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18 Dec 2023, 07:00
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E
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12 Days of Christmas 🎅 GMAT Competition with Lots of Questions & Fun
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.
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.
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19 Dec 2023, 08:52
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GMAT Club Official Explanation:
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.
General Discussion
18 Dec 2023, 13:31
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Bunuel
(1) The ratio m to n is 3 to 1.
This statement provides the proportion between the percentages of helium released from the red balloon and air released from the blue balloon. Yet, lacking details about the initial volumes or daily release volumes, it is impossible to ascertain the absolute volumes for either balloon. Therefore, this statement alone does not offer sufficient information.
(2) The initial ratio of volumes of helium and air in the balloons were 6 to 5.
The initial balloon volume ratio is given, but daily gas release percentages are missing. We cannot determine relative volumes after 10 days without this information.
Statement (1) & (2)
By merging the two statements, we are aware of the initial volume ratio (from statement 2) and the percentage ratio by which the Grinch releases helium and air (from statement 1). Nevertheless, the details about the daily absolute volumes released are still missing. Consequently, we are unable to calculate the relative volumes of helium and air after 10 days. The combined statements do not provide sufficient information.
IMO E
