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31 Dec 2023, 01:46
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E
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Difficulty:
95%
(hard)
Question Stats:
35% (01:48) correct
65%
(01:49)
wrong
based on 82
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Starting December 1st, the Grinch begins deflating a red balloon filled with helium and a blue balloon filled with air at Santa's workshop. Each day, he releases \(m\%\) of that day's remaining helium volume from the red balloon and \(n\%\) of that day's remaining air volume from the blue balloon. After 10 days, will there be a greater volume of helium in the red balloon compared to the volume of air in the blue balloon?
(1) The ratio \(m\) to \(n\) is 3 to 1.
(2) The initial ratio of volumes of helium and air in the balloons were 6 to 5.
(1) The ratio \(m\) to \(n\) is 3 to 1.
(2) The initial ratio of volumes of helium and air in the balloons were 6 to 5.
31 Dec 2023, 01:46
Kudos
Bookmarks
Official Solution:
Starting December 1st, the Grinch begins deflating a red balloon filled with helium and a blue balloon filled with air at Santa's workshop. Each day, he releases \(m\%\) of that day's remaining helium volume from the red balloon and \(n\%\) of that day's remaining air volume from the blue balloon. After 10 days, will there be a greater volume of helium in the red balloon compared to the volume of air in the blue balloon?
Essentially we are given two quantities that decrease daily by \(m\%\) and \(n\%\), respectively. The question is whether, after 10 days, the first quantity (helium) is greater than the second one (air).
(1) The ratio \(m\) to \(n\) is 3 to 1.
This tells us the ratio of the percent decrease. However, we know nothing about the initial values (volumes). Not sufficient.
(2) The initial ratio of volumes of helium and air in the balloons were 6 to 5.
This gives us the initial ratio of the quantities. However, we know nothing about the percent decreases. Not sufficient.
(1)+(2) Consider this logically rather than algebraically. Suppose the initial volumes are 60 \(m^3\) of helium and 50 \(m^3\) of air. If \(m\) and \(n\) are large, say 90% and 30%, then even after one day, more air than helium will remain. Conversely, if \(m\) and \(n\) are very small, like 0.00003% and 0.00001%, even after 100 days, more helium will remain due to the minuscule decrease rate. Therefore, even when combined, these statements do not provide a definitive answer. Not sufficient.
Answer: E
Starting December 1st, the Grinch begins deflating a red balloon filled with helium and a blue balloon filled with air at Santa's workshop. Each day, he releases \(m\%\) of that day's remaining helium volume from the red balloon and \(n\%\) of that day's remaining air volume from the blue balloon. After 10 days, will there be a greater volume of helium in the red balloon compared to the volume of air in the blue balloon?
Essentially we are given two quantities that decrease daily by \(m\%\) and \(n\%\), respectively. The question is whether, after 10 days, the first quantity (helium) is greater than the second one (air).
(1) The ratio \(m\) to \(n\) is 3 to 1.
This tells us the ratio of the percent decrease. However, we know nothing about the initial values (volumes). Not sufficient.
(2) The initial ratio of volumes of helium and air in the balloons were 6 to 5.
This gives us the initial ratio of the quantities. However, we know nothing about the percent decreases. Not sufficient.
(1)+(2) Consider this logically rather than algebraically. Suppose the initial volumes are 60 \(m^3\) of helium and 50 \(m^3\) of air. If \(m\) and \(n\) are large, say 90% and 30%, then even after one day, more air than helium will remain. Conversely, if \(m\) and \(n\) are very small, like 0.00003% and 0.00001%, even after 100 days, more helium will remain due to the minuscule decrease rate. Therefore, even when combined, these statements do not provide a definitive answer. Not sufficient.
Answer: E
02 Jan 2024, 06:47
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Hi Bunuel, I was wondering if it is important to mention that the capacity of the two types of balloons is same.
