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Miguel is mixing up a salad dressing. Regardless of the numb [#permalink]

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13 Aug 2009, 15:25

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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?

Re: Miguel is mixing up a salad dressing. [#permalink]

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13 Aug 2009, 16:29

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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Schools: NUS, NTU, SMU, AGSM, Melbourne School of Business

Re: Miguel is mixing up a salad dressing. [#permalink]

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14 Aug 2009, 05:29

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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]

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25 Mar 2010, 13:10

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

Re: Miguel is mixing up a salad dressing. [#permalink]

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12 Jul 2010, 04:25

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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.

Re: Miguel is mixing up a salad dressing. [#permalink]

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13 Jul 2010, 03:51

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.

Re: Miguel is mixing up a salad dressing. [#permalink]

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15 Jul 2010, 08:17

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.

Re: Miguel is mixing up a salad dressing. [#permalink]

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16 Jul 2010, 02:07

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.

Re: Miguel is mixing up a salad dressing. [#permalink]

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16 Jul 2010, 03:09

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

Re: Miguel is mixing up a salad dressing. [#permalink]

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16 Jul 2010, 03:19

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!

Re: Miguel is mixing up a salad dressing. [#permalink]

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26 Jul 2010, 10:05

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.

Re: Miguel is mixing up a salad dressing. [#permalink]

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23 Jul 2011, 05:30

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.

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