent to 1,000,000 cubic centimeters then 1 g is equivalent to how many cubic centimeters? --> 1 g - 1,000,000/800,000 = 10/8 = 1.25 cubic centimeters.

Hope it's clear.

BrentGMATPrepNow · Answer

GIVEN:  1  cubic METER of the substance weighs  800  KILOGRAMS
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

fskilnik · Answer

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

PERFECT opportunity for the  UNITS CONTROL , one of the most powerful tools in our method!

?\,\,\, = \,\,\,1\,\,{m{g}}\,\,\,\left( {{{1\,{m{kg}}\,} \over {{{10}^3}\,{m{g}}}}\matrix{
 
earrow \cr 
 
earrow \cr

} } ight)\,\,\,\,\left( {{{1\,{{m{m}}^3}\,} \over {800\,{m{kg}}}}\matrix{
 
earrow \cr 
 
earrow \cr

} } ight)\,\,\,\,\left( {{{{{10}^6}\,{m{c}}{{m{m}}^3}\,} \over {1\,{{m{m}}^3}}}\matrix{
 
earrow \cr 
 
earrow \cr

} } ight)\,\,\,\,\,\, = \,\,\,\,{{{{10}^6}} \over {{{10}^3} \cdot 800}} = {{10} \over 8} = 1{1 \over 4}\,\,\,\,\,\,\,\,\left

Obs.: arrows indicate licit converters.

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

Regards, 
Fabio.

ScottTargetTestPrep · Answer

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:

800,000/1,000,000 = 1/x

8/10 = 1/x

8x = 10

x = 1.25

Answer: B

KarishmaB · Answer

Just replace the given units with the required units as per the relation.

Weight 800 kg => Volume 1 m^3

Weight 800 * 1000 grams => Volume 1 *100 cm *100 cm * 100 cm

Weight 1 gram => Volume 1000000 cm^3 /800 * 1000

Weight 1 gram => Volume 5/4 = 1.25 cm^3

sarthak1701 · Answer

Think of it as a rate. 800 kg/1 m^3

What would be the rate of 1 kg? = 1kg/800m^3

Since 1 kg = 1000 grams, we get 1000 grams/800m^3

Follow the same logic to get the 'rate' of 1 gram = 1 gram/8*10^5 m^3.

Since we need the answer for 1g/1cm^3, we multiply the numerator by 10^6. Solving for it we get 10/8 = 5/4 = 1.25

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