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A convenience store currently stocks 48 bottles of mineral water. The

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Re: A convenience store currently stocks 48 bottles of mineral water. The  [#permalink]

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New post 09 May 2017, 20:31
total ounce=35*48=1680
atq
(1680-40x)/(48-x)=25
x=32
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A convenience store currently stocks 48 bottles of mineral water. The  [#permalink]

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New post 14 Apr 2018, 03:23
chetan2u Bunuel VeritasPrepKarishma niks18

Quote:
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?

Quote:
Hi,
the other method would be weighted average method.. people have already used it above, still ill do it once again..

TWO steps..


first - initial numbers
20 and 40 avail and average is 35..
so \(\frac{# of 20}{# of 40} = \frac{40-35}{35-20} = \frac{1}{3}\)
so # of 20 \(= \frac{1}{1+3} *48 =12\)..
and # of 40 ounces = 48-12 = 36

second -
20 and 40 avail and average is 25..
so\(\frac{# of 20}{# of 40} = \frac{40-25}{25-20} =\frac{3}{1}\)
so # of 20\(= \frac{3}{1+3} *x =12\), here we know # of 20 ounces remains constant..
so x= 16
and # of 40 ounces = 16-12 = 4..
now # of 40 ounces bottle sold = 36-4 = 32


question stem says:if no 20 ounce bottles are sold, meaning no bottles are sold at all , not : additional bottles are not sold.
Are we on same page?
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Re: A convenience store currently stocks 48 bottles of mineral water. The  [#permalink]

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New post 14 Apr 2018, 18:15
adkikani wrote:
chetan2u Bunuel VeritasPrepKarishma niks18

Quote:
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?

Quote:
Hi,
the other method would be weighted average method.. people have already used it above, still ill do it once again..

TWO steps..


first - initial numbers
20 and 40 avail and average is 35..
so \(\frac{# of 20}{# of 40} = \frac{40-35}{35-20} = \frac{1}{3}\)
so # of 20 \(= \frac{1}{1+3} *48 =12\)..
and # of 40 ounces = 48-12 = 36

second -
20 and 40 avail and average is 25..
so\(\frac{# of 20}{# of 40} = \frac{40-25}{25-20} =\frac{3}{1}\)
so # of 20\(= \frac{3}{1+3} *x =12\), here we know # of 20 ounces remains constant..
so x= 16
and # of 40 ounces = 16-12 = 4..
now # of 40 ounces bottle sold = 36-4 = 32


question stem says:if no 20 ounce bottles are sold, meaning no bottles are sold at all , not : additional bottles are not sold.
Are we on same page?


Hi adkikani

Yes you are right in your assessment that no new 20 ounce bottles are added or sold.

In the second part of the solution, "x" denotes the total number of bottles left after selling 40 ounce bottles. In this solution number of 20 ounce bottle remains 12. So on solving, we get x=16 i.e. only 16 bottles are left after 40 ounce bottles are sold. so out of 16, 12 are 20 ounce bottles and the remaining 4 are 40 ounce bottles. As there are 36, 40 ounce bottles, so 36-4=32, 40 ounce bottles were sold.
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Re: A convenience store currently stocks 48 bottles of mineral water. The  [#permalink]

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New post 09 Oct 2019, 05:53
Hi Bunuel
It takes me ~3 mins to solve this one because of operations...could you suggest a method that takes < 2 mins?
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Re: A convenience store currently stocks 48 bottles of mineral water. The  [#permalink]

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New post 15 Dec 2019, 09:44
ArvGMAT wrote:
32

Here is how I got it:

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


Thanks! I think it is the most fast and clear explanation!
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Re: A convenience store currently stocks 48 bottles of mineral water. The  [#permalink]

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New post 15 Dec 2019, 10:05
dred wrote:
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


Total bottles = 48
Present ratio of 20 to 40 ounces bottles to make average 35 ounces = 1:3
20 ounces bottles = 12
40 ounces bottles = 36

To make average 25 ounces , ratio of 20 to 40 ounces bottles = 3:1
Since no 20 ounces bottles are sold, number of 40 ounces bottles = 12/3 = 4

Number of 40 ounces bottles to be sold = 36-4 = 32 bottles

IMO D

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Re: A convenience store currently stocks 48 bottles of mineral water. The   [#permalink] 15 Dec 2019, 10:05
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