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Chef Matthew served a rice and sauce dish by mixing already

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Chef Matthew served a rice and sauce dish by mixing already  [#permalink]

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New post Updated on: 11 Aug 2018, 11:45
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Chef Mathew served a rice and sauce dish by mixing already cooked ingredients. The dish contains pecov and anchaer spices of two components. The liquid component of the spices are 85% and 55% respectively for the sauce. Also, the rice is laced with same spices with liquid components of 30% and 20% respectively.
What is the percentage of non-liquid pecov in the dish served if it contains rice and sauce in the ratio of 3:2 respectively?

A. 48%
B. 48.5%
C. 38%
D. 38.5%
E. 28%

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Originally posted by S1937 on 10 Aug 2018, 06:37.
Last edited by S1937 on 11 Aug 2018, 11:45, edited 1 time in total.
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Re: Chef Matthew served a rice and sauce dish by mixing already  [#permalink]

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New post 10 Aug 2018, 06:41
Was served this question by a local GMAT tutor. I need clear solution cos it's unclear on so many levels. Thanks experts!

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Re: Chef Matthew served a rice and sauce dish by mixing already  [#permalink]

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New post 11 Aug 2018, 10:09
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S1937 wrote:
Chef Mathew served a rice and sauce dish by mixing already cooked ingredients. The dish contains pecov and anchaer spices of two components. The liquid component of the spices are 85% and 55% respectively for the stew. The rice is also is laced with same spices with liquid componentsm of 30% and 20% respectively.
What is the percentage of non-liquid pecov in the dish served if it contains rice and sauce in the ratio of 2:3 respectively?

A. 48%
B. 48.5%
C. 38%
D. 38.5%
E. 28%

Posted from my mobile device


Please experts in the forum, can I get some help with this question pls?

JeffYin Bunuel KarishmaB kindly assist
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Re: Chef Matthew served a rice and sauce dish by mixing already  [#permalink]

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New post 11 Aug 2018, 11:00
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Sure, I'm happy to help, S1937!

The only way that I can see to arrive at any of the answer choices is to assume that there is an error in the question. If we say that the ratio of rice to sauce is 3:2, instead of 2:3, I arrive at answer A by interpreting the question in the following way:

1) When it says "stew", this means the same thing as "sauce", so the dish is just made up of sauce and rice.
2) I also have to assume that the ratio of the amount of pecov in the rice to the amount of pecov in the sauce is 3:2, the same as the ratio of rice to sauce.

Once I make those assumptions, this becomes a straightforward weighted average or mixture question, which I would solve using:

100% - 85% = 15% non-liquid pecov in the sauce, with a weight of 2
100% - 30% = 70% non-liquid pecov in the rice, with a weight of 3

I would solve this using the weighted average mapping strategy, also known as the tug of war, by drawing a diagram like the following:

Image

The key idea is that, because the ratio of weights is 3:2, the ratio of distances from 15% and 70% to the weighted average also has to be 3:2. Since the total distance is 55, the two distances have to be 22 and 33. The weighted average is closer to the end with the larger weight (70%), so it's 70%-22% = 48%.

Please let me know if you have questions about that!
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Re: Chef Matthew served a rice and sauce dish by mixing already  [#permalink]

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New post 11 Aug 2018, 11:53
JeffYin wrote:
Sure, I'm happy to help, S1937!

The only way that I can see to arrive at any of the answer choices is to assume that there is an error in the question. If we say that the ratio of rice to sauce is 3:2, instead of 2:3, I arrive at answer A by interpreting the question in the following way:

1) When it says "stew", this means the same thing as "sauce", so the dish is just made up of sauce and rice.
2) I also have to assume that the ratio of the amount of pecov in the rice to the amount of pecov in the sauce is 3:2, the same as the ratio of rice to sauce.

Once I make those assumptions, this becomes a straightforward weighted average or mixture question, which I would solve using:

100% - 85% = 15% non-liquid pecov in the sauce, with a weight of 2
100% - 30% = 70% non-liquid pecov in the rice, with a weight of 3

I would solve this using the weighted average mapping strategy, also known as the tug of war, by drawing a diagram like the following:

Image

The key idea is that, because the ratio of weights is 3:2, the ratio of distances from 15% and 70% to the weighted average also has to be 3:2. Since the total distance is 55, the two distances have to be 22 and 33. The weighted average is closer to the end with the larger weight (70%), so it's 70%-22% = 48%.

Please let me know if you have questions about that!


Wao! JeffYin I just confirmed the errors you pointed out and corrected them. It was a typo as I had to type out from the question paper. You're a higher spirit in GMAT!
Is their any other method apart from the one you just showed. Among all methods u know, which would you advice me to practice most based on test environment?
I anticipate your reply. Thanks again!
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Re: Chef Matthew served a rice and sauce dish by mixing already  [#permalink]

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New post 11 Aug 2018, 13:04
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Sure! You're welcome, S1937.

I do recommend using the weighted average mapping strategy (I've also seen it called the "tug of war" or "teeter-totter" approach) for weighted average and mixture problems, because it will save you time over doing the algebra. In fact, this approach is just a shortcut for the algebra, allowing you to go straight to finding the ratio between the weights. However, in order to be able to feel comfortable using this strategy, you will need to practice it. I have a list of Official Guide and Veritas Prep questions that you can use to practice the weighted average mapping strategy at the following link:

Weighted Average Mapping Strategy practice questions

The only time when the weighted average mapping strategy won't work well is when the ratio between the weights is messy. In the vast majority of weighted average and mixture problems, including this one, the ratio is nice, so it works well.

