Randy's Bar

kartikshah wrote:Randy's" bar serves customers every weeknight from 5 pm to 1 am. In Randy's bar "Silvermoon" beer is sold at a constant rate except during happy hour, from 6:30 to 7:30 pm, when the rate triples.

If a keg of Silvermoon beer is half empty at 5pm on Monday, and two-thirds empty at the beginning of the happy hour, when will it be completely empty?

Monday, 7:30 pm
Monday, 9 pm
Monday, 7 pm
Monday, 6:45 pm
Monday, 9:30 pm

Source: Master GMAT

I did not understand the explanation provided by Master GMAT at all. Would appreciate a clear explanation.

Let me try:

Let's assume keg means a bottle. So, suppose there were 120 bottles of the beer.

At 5 Pm there are 1/2 bottles are sold. Remaining are 60 bottles.

At 6.30 PM (i.e beginning if happy hour) 2/3 bottles are sold. Remaining are 1/3 of 120 = 40 bottles.

Lets calculate the rate of consumption (during normal hours): 20 bottles in 1.5 hrs ie 40/3 bottles per hour.

We are given that 6.30 pm to 7.30 pm is the happy hour and rate of consumption triples. So, the rate of consumption of the beer in happy hour is (40/3)*3 = 40 bottles per hour.

As we had calculated that at the beginning of happy hour 40 bottles are left, they will be sold in one our. So the beer would be over at 7.30PM. Ans is A.

Let the constant rate of consumption during normal hours be X
then the rate of consumption during happy hours is 3X

Consumption from 5p.m to 6p.m = X
Consumption from 6p.m - 6:30p.m = X/2 (Half an hour)
Consumption from 6:30p.m to 7:30p.m = 3X (Happy hours)
Consumption from 7:30p.m - 8p.m = X/2 (Half an hour)
Consumption from 8p.m - 9p.m = X
Consumption from 9p.m - 10p.m = X
Consumption from 10p.m - 11p.m = X
Consumption from 11p.m - 12a.m = X
Consumption from 12a.m - 1a.m = X

Consumption from 5p.m to start of happy hour,i.e.6:30p.m = 1.5X
At 5p.m, The keg was half empty. i,e it was half full
At 6:30p.m, the keg was 2/3rd empty. i.e it was 1/3 full
Consumption from 5p.m to start of happy hour,i.e.6:30p.m = 1/2-1/3 = 1/6 of the keg
1.5X = 1/6
X = 1/9.

At the start of happy hour, the keg is 1/3rd full.
Consumption from start of happy hour,i.e.6:30p.m to end of happy hour, i.e. 7:30p.m = 3X = 3/9 = 1/3rd of the keg. So the half is empty by the end of Happy hour, i.e at 7:30 PM

Answer A