Last Updated on May 3, 2023
GMAT OFFICIAL GUIDE PS
Solution:
We are given that orangeade is made on Day 1 with an EQUAL AMOUNT of water and orange juice. We can set this information up into a ratio using a variable multiplier:
W : OJ = x : x
Thus, orangeade quantity = amount of water + amount of OJ = x + x = 2x
We are next given that orangeade on Day 2 was made by mixing the SAME AMOUNT of orange juice with TWICE THE AMOUNT of water. We can set this information up into a ratio using a variable multiplier:
W : OJ = 2x : x
Thus, orangeade quantity = amount of water + amount of OJ = 2x + x = 3x
We also know that all orangeade made was sold and that the revenue on both days was the same. We can therefore set up the following equation:
Day 1 Revenue = Day 2 Revenue
That is,
(quantity sold Day 1)(price per glass Day 1) = (quantity sold Day 2)(price per glass Day 2)
Let a be the amount of orangeade a glass can hold, then
quantity sold Day 1 = the number of glasses of orangeade sold on Day 1 = 2x/a
Similarly,
quantity sold Day 2 = the number of glasses of orangeade sold on Day 2 = 3x/a
We also know that the price per glass on day 1 = $0.6
But we don’t know the price per glass on day 2, so let’s label it as variable p.
We now have:
(2x/a)(0.6) = (3x/a)(p)
Multiplying both sides by a, we have:
(2x)(0.6) = (3x)(p)
1.2x = 3xp
1.2 = 3p
p = 0.4
Thus, each glass of orangeade was sold for $0.40 on Day 2.
Answer: D
