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Re: M07-28 [#permalink]
gmatophobia

can it be done with allegation diagram method ?
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Re: M07-28 [#permalink]
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AnujL
gmatophobia

can it be done with allegation diagram method ?

AnujL - Yes! it can be

Lemonade A has one part of lemon acid to 4 parts of water. So the ratio of acid to the liquid = \(\frac{1}{5}\)

Lemonade B has one part of lemon acid to 5 parts of water. So the ratio of acid to the liquid = \(\frac{1}{6}\)

The mixture has nine parts of lemon acid to 41 parts of water. So the ratio of acid to the liquid = \(\frac{9}{50}\)

Now, we can set up the diagram as shown below and find the ratio -

Attachment:
Screenshot 2023-07-18 150851.jpg
Screenshot 2023-07-18 150851.jpg [ 40.5 KiB | Viewed 4420 times ]

Option B
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Re: M07-28 [#permalink]
Bunuel
Lemonade A has a lemon acid to water ratio of 1:4, and Lemonade B has a lemon acid to water ratio of 1:5. In a mixture combining the two lemonades, the lemon acid to water ratio is 9:41. What is the ratio of the amount of Lemonade A to the amount of Lemonade B in this combined mixture?

A. 1:3
B. 16:25
C. 2:3
D. 3:4
E. 3:2

Hi Bunuel,

Why cant we consider A = 1/4 and B = 1/5

1/5----9/41----1/4

But Im getting the anwer as 4:5

Why do we need to convert it to lemonade/total
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Re: M07-28 [#permalink]
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Aishyk97
Bunuel
Lemonade A has a lemon acid to water ratio of 1:4, and Lemonade B has a lemon acid to water ratio of 1:5. In a mixture combining the two lemonades, the lemon acid to water ratio is 9:41. What is the ratio of the amount of Lemonade A to the amount of Lemonade B in this combined mixture?

A. 1:3
B. 16:25
C. 2:3
D. 3:4
E. 3:2

Hi Bunuel,

Why cant we consider A = 1/4 and B = 1/5

1/5----9/41----1/4

But Im getting the anwer as 4:5

Why do we need to convert it to lemonade/total

That's how allegation method works. Check the links below:

18. Mixture Problems



For more check Ultimate GMAT Quantitative Megathread

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Re: M07-28 [#permalink]
Hi, I am confused in my approach, I always try to avoid algebra, so I used a weighted average method.

A = 20% and B =16.66%.

The final mixture is 18% (9:41 = 9/50 = 18/100)

As we can see, the final mixture is closer to B (1.3% vs 2%), therefore there must be more of B than A.

Judging from the answers, 16:25 matches up quite comically, as you get 13:20 = 16.x:25.

It's quite early and not sure where I'm making a mistake, would appreciate any clarity, thanks.
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Re: M07-28 [#permalink]
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eggybezos
Hi, I am confused in my approach, I always try to avoid algebra, so I used a weighted average method.

A = 20% and B =16.66%.

The final mixture is 18% (9:41 = 9/50 = 18/100)

As we can see, the final mixture is closer to B (1.3% vs 2%), therefore there must be more of B than A.

Judging from the answers, 16:25 matches up quite comically, as you get 13:20 = 16.x:25.

It's quite early and not sure where I'm making a mistake, would appreciate any clarity, thanks.
­
Yes, everything there is accurate. However, 2:3 = 0.66..., and 1.33.../2 = 0.66... match exactly. The main point is that 2:3 = 0.66... and 16:25 = 0.64 are very close, so you can easily overlook the correct answer. Therefore, you need to be more precise.
 
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M07-28 [#permalink]
Bunuel
Aishyk97
Bunuel
Lemonade A has a lemon acid to water ratio of 1:4, and Lemonade B has a lemon acid to water ratio of 1:5. In a mixture combining the two lemonades, the lemon acid to water ratio is 9:41. What is the ratio of the amount of Lemonade A to the amount of Lemonade B in this combined mixture?

A. 1:3
B. 16:25
C. 2:3
D. 3:4
E. 3:2

Hi Bunuel,

Why cant we consider A = 1/4 and B = 1/5

1/5----9/41----1/4

But Im getting the anwer as 4:5

Why do we need to convert it to lemonade/total

That's how allegation method works. Check the links below:

18. Mixture Problems



For more check Ultimate GMAT Quantitative Megathread

­

Hi Aishyk97
I just hang around and want to answer your question.
we can consider 1/4 and 1/5 
But than A:B should be  16:25 because 
1/4 - 9/41 = 5/164 and 9/41 - 1/5 = 4/205 
---> so, 5/164: 4/205 = 25:16 
But the question asks bout amount of lemonade A to amount of lemonade B
so we have to 16 * 5/4 : 25 * 6/5 -> 2:3 the point in here is just what ratio should we focus (target)

when calculate 1/6 --- 9/50 --- 1/5, we focus on water + salt
but when calculate 1/5 --- 9/41 --- 1/4, we focus on just water  
cc Bunuel­
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M07-28 [#permalink]
­How I solved this (in case it helps someone):



___
Harsha
Enthu about all things GMAT | Exploring the GMAT space | My website: gmatanchor.com

Originally posted by HarshR9 on 19 Apr 2024, 06:51.
Last edited by HarshR9 on 21 Apr 2024, 21:06, edited 1 time in total.
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Re: M07-28 [#permalink]
I made LCM of of 5, 6 and 50. The LCM is 150.
Therefore with LCM of 150,
Lemonade A has a lemon acid to water ratio of 30:120, and Lemonade B has a lemon acid to water ratio of 25:125.

A mixture combining the two lemonades, the lemon acid to water ratio is 27:123.

It is easy to see that the mixture has 2 lemonade A for every 3 lemonade B.
(30+30+25+25+25)/5 = 27. Therefore option C is the answer.
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Re: M07-28 [#permalink]
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