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Miguel is mixing up a salad dressing. Regardless of the numb

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Miguel is mixing up a salad dressing. Regardless of the numb [#permalink] New post 13 Aug 2009, 14:25
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Miguel is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be olive oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar. If Miguel accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be olive oil?

A) 15/29
B) 5/8
C) 5/16
D) 1/2
E) 13/27

OPEN DISCUSSION OF THIS QUESTION IS HERE: miguel-is-mixing-up-a-salad-dressing-regardless-of-the-109740.html
[Reveal] Spoiler: OA

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Re: Miguel is mixing up a salad dressing. [#permalink] New post 13 Aug 2009, 15:29
tejal777 wrote:
Miguel is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be olive oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar. If Miguel accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be olive oil?
15/29
5/8
5/16
1/2
13/27

I got 15/29 is it correct?


Please explain how you reached this answer. I am not very clear with the question.
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Re: Miguel is mixing up a salad dressing. [#permalink] New post 14 Aug 2009, 04:29
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Quote:
tejal777 wrote:
Miguel is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be olive oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar. If Miguel accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be olive oil?
15/29
5/8
5/16
1/2
13/27


Thats is right, tejal777. Take the total mixture as 240 and carry find the results for each of the components
Olive Oil = 240*5/8 = 150
Vinegar = 240*1/4 = 60
Remainder (240-210) equally divided in three parts
Salt = 10
Pepper = 10
Sugar = 10

The question then says Miquel doubles the vinegar and forgets sugar. Therefore, we will bad salad will have
150 + 120 (for 60*2) + 10+10 = 290

Ratio of Olive Oil/ New salad = 150/290 ie 15/29.

I had solved this problem a month ago but the good thing I just realised is that I still remembered how to solve it. :)
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Re: Miguel is mixing up a salad dressing. [#permalink] New post 14 Aug 2009, 16:43
Bang on bhanushalinikhil!Same approach.
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Re: Miguel is mixing up a salad dressing. [#permalink] New post 25 Mar 2010, 07:59
i am doing it this way pls tell where i am wrong

Originaly

Olive oil = 5/8

Vinegar = 1/4

Remaining = 1 -(5/8+1/4) = 1/8

Even mixture of salt, pepper and sugar = (1/8)/3 = 1/24


Later


Olive Oil = x

Vinegar = 1/4 *2 = 1/2

Remaining = 1 -(x+1/2) = 1 - x - (1/2)

Even mixture of salt, pepper = 1/2( 1 - x - (1/2) )

Total = 1

1/2( 1 - x - (1/2) ) + 1/2( 1 - x - (1/2) ) + x+ 1/2 = 1

Lost after it .. doing something wrong ..surely

help plssss
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Re: Miguel is mixing up a salad dressing. [#permalink] New post 25 Mar 2010, 12:10
tejal777 wrote:
Miguel is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be olive oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar. If Miguel accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be olive oil?
15/29
5/8
5/16
1/2
13/27

I got 15/29 is it correct?


I think the best way to solve this problem is to write each of the original amounts using 24 as the common denominator. Thus you have

15 parts o.o.
6 parts vin
1 part salt
1 part pep
1 part sugar

Now Miguel makes a new mixture in which he uses double the amount of vinegar, so he uses 6 * 2 = 12 parts vinegar. He also skips the sugar. So the new mixture is

15 parts o.o.
12 parts vin
1 part salt
1 part pep

= 29 parts total, of which 15 is olive oil. So the answer is

15/29
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Re: Miguel is mixing up a salad dressing. [#permalink] New post 25 Mar 2010, 14:24
bnagdev282 wrote:
i am doing it this way pls tell where i am wrong

Originaly

Olive oil = 5/8

Vinegar = 1/4

Remaining = 1 -(5/8+1/4) = 1/8

Even mixture of salt, pepper and sugar = (1/8)/3 = 1/24



Up till this point you are right. This is how I would continue,

We know,
Olive oil = \frac{5}{8}
Vinegar = \frac{1}{4}
salt = \frac{1}{24}
Pepper = \frac{1}{24}
Sugar = \frac{1}{24}

from here we see that the least common multiple of all the denominators is 24. So multiply all the fractions with 24.

Olive Oil = 15
Vinegar = 6
salt = 1
Pepper =1
Sugar = 1

Now that Miquel doubles the vinegar and forgot the sugar,
Total Portion = 15 (Olive Oil) + 12 (Vinegar 6*2) + 1 (salt) + 1 (pepper) = 29

Percentage of Olive oil = \frac{15}{29}

Please let me know if you need any more help

Ravi

Last edited by sudgmat on 26 Mar 2010, 07:58, edited 1 time in total.
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Re: Miguel is mixing up a salad dressing. [#permalink] New post 26 Mar 2010, 06:33
sudgmat wrote:
bnagdev282 wrote:
i am doing it this way pls tell where i am wrong

Originaly

Olive oil = 5/8

Vinegar = 1/4

Remaining = 1 -(5/8+1/4) = 1/8

Even mixture of salt, pepper and sugar = (1/8)/3 = 1/24



Up till this point you are right. This is how I would continue,

We know,
Olive oil = \frac{5}{8}
Vinegar = \frac{1}{4}
salt = \frac{1}{8}
Pepper = \frac{1}{8}
Sugar = \frac{1}{8}

from here we see that the least common multiple of all the denominators is 24. So multiply all the fractions with 24.

