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A glass was filled with 10 ounces of water and spirit mixture with the

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A glass was filled with 10 ounces of water and spirit mixture with the  [#permalink]

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New post 30 Jun 2017, 03:09
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A glass was filled with 10 ounces of water and spirit mixture with the components in the ratio 2 : 3 respectively. If 1 percent of the initial quantity of water and 3 percent of the initial quantity of spirit evaporated each day during a twenty-day period, what percent of the original amount of mixture evaporated during this period?

(A) 4.4%
(B) 24.4%
(C) 44.0%
(D) 50.0%
(E) 80.0%

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Re: A glass was filled with 10 ounces of water and spirit mixture with the  [#permalink]

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New post 30 Jun 2017, 03:10
Bunuel wrote:
A glass was filled with 10 ounces of water and spirit mixture with the components in the ratio 2 : 3 respectively. If 1 percent of the initial quantity of water and 3 percent of the initial quantity of spirit evaporated each day during a twenty-day period, what percent of the original amount of mixture evaporated during this period?

(A) 4.4%
(B) 24.4%
(C) 44.0%
(D) 50.0%
(E) 80.0%


This is a modified question of the the following OG question: https://gmatclub.com/forum/a-glass-was- ... 40242.html
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Re: A glass was filled with 10 ounces of water and spirit mixture with the  [#permalink]

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New post 30 Jun 2017, 03:24
Since the glass is filled with 10 ounces of water and spirit mix, in the ratio 2:3
Water(weight) - 4 ounces
Spirit(weight) - 6 ounces

Since 1% of the water evaporates each day for 20 days, 20% of the water will evaporate(0.8 ounces)
Since 3% of the spirit evaporates each day for 20 days, 60% of the spirit will evaporate(3.6 ounces)

Total amount lost due to evaporation : 0.8 ounces(Water) + 3.6 ounces(Spirit) = 4.4 ounces(44% of the solution) (Option C)
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A glass was filled with 10 ounces of water and spirit mixture with the  [#permalink]

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New post Updated on: 03 Jul 2017, 08:42
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Bunuel wrote:
A glass was filled with 10 ounces of water and spirit mixture with the components in the ratio 2 : 3 respectively. If 1 percent of the initial quantity of water and 3 percent of the initial quantity of spirit evaporated each day during a twenty-day period, what percent of the original amount of mixture evaporated during this period?

(A) 4.4%
(B) 24.4%
(C) 44.0%
(D) 50.0%
(E) 80.0%

1. The ratio of water to spirits is \(\frac{2x}{3x}\)

Sum of the ratio is 2x + 3x = 5x, and 5x = 10 ounces of water and spirit mixture

Multiplier x = 2, so

original amount of water = 2x * 2 = 4 ounces
original amount of spirits = 3x * 2 = 6 ounces

2. 1% of original quantity of water evaporated for 20 days

(.01)(4) x 20 = .04 x 20 = .8 ounces evaporated

3. 3% of original quantity of spirits evaporated for 20 days

(.03)(6) x 20 = .18 x 20 = 3.6 ounces evaporated

4. Total amount evaporated is 3.6 + .8 = 4.4 ounces

Evaporated amount as percentage of original = \(\frac{4.4}{10}\) * 100 = 44%

Answer (C)

To check my work, I also calculated what amount remained after 20 days and subtracted from original amount of 10 ounces

Amount of water remaining is (original) 4 - .8 (evaporated) = 3.2 ounces

Amount of spirits remaining is (original) 6 - 3.6 (evaporated) = 2.4 ounces

Total amount remaining is 3.2 ounces + 2.4 ounces = 5.6 ounces

Amount that evaporated is 10 - 5.6 = 4.4 ounces. That works.
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Originally posted by generis on 30 Jun 2017, 09:38.
Last edited by generis on 03 Jul 2017, 08:42, edited 1 time in total.
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Re: A glass was filled with 10 ounces of water and spirit mixture with the  [#permalink]

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New post 30 Jun 2017, 11:33
Bunuel wrote:
A glass was filled with 10 ounces of water and spirit mixture with the components in the ratio 2 : 3 respectively. If 1 percent of the initial quantity of water and 3 percent of the initial quantity of spirit evaporated each day during a twenty-day period, what percent of the original amount of mixture evaporated during this period?

(A) 4.4%
(B) 24.4%
(C) 44.0%
(D) 50.0%
(E) 80.0%


20(.01*4+.03*6)/10=44%
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Re: A glass was filled with 10 ounces of water and spirit mixture with the  [#permalink]

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New post 03 Jul 2017, 06:11
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genxer123 wrote:
Bunuel wrote:
A glass was filled with 10 ounces of water and spirit mixture with the components in the ratio 2 : 3 respectively. If 1 percent of the initial quantity of water and 3 percent of the initial quantity of spirit evaporated each day during a twenty-day period, what percent of the original amount of mixture evaporated during this period?

