Tomasa is making sangria for a party. She pours into a vat 4

Question

Tomasa is making sangria for a party. She pours into a vat 40 ounces of wine that is 13% alcohol by volume and 24 ounces of rum that is 35% alcohol by volume. At least how many entire 16-ounce bottles of alcohol-free soda must she add to the vat so that the resulting mixture is less than 5% alcohol?

A) 11
B) 12
C) 13
D) 14
E) 15

A) 11
B) 12
C) 13
D) 14
E) 15

tryorcry · Answer

there are two mixtures here. 1st that is formed by wine and rum containing some alcohol %age and 2nd mixting soda(0 alcohol) with mixture obtained from 1st calc.

1st mixture. 
13%----x-------35%

(35-x)/(x-13) = 40/24 ( ratio of their presence in the newly formed mixture = ratio of actual weights of wine and rum )
x= 21.5

now next mixture
0%-----5%-------21.5%
SODA MIX

Presence of soda weight of soda Y
------------------ = ----------------- = ------------
mix weight of mix 64

16.5/5 = Y/64

Y= 33*64

now to get the number of bottles we must divide Y with 16

i.e, Y/16 = 13.2

So we need atleast 13.2 or more bottles of soda to ensure that alcohol is less than 5%

Hence   Answer D.

Adit_ · Answer

24% alcohol in 40 = 5.2.
35% alcohol in 24 = 8.4.

Our net result:

5.2+8.4/(64+x) < 1/20
x>208.
No.of 16 ounce bottles asked, thus
208/16 = 13.
But we need x>13. So 14 is the least number of such bottles.

Answer:  Option D

Adit_ · Answer

The x value in the first alligation must be 21.25 and not 21.5. Kindly check it out!

work2 · Answer

here's how I solved this:

Wine: 13% of 40= 5.2
Rum: 35% of 24= 8.4
Total alcohol content= 13.6

Total mixture needs to be less than 5% or 1/20:

<

13.6/ Total vol < 1/20

Total Volume> 13.6 x 20 = 272

Current liquid in the vat = 40 + 24 = 64
Additional needed = 272 - 64 = 208

Since each bottle is 16 ounce:

Number of bottles= 208/16 = 13

13 bottles would give exactly 5%. Therefore, she must add at-least 14 bottles.

Kinshook · Answer

Tomasa is making sangria for a party. She pours into a vat 40 ounces of wine that is 13% alcohol by volume and 24 ounces of rum that is 35% alcohol by volume.

At least how many entire 16-ounce bottles of alcohol-free soda must she add to the vat so that the resulting sangria is less than 5% alcohol?

Wine: - 
Total = 40 ounces
Alcohol = 13%*40 = 5.2 ounces

Rum: - 
Total = 24 ounces
Alcohol = 35%*24 = 8.4 ounces

Total alcohol = 5.2 + 8.4 = 13.6 ounces

Since alcohol is 5%, total volume of sangria = 13.6/5% = 272 ounces

Soda to be added = 272 - 40 - 24 = 208 ounces

16-ounce bottles of alcohol-free soda to be added = 208/16 = 13 bottles

13 bottles will give exactly 5% alcohol, for less than 5% alcohol, we must add at least 14 bottles

IMO D

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=89438 --- Harsha GMAT-Club-Forum-xizs8rnh.png

Tomasa is making sangria for a party. She pours into a vat 4

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