Olive Oil = 15
Vinegar = 6
salt = 3
Pepper =3
Sugar = 3

No that Miquel doubles the vinegar and forgot the sugar,
Total Portion = 15 (Olive Oil) + 12 (Vinegar 6*2) + 3 (salt) + 3 (pepper) = 29

Percentage of Olive oil = \frac{15}{29}

Please let me know if you need any more help

Ravi



salt+pepper+sugar comes to be 1/8

so take salt = sugar = pepper = 1/24

Olive Oil = 15
Vinegar = 6
salt = 1
Pepper =1
Sugar = 1
Total Portion = 15 (Olive Oil) + 12 (Vinegar 6*2) + 1 (salt) + 1 (pepper) = 29
and thus 15/29
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Re: Miguel is mixing up a salad dressing. [#permalink] New post 26 Mar 2010, 08:34
@gurpreetsingh

Thanks a lot, Corrected all the typos.
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Re: Miguel is mixing up a salad dressing. [#permalink] New post 12 Jul 2010, 03:25
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gmatinfoonline wrote:
tejal777 wrote:
Miguel is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be olive oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar. If Miguel accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be olive oil?
15/29
5/8
5/16
1/2
13/27

I got 15/29 is it correct?


I think the best way to solve this problem is to write each of the original amounts using 24 as the common denominator. Thus you have

15 parts o.o.
6 parts vin
1 part salt
1 part pep
1 part sugar

Now Miguel makes a new mixture in which he uses double the amount of vinegar, so he uses 6 * 2 = 12 parts vinegar. He also skips the sugar. So the new mixture is

15 parts o.o.
12 parts vin
1 part salt
1 part pep

= 29 parts total, of which 15 is olive oil. So the answer is

15/29


Can someone explain to me this solution? The question asks: what proportion of the botched dressing will be olive oil? IMO it should be: 1 - (1/4 * 2 + 1/24 + 1/24) = 5/12. I can't see where I am mistaken in my reasoning.
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Re: Miguel is mixing up a salad dressing. [#permalink] New post 12 Jul 2010, 04:45
I prefer to picking numbers on that kind of questions.

Lets chose 24x is total

24x * 5/8= 15x olive oil

24x/4 = 6x vinegar

the remainder is 3x(x for sugar,x for salt,x for pepper)

Double the vinegar is 12x and lack of sugar means we have 2x(salt and pepper)

In total 15x+12x+2x= 29x

15x/29x=15/29

hope it helps
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Re: Miguel is mixing up a salad dressing. [#permalink] New post 12 Jul 2010, 10:07
Quote:
In total 15x+12x+2x= 29x
15x/29x=15/29


I don't get why oil is 15 and not a 1's complement? Please explain.
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Re: Miguel is mixing up a salad dressing. [#permalink] New post 13 Jul 2010, 00:04
nonameee wrote:
Quote:
In total 15x+12x+2x= 29x
15x/29x=15/29


I don't get why oil is 15 and not a 1's complement? Please explain.


24x*5/8= 15 x

ı choose 24 x because of divisible with 8 and 4
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Re: Miguel is mixing up a salad dressing. [#permalink] New post 13 Jul 2010, 02:51
fatihaysu wrote:
nonameee wrote:
Quote:
In total 15x+12x+2x= 29x
15x/29x=15/29


I don't get why oil is 15 and not a 1's complement? Please explain.


24x*5/8= 15 x

ı choose 24 x because of divisible with 8 and 4


That's not what I've asked. I understand where you got the numbers and 24 is very clear to me.

I just thought that since he changed the ratio of various ingredients, the ratio of oil will be different as well. So I don't understand why we can assume that the ratio of the oil should remain the same? It if remains the same (as in your calculations, i.e., oil = 15x) the weight of the mixture will change. In my calculations I assumed that the weight of the mixture stays the same and the rate of the oil changes.

Maybe I didn't understand the the question well.
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Re: Miguel is mixing up a salad dressing. [#permalink] New post 15 Jul 2010, 07:17
Quote:

That's not what I've asked. I understand where you got the numbers and 24 is very clear to me.

I just thought that since he changed the ratio of various ingredients, the ratio of oil will be different as well. So I don't understand why we can assume that the ratio of the oil should remain the same? It if remains the same (as in your calculations, i.e., oil = 15x) the weight of the mixture will change. In my calculations I assumed that the weight of the mixture stays the same and the rate of the oil changes.