If you wanted to just do the math without the weighted average mapping strategy, you could use 2 and 3 as the amounts of pecov in the rice and sauce, then use the percentages of non-liquid pecov (15% and 70%) to calculate the total non-liquid pecov:

2*0.15 + 3*0.7 = 0.3 + 2.1 = 2.4

Then divide that by the total amount of pecov (2+3 = 5) to get the overall percent of non-liquid pecov:

2.4/5 = 48%

However, I think that the weighted average mapping strategy is faster, if you are comfortable with it. Please let me know if you have more questions about this!
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Re: Chef Matthew served a rice and sauce dish by mixing already  [#permalink]

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New post 12 Aug 2018, 06:19
JeffYin wrote:
Sure! You're welcome, S1937.

I do recommend using the weighted average mapping strategy (I've also seen it called the "tug of war" or "teeter-totter" approach) for weighted average and mixture problems, because it will save you time over doing the algebra. In fact, this approach is just a shortcut for the algebra, allowing you to go straight to finding the ratio between the weights. However, in order to be able to feel comfortable using this strategy, you will need to practice it. I have a list of Official Guide and Veritas Prep questions that you can use to practice the weighted average mapping strategy at the following link:

Weighted Average Mapping Strategy practice questions

The only time when the weighted average mapping strategy won't work well is when the ratio between the weights is messy. In the vast majority of weighted average and mixture problems, including this one, the ratio is nice, so it works well.

If you wanted to just do the math without the weighted average mapping strategy, you could use 2 and 3 as the amounts of pecov in the rice and sauce, then use the percentages of non-liquid pecov (15% and 70%) to calculate the total non-liquid pecov:

2*0.15 + 3*0.7 = 0.3 + 2.1 = 2.4

Then divide that by the total amount of pecov (2+3 = 5) to get the overall percent of non-liquid pecov:

2.4/5 = 48%

However, I think that the weighted average mapping strategy is faster, if you are comfortable with it. Please let me know if you have more questions about this!

Thanks innumerable times, JeffYin! The mapping strategy is not just easy. It's a miracle. I've seen it a number of times but never had the courage to look at it. Your first response gave me an assurance sort of. Just looked at a video of it in YouTube. Right now laughing at myself for thinking those questions I were hard. It makes it unbelievably easy. This is crazy!
Thanks again!
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Re: Chef Matthew served a rice and sauce dish by mixing already  [#permalink]

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New post 12 Aug 2018, 12:49
S1937 wrote:
Thanks innumerable times, JeffYin! The mapping strategy is not just easy. It's a miracle. I've seen it a number of times but never had the courage to look at it. Your first response gave me an assurance sort of. Just looked at a video of it in YouTube. Right now laughing at myself for thinking those questions I were hard. It makes it unbelievably easy. This is crazy!
Thanks again!


Awesome, S1937, I'm glad that the mapping strategy is helping to make weighted average questions easier for you! I agree that the mapping strategy makes these questions much easier and faster, and can save valuable time on your GMAT that you can use on other questions. I'm glad to help!
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Re: Chef Matthew served a rice and sauce dish by mixing already  [#permalink]

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New post 12 Aug 2018, 14:03
Dear JeffYin thanks for your explanation ! Could you please tell me if this question is in the range of over 700 on the GMAT?
Thanks for your reply in advance


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Re: Chef Matthew served a rice and sauce dish by mixing already  [#permalink]

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New post 12 Aug 2018, 16:19
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venky964 wrote:
Dear JeffYin thanks for your explanation ! Could you please tell me if this question is in the range of over 700 on the GMAT?
Thanks for your reply in advance


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You're welcome, venky964! Here are my thoughts on your question:

This question may be as difficult as a 700-level GMAT question, but it's difficult for some of the wrong reasons. In particular, people may miss it because it's not worded precisely enough, something that you will not see on GMAT questions (at least those that count towards your score). As it is worded, we have to make some assumptions about the ratio of the amount of pecov in the rice to the amount of pecov in the sauce, because it's entirely possible that the rice has a much smaller amount of pecov than the sauce, even though the ratio of rice to sauce is 3:2. If it were worded precisely enough, saying something like "the ratio of pecov in the rice to pecov in the sauce is 3:2", I'd guess it would be more in the 600-700 difficulty range.
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Re: Chef Matthew served a rice and sauce dish by mixing already  [#permalink]

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New post 08 Oct 2018, 02:22
I tried to map out all the information provided in the question stem. Althougth I made the assumption, that the amount of pecov and anchaer spices are equal in booth the sauce and the rice.

Attachment:
Screen Shot 2018-10-08 at 11.16.43.png
Screen Shot 2018-10-08 at 11.16.43.png [ 25.81 KiB | Viewed 905 times ]


We know that the ratio of \(\frac{Rice}{Sauce}\) is \(\frac{3}{2}\). And we are looking for the percentage of non-liquid pecov.

I then simpy applied the weighted average formula using the percentages for non-liquid pecov: \(\frac{3*70+2*15}{2+3}=48\)
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Re: Chef Matthew served a rice and sauce dish by mixing already   [#permalink] 08 Oct 2018, 02:22
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