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08 Nov 2022, 02:30
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
69% (02:13) correct
31%
(01:51)
wrong
based on 387
sessions
History
Date
Time
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A factory makes barrels of the same shape but different sizes; the amount of water they hold varies directly as the cube of their height. The four-foot-high barrel holds 20 gallons of water; how much water would the six-foot-high barrel hold?
A. 80 gal
B. 67 1/2 gal
C. 64 gal
D. 45 gal
E. 30 gal
A. 80 gal
B. 67 1/2 gal
C. 64 gal
D. 45 gal
E. 30 gal
08 Nov 2022, 09:28
Kudos
Bookmarks
A factory makes barrels of the same shape but different sizes; the amount of water they hold varies directly as the cube of their height. The four-foot-high barrel holds 20 gallons of water; how much water would the six-foot-high barrel hold?
A. 80 gal
B. 67 1/2 gal
C. 64 gal
D. 45 gal
E. 30 gal
Trying to solve just by thinking it.
If height is increased by 50% then the volume of water would increase proportionately i.e. 1.5 times but thrice.
Therefore 20 gallon would become 20*1.5*1.5*1.5 = 67.5
This calc looks cumbersome so better approximation works. 1.5 * 1.5 = 2.25
Therefore D and E are out. 2.25 if increased by 150%(1.5 times) would definitely be more than 60. So, B and C look good. A is not since 20 needs to have a factor of more than 1.5 after multiplying with 2.25 i.e. 45. Out of B and C, B is right since .5*.5*.5 gives 5 as unit digit if decimals are ignored for a while. In fact, no need to think too much as we have done above. Just the 5 as unit digit leads us to B.
Answer B.
A. 80 gal
B. 67 1/2 gal
C. 64 gal
D. 45 gal
E. 30 gal
Trying to solve just by thinking it.
If height is increased by 50% then the volume of water would increase proportionately i.e. 1.5 times but thrice.
Therefore 20 gallon would become 20*1.5*1.5*1.5 = 67.5
This calc looks cumbersome so better approximation works. 1.5 * 1.5 = 2.25
Therefore D and E are out. 2.25 if increased by 150%(1.5 times) would definitely be more than 60. So, B and C look good. A is not since 20 needs to have a factor of more than 1.5 after multiplying with 2.25 i.e. 45. Out of B and C, B is right since .5*.5*.5 gives 5 as unit digit if decimals are ignored for a while. In fact, no need to think too much as we have done above. Just the 5 as unit digit leads us to B.
Answer B.