Maybe I didn't understand the the question well.


Yes I had the same problem!

I filled the mixture with 1/2 vinegar (i.e. 12), 1 salt and 1 pepper --> ending up with 10 left for oil, hence 10/24 = 5/12 is the proportion of oil in the dressing.

Someone please clarify where we went wrong... :(
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Re: Miguel is mixing up a salad dressing. [#permalink] New post 16 Jul 2010, 01:07
AndreG wrote:
Quote:

That's not what I've asked. I understand where you got the numbers and 24 is very clear to me.

I just thought that since he changed the ratio of various ingredients, the ratio of oil will be different as well. So I don't understand why we can assume that the ratio of the oil should remain the same? It if remains the same (as in your calculations, i.e., oil = 15x) the weight of the mixture will change. In my calculations I assumed that the weight of the mixture stays the same and the rate of the oil changes.

Maybe I didn't understand the the question well.


Yes I had the same problem!

I filled the mixture with 1/2 vinegar (i.e. 12), 1 salt and 1 pepper --> ending up with 10 left for oil, hence 10/24 = 5/12 is the proportion of oil in the dressing.

Someone please clarify where we went wrong... :(


Yeah, I had the same reasoning.
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Re: Miguel is mixing up a salad dressing. [#permalink] New post 16 Jul 2010, 02:09
I am not sure whether my reasoning is right but this is what i thought.

Question says that Miguel is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be olive oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar.

Lets chose 24x is total
24x * 5/8= 15x olive oil
24x/4 = 6x vinegar
the remainder is 3x(x for sugar,x for salt,x for pepper)

If Miguel accidentally doubles the vinegar and forgets the sugar altogether.

In this nowhere the question says that quantity of olive oil added is changed.. It is still 15x. Also there is nothing given regarding weight. Question asks us to find that we need to find , proportion of the botched dressing will be olive oil.(i.e. the new mixture whether it is of more weioght than previous one. - 29x is the new weight.)

Double the vinegar is 12x and lack of sugar means we have 2x(salt and pepper)
In total 15x+12x+2x= 29x
15x/29x=15/29

Hope this helps!! :)
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Re: Miguel is mixing up a salad dressing. [#permalink] New post 16 Jul 2010, 02:19
varunmaheshwari wrote:
I am not sure whether my reasoning is right but this is what i thought.

Question says that Miguel is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be olive oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar.

Lets chose 24x is total
24x * 5/8= 15x olive oil
24x/4 = 6x vinegar
the remainder is 3x(x for sugar,x for salt,x for pepper)

If Miguel accidentally doubles the vinegar and forgets the sugar altogether.

In this nowhere the question says that quantity of olive oil added is changed.. It is still 15x. Also there is nothing given regarding weight. Question asks us to find that we need to find , proportion of the botched dressing will be olive oil.(i.e. the new mixture whether it is of more weioght than previous one. - 29x is the new weight.)

Double the vinegar is 12x and lack of sugar means we have 2x(salt and pepper)
In total 15x+12x+2x= 29x
15x/29x=15/29

Hope this helps!! :)



The more I think about it, the more it makes sense... I guess the key is indeed in the phrase "regardless of the number of servings..."

Since our chosen 24 is only arbitrary, to make the calculation easier, there is indeed no reasoning why it shouldn't be allowed to change to 29!

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Re: Miguel is mixing up a salad dressing. [#permalink] New post 26 Jul 2010, 09:05
The wording of this really confused me. It seems like you could either double the proportion of vinegar or the actual amount and get completely different answers. I wasted a lot of time assuming it was the proportion he got wrong - I thought he went from 1/4 vinegar to 1/2 vinegar.
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Re: Miguel is mixing up a salad dressing. [#permalink] New post 23 Jul 2011, 04:30
Hi,

nonameee wrote:
AndreG wrote:
Quote:

That's not what I've asked. I understand where you got the numbers and 24 is very clear to me.

I just thought that since he changed the ratio of various ingredients, the ratio of oil will be different as well. So I don't understand why we can assume that the ratio of the oil should remain the same? It if remains the same (as in your calculations, i.e., oil = 15x) the weight of the mixture will change. In my calculations I assumed that the weight of the mixture stays the same and the rate of the oil changes.

Maybe I didn't understand the the question well.


Yes I had the same problem!

I filled the mixture with 1/2 vinegar (i.e. 12), 1 salt and 1 pepper --> ending up with 10 left for oil, hence 10/24 = 5/12 is the proportion of oil in the dressing.

Someone please clarify where we went wrong... :(


Yeah, I had the same reasoning.



Though I understood the correct reasoning, I am still not clear on what is wrong in these ones.

Can someone please clarify..

Thanks
Re: Miguel is mixing up a salad dressing.   [#permalink] 23 Jul 2011, 04:30
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