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A convenience store currently stocks 48 bottles of mineral water. The
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ishaan.wares
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Re: A convenience store currently stocks 48 bottles of mineral water. The [#permalink] New post  09 May 2017, 20:31
total ounce=35*48=1680
atq
(1680-40x)/(48-x)=25
x=32
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adkikani
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A convenience store currently stocks 48 bottles of mineral water. The [#permalink] 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] 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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menonpriyanka92
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Re: A convenience store currently stocks 48 bottles of mineral water. The [#permalink] 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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gulsam
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Re: A convenience store currently stocks 48 bottles of mineral water. The [#permalink] 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] 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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Checkmate22
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Re: A convenience store currently stocks 48 bottles of mineral water. The [#permalink] New post  08 Oct 2020, 18:04
Best sources for learning weighted averages: material by VeritasKarishma and Bunuel.

20 ounce : 40 ounce = 5 (40-35) : 15 (35-20) = 1 : 3
So, 4x = 48 -> x = 12 -> 20 ounce (12 bottles) & 40 ounce (36 bottles)

GOAL = drop weighted average to 25 by keeping 20 ounce (12 bottles) static.
So, 20 ounce : 40 ounce = 15 (40-25) : 5 (25-20) = 3 : 1
Therefore, 3x corresponds 12 bottles so x must be 4. We need to go from 36 to 4 -> reduce by 32 bottles.

D
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Re: A convenience store currently stocks 48 bottles of mineral water. The [#permalink] New post  04 Jan 2021, 22:01
Similar Question: https://gmatclub.com/forum/at-a-certain ... 07396.html
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Re: A convenience store currently stocks 48 bottles of mineral water. The [#permalink] New post  17 Mar 2021, 23:31
Bunuel wrote:
shreygupta3192 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

hey can any1 plz tell me ..
if ques says that no 20 ounce bottles are sold..
then y r we considering "20*12" while calculating the new ratio..
wats the meaning and the use of that line above.." no 20 ounce bottles are sold"
y can`t we directly put 0 bottles for 20 ounces..

y can`t we go directly for ..

25=(20(0)+40(x))/x..

confused..:(


No. The question asks about the average weight of bottles which are not sold.

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

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 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.

Answer: D.

Hope it's clear.


I think this is the only way to solve this question in under 2 minutes. Kudos Bunuel..
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VeritasKarishma
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Re: A convenience store currently stocks 48 bottles of mineral water. The [#permalink] New post  18 Mar 2021, 03:09
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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


Use weighted averages formula: https://www.veritasprep.com/blog/2011/0 ... -averages/

w1/w2 = (A2 - Aavg)/(Aavg - A1) = (40 - 35)/(35 - 20) = 1/3
Ratio of 20 ounce bottles : 40 ounce bottles = 1 : 3
So of the 48 bottles, 12 are 20-ounce bottles and 36 are 40-ounce bottles.

New Avg = 25
w1/w2 = (A2 - Aavg)/(Aavg - A1) = (40 - 25)/(25 - 20) = 3/1
New Ratio of 20 ounce bottles : 40 ounce bottles = 3 : 1
We still have 12 20-ounce bottles so we must have only 4 40-ounce bottles.

Hence from 36, the number of bottles of 40-ounces has dropped to 4. This means 32 bottles were sold.
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Re: A convenience store currently stocks 48 bottles of mineral water. The [#permalink] New post  18 Mar 2021, 03:25
The last sentence is so confusing.

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?

i was thinking #20 is 0 and i made complete mess of this problem. :(

Not able to understand whether my concept is clear or not about weighted average.

Request to provide your inputs

Bunuel chetan2u VeritasKarishma
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Re: A convenience store currently stocks 48 bottles of mineral water. The [#permalink] New post  18 Mar 2021, 19:29
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rsrighosh wrote:
The last sentence is so confusing.

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?

i was thinking #20 is 0 and i made complete mess of this problem. :(

Not able to understand whether my concept is clear or not about weighted average.

Request to provide your inputs

Bunuel chetan2u VeritasKarishma


You are given "no 20 ounce bottles are sold".
It means none of them are sold. So all 20 ounce bottles are still there.
If all 20 ounce bottles were sold, how could the average be anything other than 40 since there would be only 40 ounce bottles.
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Re: A convenience store currently stocks 48 bottles of mineral water. The [#permalink]
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