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A convenience store stocks soda in 12-ounce and 24-ounce bottles. If t 15 Oct 2018, 10:09
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79% (01:31) correct 21% (01:58) wrong based on 807 sessions

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A convenience store stocks soda in 12-ounce and 24-ounce bottles. If the average capacity of all the bottles in the store is 22 ounces, then what fraction of the bottles in the store are 12 ounces?

A) 1/3
B) 1/6
C) 2/3
D) 5/6
E) 2/5
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B
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A convenience store stocks soda in 12-ounce and 24-ounce bottles. If t 15 Oct 2018, 10:25
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dimmak
A convenience store stocks soda in 12-ounce and 24-ounce bottles. If the average capacity of all the bottles in the store is 22 ounces, then what fraction of the bottles in the store are 12 ounces?

A) 1/3
B) 1/6
C) 2/3
D) 5/6
E) 2/5
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We can apply the weighted average formula, which says:

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

So, we get: group average = (proportion of 12-ounce sodas in stock)(average weight of 12-ounce sodas) + (proportion of 24-ounce sodas in stock)(average weight of 24-ounce sodas)

Let F = the fraction (proportion) of 12-ounce sodas in stock
This means 1 - F = the fraction (proportion) of 24-ounce sodas in stock
We also know the weighted average of all sodas is 22 ounces.

So, we can write: 22 = (F)(12) + (1 - F)(24)
Expand: 22 = 12F + 24 - 24F
So: 22 = 24 - 12F
So: -2 = -12F
So: F = 2/12 = 1/6

Answer: B

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A convenience store stocks soda in 12-ounce and 24-ounce bottles. If t Updated on: 18 Oct 2018, 02:43
Originally posted by AnupamKT on 15 Oct 2018, 10:38.
Last edited by AnupamKT on 18 Oct 2018, 02:43, edited 1 time in total.
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dimmak
A convenience store stocks soda in 12-ounce and 24-ounce bottles. If the average capacity of all the bottles in the store is 22 ounces, then what fraction of the bottles in the store are 12 ounces?

A) 1/3
B) 1/6
C) 2/3
D) 5/6
E) 2/5
Show more

Let
The number of 12 ounce bottles = X and
The number of 24 ounce bottles = Y
Then, it is given in question stem that average of all the bottles are 22 ounces
so, (12*X+24*Y)/(X+Y)= 22
Solving this we get-> 12X+24Y=22X+22Y
=> 2Y=10X
=>Y/X=5

Now, we have to find what fraction of the bottles are 12 ounces=> X/(X+Y)=>1/(1+Y/X)
=> 1/(1+5)=>1/6. Hence correct option is B.
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A convenience store stocks soda in 12-ounce and 24-ounce bottles. If t 15 Oct 2018, 19:35
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dimmak
A convenience store stocks soda in 12-ounce and 24-ounce bottles. If the average capacity of all the bottles in the store is 22 ounces, then what fraction of the bottles in the store are 12 ounces?

A) 1/3
B) 1/6
C) 2/3
D) 5/6
E) 2/5

Let
The number of 12 ounce bottles = X and
The number of 24 ounce bottles = Y
Then, it is given in question stem that average of all the bottles are 22 ounces
so, (12*X+24*Y)/(X+Y)= 22
Solving this we get-> 12X+24Y=22X+22Y
=> 2Y=10X
=>Y/X=5

Now, we have to find what fraction of the bottles are 12 ounces=> X/(X+Y)=>1/(1-Y/X)
=> 1/(1-5)=>1/6. Hence correct option is B.
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Hi AnupamKT,
Please check X/(X+Y)=1/(1+Y/X)
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A convenience store stocks soda in 12-ounce and 24-ounce bottles. If t 16 Oct 2018, 06:41
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AnupamKT
dimmak
A convenience store stocks soda in 12-ounce and 24-ounce bottles. If the average capacity of all the bottles in the store is 22 ounces, then what fraction of the bottles in the store are 12 ounces?

A) 1/3
B) 1/6
C) 2/3
D) 5/6
E) 2/5

Let
The number of 12 ounce bottles = X and
The number of 24 ounce bottles = Y
Then, it is given in question stem that average of all the bottles are 22 ounces
so, (12*X+24*Y)/(X+Y)= 22
Solving this we get-> 12X+24Y=22X+22Y
=> 2Y=10X
=>Y/X=5

Now, we have to find what fraction of the bottles are 12 ounces=> X/(X+Y)=>1/(1-Y/X)
=> 1/(1-5)=>1/6. Hence correct option is B.