(A) 4.4%
(B) 24.4%
(C) 44.0%
(D) 50.0%
(E) 80.0%

1. The ratio of water to spirits is \(\frac{2x}{3x}\)

Sum of the ratio is 2x + 3x = 5x, and 5x = 10 ounces of water

Multiplier x = 2, so

original amount of water = 2x * 2 = 4 ounces
original amount of spirits = 3x * 2 = 6 ounces


2. 1% of original quantity of water evaporated for 20 days

(.01)(4) x 20 = .04 x 20 = .8 ounces evaporated

3. 3% of original quantity of spirits evaporated for 20 days

(.03)(6) x 20 = .18 x 20 = 3.6 ounces evaporated

4. Total amount evaporated is 3.6 + .8 = 4.4 ounces

Evaporated amount as percentage of original = \(\frac{4.4}{10}\) * 100 = 44%

Answer (C)

To check my work, I also calculated what amount remained after 20 days and subtracted from original amount of 10 ounces

Amount of water remaining is (original) 4 - .8 (evaporated) = 3.2 ounces

Amount of spirits remaining is (original) 6 - 3.6 (evaporated) = 2.4 ounces

Total amount remaining is 3.2 ounces + 2.4 ounces = 5.6 ounces

Amount that evaporated is 10 - 5.6 = 4.4 ounces. That works.


Can you please explain me this passage?
I can't understand the wording of the problem: it states that there are 10 ounces of water, how can I relate them to the solution?
The rest of the problem is crystal clear, I just don't understand how to calculate the ammount of water and of the substance.

Thanks a lot!
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A glass was filled with 10 ounces of water and spirit mixture with the  [#permalink]

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New post 03 Jul 2017, 06:46
MvArrow wrote:
genxer123 wrote:
Bunuel wrote:
A glass was filled with 10 ounces of water and spirit mixture with the components in the ratio 2 : 3 respectively. If 1 percent of the initial quantity of water and 3 percent of the initial quantity of spirit evaporated each day during a twenty-day period, what percent of the original amount of mixture evaporated during this period?

(A) 4.4%
(B) 24.4%
(C) 44.0%
(D) 50.0%
(E) 80.0%

1. The ratio of water to spirits is \(\frac{2x}{3x}\)

Sum of the ratio is 2x + 3x = 5x, and 5x = 10 ounces of water water and spirit mixture

Multiplier x = 2, so

original amount of water = 2x * 2 = 4 ounces
original amount of spirits = 3x * 2 = 6 ounces


2. 1% of original quantity of water evaporated for 20 days

(.01)(4) x 20 = .04 x 20 = .8 ounces evaporated

3. 3% of original quantity of spirits evaporated for 20 days

(.03)(6) x 20 = .18 x 20 = 3.6 ounces evaporated

4. Total amount evaporated is 3.6 + .8 = 4.4 ounces

Evaporated amount as percentage of original = \(\frac{4.4}{10}\) * 100 = 44%

Answer (C)

To check my work, I also calculated what amount remained after 20 days and subtracted from original amount of 10 ounces

Amount of water remaining is (original) 4 - .8 (evaporated) = 3.2 ounces

Amount of spirits remaining is (original) 6 - 3.6 (evaporated) = 2.4 ounces

Total amount remaining is 3.2 ounces + 2.4 ounces = 5.6 ounces

Amount that evaporated is 10 - 5.6 = 4.4 ounces. That works.


Can you please explain me this passage?
I can't understand the wording of the problem: it states that there are 10 ounces of water, how can I relate them to the solution?
The rest of the problem is crystal clear, I just don't understand how to calculate the ammount of water and of the substance.

Thanks a lot!

MvArrow

Disregard this post's questions posted earlier. I have removed them.

You caught a typographical mistake I made! Sorry to confuse you! See above, where I have crossed out "water" and inserted, in underlined text, "water and spirit mixture." Edited original, too.

You are correct: the ratios apply to the total mixture/solution, not to the water alone. Nice catch, thanks! :-D
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Re: A glass was filled with 10 ounces of water and spirit mixture with the  [#permalink]

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New post 03 Jul 2017, 10:07
Thanks a lot! Now I understand :)
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Re: A glass was filled with 10 ounces of water and spirit mixture with the  [#permalink]

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New post 04 Jul 2017, 08:09
Bunuel wrote:
A glass was filled with 10 ounces of water and spirit mixture with the components in the ratio 2 : 3 respectively. If 1 percent of the initial quantity of water and 3 percent of the initial quantity of spirit evaporated each day during a twenty-day period, what percent of the original amount of mixture evaporated during this period?

(A) 4.4%
(B) 24.4%
(C) 44.0%
(D) 50.0%
(E) 80.0%


We are given that a glass has 10 ounces of water and spirit mixture with the components in the ratio 2 : 3, respectively, or water : spirit = 2x : 3x. Thus:

5x = 10

x = 2, so there are 4 ounces of water and 6 ounces of spirit.

Since 1% of water evaporates each day over a 20-day period, the amount of water that evaporates is:

20(0.01)(4) = 0.8 ounces

Since 3% of spirit evaporates each day over a 20-day period, the amount of spirit that evaporates is:

20(0.03)(6) = 3.6 ounces

Thus, the amount of mixture that evaporated is 3.6 + 0.8 = 4.4 ounces.

So, the percentage of mixture that evaporated is 4.4/10 = 44/100 = 44%.

Answer: C
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Re: A glass was filled with 10 ounces of water and spirit mixture with the   [#permalink] 04 Jul 2017, 08:09
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