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Bunuel
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.


 


This question was provided by GMAT Club
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Volume of Red Ballon filled with helium is 'Vr'

Volume of Blue Ballon filled with air is 'Vb'

After 10 days Volume of Red Ballon \(V_1\)= \(Vr*(1-\frac{m}{100})^{10}\)

After 10 days Volume of Blue Ballon \(V_2\)= \(Vb*(1-\frac{n}{100})^{10}\)

(1) The ratio m to n is 3 to 1.
Insufficient. From this, without the information about Vr and Vb, we cannot determine the Ratio of \(V_1\) and \(V_2\)


(2) The initial ratio of volumes of helium and air in the balloons were 6 to 5.
Insufficient. From this, without the information about m and n, we cannot determine the Ratio of \(V_1\) and \(V_2\)

Combining 1 and 2 , we get
\(V_1\)/\(V_2\) = \(Vr*(1-\frac{m}{100})^{10}\) / \(Vb*(1-\frac{n}{100})^{10}\)

\(V_1\)/\(V_2\) = \(6*(1-\frac{3n}{100})^{10}\) / \(5*(1-\frac{n}{100})^{10}\)

We cannot solve this untill we know the exact value of n.

IMO E.
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