Hi AnupamKT,
Please check X/(X+Y)=1/(1+Y/X)
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Thanks. Noted. Typo error.
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A convenience store stocks soda in 12-ounce and 24-ounce bottles. If t 17 Oct 2018, 19:06
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dimmak
A convenience store stocks soda in 12-ounce and 24-ounce bottles. If the average capacity of all the bottles in the store is 22 ounces, then what fraction of the bottles in the store are 12 ounces?

A) 1/3
B) 1/6
C) 2/3
D) 5/6
E) 2/5
Show more

We can let a = the number of 12-ounce bottles and b = the number of 24-ounce bottles. We can create the equation:

12a + 24b = 22(a + b)

12a + 24b = 22a + 22b

2b = 10a

b = 5a

Thus, a/(a + b) = a/(a + 5a) = a/6a = 1/6 of the bottles are 12 ounces.

Answer: B
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A convenience store stocks soda in 12-ounce and 24-ounce bottles. If t 23 Oct 2018, 15:10
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dimmak
A convenience store stocks soda in 12-ounce and 24-ounce bottles. If the average capacity of all the bottles in the store is 22 ounces, then what fraction of the bottles in the store are 12 ounces?

A) 1/3
B) 1/6
C) 2/3
D) 5/6
E) 2/5
Show more

This question can be solved by using allegation method :
Attachments

Untitledbottles.png
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A convenience store stocks soda in 12-ounce and 24-ounce bottles. If t 27 Oct 2018, 01:35
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"Teeter Totter" method for solving in 1 minute.

12----------22--24

12 is further away from 22 than 24 is (the respective differences are: 10 and 2).
Take the differences and write them above the teeter totter.
Take the total difference (24-12) and write that below the teeter totter.

10 2
12----------22--24
12

Since the total average (22) is much closer to 24, it means there must be a greater number of 24 ounce bottles than 12 ounce bottles.
To find proportion, take the individual differences and divide by total difference.

Hence, proportion of 24 ounce bottles = 10/12 = 5/6
and proportion of 12 ounce bottles = 2/12 = 1/6

Answer B.

P.S the Manhattan guides discuss this method in greater detail.
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A convenience store stocks soda in 12-ounce and 24-ounce bottles. If t 27 Jan 2020, 19:33
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VeritasKarishma
Hi Karishma,

I think that I have some gaps in my understanding about the weighted average. If I am applying the weighted average method
w1/w2 = (a2-Aavg)/(Aavg-a1) ----> w1/w2 = 24-22/22-12 ------>w1/w2 = 2/10 -----> w1/w2 = 1/5 ----> As mentioned in one of your posts, the w2(24ounces) will be 1 and w1(12 ounces) will be 5. Isn't the resultant ratio 5/6? can you please comment?
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A convenience store stocks soda in 12-ounce and 24-ounce bottles. If t 28 Jan 2020, 21:30
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VeritasKarishma
Hi Karishma,

I think that I have some gaps in my understanding about the weighted average. If I am applying the weighted average method
w1/w2 = (a2-Aavg)/(Aavg-a1) ----> w1/w2 = 24-22/22-12 ------>w1/w2 = 2/10 -----> w1/w2 = 1/5 ----> As mentioned in one of your posts, the w2(24ounces) will be 1 and w1(12 ounces) will be 5. Isn't the resultant ratio 5/6? can you please comment?
Show more

The highlighted part is not correct. You can't flip the ratio

You get
w1/w2 = 1/5

So w1 is 1/6th of the total.
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A convenience store stocks soda in 12-ounce and 24-ounce bottles. If t 30 Jan 2020, 08:11
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VeritasKarishma
Hi Karishma,

I think that I have some gaps in my understanding about the weighted average. If I am applying the weighted average method
w1/w2 = (a2-Aavg)/(Aavg-a1) ----> w1/w2 = 24-22/22-12 ------>w1/w2 = 2/10 -----> w1/w2 = 1/5 ----> As mentioned in one of your posts, the w2(24ounces) will be 1 and w1(12 ounces) will be 5. Isn't the resultant ratio 5/6? can you please comment?

The highlighted part is not correct. You can't flip the ratio

You get
w1/w2 = 1/5

So w1 is 1/6th of the total.
Show more

Got it.

Thanks
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A convenience store stocks soda in 12-ounce and 24-ounce bottles. If t 21 Dec 2025, 15:43
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