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# Can you make the following assumption???

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Intern
Joined: 26 Jan 2018
Posts: 12
Can you make the following assumption???  [#permalink]

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08 Aug 2018, 13:37
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Difficulty:

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Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

A store sells only 10oz cans of soda for $2 and 40oz cans of soda for$5 on a given day, and the average oz of all cans sold is 30oz. Therefore, can you assume that the average dollar value of cans sold is $4? My logic is as follows: 10oz-$2 / 20oz-$3 / (AVG) 30oz-$4 / 40oz-$5 Please clarify. Thanks. Intern Joined: 28 Apr 2018 Posts: 16 GMAT 1: 740 Q48 V42 Re: Can you make the following assumption??? [#permalink] ### Show Tags 08 Aug 2018, 19:27 coolo wrote: A store sells only 10oz cans of soda for$2 and 40oz cans of soda for $5 on a given day, and the average oz of all cans sold is 30oz. Therefore, can you assume that the average dollar value of cans sold is$4?

My logic is as follows: 10oz-$2 / 20oz-$3 / (AVG) 30oz-$4 / 40oz-$5

Thanks.

Another way of proving it is:

Say "x" is the number of 10oz cans and "y" is the number of 40oz cans. We know that they have an average capacity of 30oz, therefore:
$$\frac{10x+40y}{x+y} = 30$$ (total number of oz divided by total number of cans [x+y] equals avg. oz)

Multiply by each side by (x+y):
$$10x + 40y = 30x + 30y$$

Combine like terms and isolate y:
$$10y = 20x$$
$$y=2x$$

Therefore, the number of 40oz cans (y) is twice the number of 10oz cans (x). You can then plug in a few numbers to test it out:
For x=3 and y=6, the average cost would be as follows: $$\frac{x(cost_of_x) + y(cost_of_y)}{x+y} = \frac{3(2) + 6(5)}{3+6} = \frac{36}{9} = 4$$
For x=8 and y= 16, the average cost would be the same: $$\frac{8(2) + 16(5)}{8+16} = \frac{96}{24} = 4$$

Hope this helps. Let me know if you have any questions!
_________________

Audra Zook
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https://audrazook.com

Math Expert
Joined: 02 Sep 2009
Posts: 51121
Re: Can you make the following assumption???  [#permalink]

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09 Aug 2018, 23:11
coolo wrote:
A store sells only 10oz cans of soda for $2 and 40oz cans of soda for$5 on a given day, and the average oz of all cans sold is 30oz. Therefore, can you assume that the average dollar value of cans sold is $4? My logic is as follows: 10oz-$2 / 20oz-$3 / (AVG) 30oz-$4 / 40oz-\$5

Thanks.

_________________
Re: Can you make the following assumption??? &nbs [#permalink] 09 Aug 2018, 23:11
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# Can you make the following assumption???

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