Question: A convenience store currently stocks 48 bottles of mineral water. The bottles have two sizes of either 20 or 40 ounces each. The average volume per bottle the store currently has in stock is 35 ounces. How many 40 ounce bottles must be sold for the average volume per bottle to be reduced to 25 ounces if no 20 ounce bottles are sold?

(A) 10
(B) 20
(C) 30
(D) 32
(E) 34

Correct Answer: D

Solution and Explanation:

Approach Solution 1:
The current average of 20 (35 - 15) and 40-ounce (40 - 5) bottles is 35, thus there must be 3 times as many 40-ounce bottles as 20-ounce bottles. Since there are a total of 48 bottles, then there must be 12 20-ounce bottles and 36 40-ounce bottles.

Now, we need to sell ONLY 40-ounce bottles so that the average to become 25. Same way, 25 is 5 away from 20 and 15 away from 40, so after selling some number of 40-ounce bottles, there must be 3 times as many 20-ounce bottles as 40-ounce bottles. So, there must be 12 20-ounce bottles and 12/3 = 4 40-ounce bottles.

Therefore, 36 - 4 = 32 40-ounce bottles must be sold.

Approach Solution 2:
Average is 35 ounces
x is # of 20 ounce bottles
y is # of 40 ounce bottles
20x+40y/x+y= 35
solve to get y= 3x
x+y= 48 bottles
x= 12, y= 36
20x+40z/x+z= 25
plug x= 12 and solve for z, we get z= 4
So, y-z is # of bottles sold i.e 36-4= 32

Approach Solution 3:
Let, the 20-ounce bottles are x. So, 40-ounce Bottles will be 48-x
So, 20x+40(48-x)=48*35
So, x=12, & 40-ounce bottles will be 36.
Now, Let "a" 40-ounce bottle be sold.
So, 20*12+40(36-a)= (48-a)*25
So, a= 32

“A convenience store currently stocks 48 bottles of mineral water.”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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