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.
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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

D.

20 p + 40 (1-p) = 35
p = 1/4
so 20 oz = 12

12 x 20 / (12+x) + 40x / (12+x) = 25

x = 4
so 32 bottles with 40 oz should be sold.

D

20x + 40y = 35*48

20x + 40 (y-t) = 25*(48-t)
20x + 40y -40t = 25*48 - 25t
35*48 -40t = 25*48 -25t
t =32
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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..

hi thanx for ur valuable answer but i`ll be glad if u could put it algebrically...that will be more easier for me to understand.

also, plz tell me wat is the point of "20 ounces bottles not sold" ... y r we still considering that while calculating the new ratio..it should be 0 ..huh..

Algebraic ways are given in posts above.

As for your other question. I think you misunderstood the problem.

There are 12 20-ounce and 36 40-ounce bottles. The average volume of those 48 bottles is 35 ounces.

We need to find how many of 36 40-ounce bottles must be sold for the average volume of the remaining bottles to be reduced to 25 ounces.
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Shrey,


We can establish from question

here x is number of 20 ounce bottles , y is 40 ounce bottles
x+y=48
20x+40y=1680

x=12,y=36
Coming to remaining part of question

Value of 20 ounce bottles will be 0 , if we consider the bottles sold.

20x+40z=25(x+z);

z = remaining bottles
x=12 , no removal here
20*12+40(z)=25(12+z);z=4

if remaining is 4 ,then 36-4 were sold=32.

However Brunel's approach is good time saving approach.

Fantastic solution Bunuel, you are a legend !!

You can also resolve this question with weighted avg formula

20 40
\ /
35
/ \
15 5

Ratio : 3: 1 or we can say that 40 ounce bottles are three time as many as 20 ounce

so number of 40 ounce bottles are 36 and 20 ounce bottles are 12

next (20(12)+ 40x)/12+x = 25 -->where x is the remaining 40 ounce bottles

x= 4 i.e. 36-4=> 32 of 40 ounce bottles have been sold

its taking a bit longer to solve using the algebraic approach..
Anyone with any other approach?
Regards
CC- Abhishek009
StoneCold
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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
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chetan2u Bunuel VeritasPrepKarishma niks18




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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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.

I think this is the only way to solve this question in under 2 minutes. Kudos Bunuel..

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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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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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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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 to be sold.
So, 20*12+40(36-a)= (48-a)*25
So, a=32 [Option D]