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Miguel is mixing up a salad dressing. Regardless of the

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

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New post Updated on: 03 Feb 2012, 05:30
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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

Originally posted by noodlesalad on 20 Feb 2011, 12:44.
Last edited by Bunuel on 03 Feb 2012, 05:30, edited 1 time in total.
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New post 20 Feb 2011, 12:57
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noodlesalad wrote:
Hi guys, can you have a go at this question? I'm not getting the one of the available answers.

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


Olive oil \(=\frac{5}{8} = \frac{15}{24}\) --> 15 parts out of 24;

Vinegar \(= \frac{1}{4} = \frac{6}{24}\) --> 6 parts out of 24;

Salt + pepper + sugar \(= 1-(\frac{15}{24}+\frac{6}{24})= \frac{3}{24}\), so each \(= \frac{1}{24}\) --> 1 part out of 24 each.

If vinegar = 12 (instead of 6) and sugar = 0 (instead of 1) then total = 15+12+1+1+0 = 29 parts out of which 15 parts are olive oil --> proportion \(= \frac{15}{29}\).

Answer: A.

P.S. Took 24 as common denominator so that shares of each ingredient to be integer.

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Re: PS - Salad Dressing Mix Problem  [#permalink]

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New post 20 Feb 2011, 12:57
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I usually solve it using parts;

Olive = 5/8
Vinegar = 1/4

Total = 7/8.
Remaining=1/8

Salt, Pepper, Sugar = (1/8)/3 = 1/24 each

Now consider the parts;
Olive = 5/8 = 15/24
Vinegar = 1/4 = 6/24
Salt=1/24
Sugar=1/24
Pepper=1/24

For 24 parts mixture; 15 part olive; 6 vinegar; 1 salt; 1 pepper; 1 sugar

Double the vinegar - 6*2=12 parts
Leave the sugar = 1-1=0

New mixture would be;
15 parts olive; 12 parts vinegar; 1 salt; 1 pepper

Total: 15+12+1+1=29 parts
Olive= 15 parts

Ratio(Olive/Mixture) = 15/29

Ans: "A"
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Re: PS - Salad Dressing Mix Problem  [#permalink]

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New post 20 Feb 2011, 13:01
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noodlesalad wrote:
Hi guys, can you have a go at this question? I'm not getting the one of the available answers.




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


Since this is a pure ratio problem, I'd probably find it easiest just to choose a convenient number for the amount of salad dressing we're making. You could also work purely with fractions, though that's a bit more awkward. Here, we know that 5/8 of the dressing is oil, 2/8 is vinegar, and the remaining 1/8 is an equal mixture ('even'? they mean 'equal') of salt, pepper and sugar, so (1/3)(1/8) = 1/24 of the dressing is salt, 1/24 is sugar, and 1/24 is pepper. So we can suppose we would normally be making 24 units of the dressing. We then normally would have:

15 units of oil
6 units of vinegar
1 unit of sugar
1 unit of salt
1 unit of pepper

Now if we double the vinegar and omit the sugar we have

15 units of oil
12 units of vinegar
0 units of sugar
1 unit of salt
1 unit of pepper

for a total of 29 units, 15 of which are oil. So the answer is 15/29.
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New post 20 Feb 2011, 13:17
Thanks for the replies. I see your answers are correct, similar to what is found in the solutions.

Here is how I interpreted the problem:

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?

If he finishes the dressing with 5/8 oil, you'd have:

12/24 vinegar
2/24 salt/pepper
10/24 olive oil
_____
24/24 dressing

Where in the problem does it clearly state that he portioned out the oil first, and added it to the vinegar and salt/pepper? Is it possible that "Regardless of the number of servings" means that he's not keeping track of the volume?

I see how you've all arrived at 15/29, but I would have never interpreted the problem that way.
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New post 20 Feb 2011, 13:38
1
noodlesalad wrote:
Thanks for the replies. I see your answers are correct, similar to what is found in the solutions.

Here is how I interpreted the problem:

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?

If he finishes the dressing with 5/8 oil, you'd have:

12/24 vinegar
2/24 salt/pepper
10/24 olive oil
_____
24/24 dressing

Where in the problem does it clearly state that he portioned out the oil first, and added it to the vinegar and salt/pepper? Is it possible that "Regardless of the number of servings" means that he's not keeping track of the volume?

I see how you've all arrived at 15/29, but I would have never interpreted the problem that way.


It is not mentioned anywhere. You are trying to keep the volume(total number of parts) unaltered. It is not mentioned as a constraint in the problem, though. The moment Miguel doubled the quantity of the vinegar and forgot to add sugar; he goofed up both; the proportion of these ingredients in the salad dressing and the volume of the salad dressing.

"Number of servings": Guess means total volume of the entire dressing. It could be 24 parts; 48 parts; 72 parts..etc.
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Re: PS - Salad Dressing Mix Problem  [#permalink]

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New post 20 Feb 2011, 20:04
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noodlesalad wrote:
Thanks for the replies. I see your answers are correct, similar to what is found in the solutions.

Here is how I interpreted the problem:

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?

If he finishes the dressing with 5/8 oil, you'd have:

12/24 vinegar
2/24 salt/pepper
10/24 olive oil
_____
24/24 dressing

Where in the problem does it clearly state that he portioned out the oil first, and added it to the vinegar and salt/pepper? Is it possible that "Regardless of the number of servings" means that he's not keeping track of the volume?

I see how you've all arrived at 15/29, but I would have never interpreted the problem that way.


The question mentions that he committed two mistakes in the recipe: doubled the vinegar and forgot the sugar. Had he put less olive oil than what the recipe asked for, that would have been another mistake.
Let's say he wanted to make 24 ml of dressing. Then the recipe asked for 15 ml olive oil, 6 ml vinegar, 1 ml sugar etc. His mistake was to put double the vinegar (so 12 ml) and no sugar. Had he put 10 ml of olive oil (instead of 15), that would have been yet another mistake and would have been mentioned in the question as such.
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Re: PS - Salad Dressing Mix Problem  [#permalink]

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New post 21 Feb 2011, 19:06
Vinegar - 1/4

Olive Oil - 5/8

5/8 + 1/4 = (5 + 2)/8 = 7/8

Remainder = 1/8

salt - 1/24

pepper - 1/24

sugar - 1/24

Let total be 24 ml


12 ml - V

15 ml - OO

1 - salt

1 - P

=> OO = 15/(12 + 15 + 1 + 1) = 10/29 = 15/29

So answer is A
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New post 11 Mar 2011, 08:00
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Total mixture = 5/8 X + 1/4 X + 1/24 X + 1/24 X + 1/24 X
This constitutes: Olive oil + Vinegar + Sugar/Spice/everything nice...

Twice the vinegar = 2x 1/4 = 1/2 X
5/8 + 1/2 + 1/24 + 1/24 = 29/24

Olive oil / total mixture = 5/8 divided by 29/24 = 15/29
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New post 28 Nov 2011, 09:35
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1
Initial Mix be x
Olive oil = 5/8x
Vinegar = 1/4x

Remainder is equally divided among salt, pepper & sugar

(1-5/8 - 1/4)x = x/8

x/8 is divided in equal quantities among salt, pepper, & sugar

x/8*(1/3) = x/24 = salt = pepper = sugar

Miguel's mistake

He doubles vinegar = 2*(x/4) = x/2
He forgets sugar = x/24 --eliminate

Total Mixture = (5/8 + 1/2 + 1/24 + 1/24)x = 29x/24

Olive Oil/ total = (5x/8) /(29x/24)= 15/29

Hence A
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New post 21 Oct 2012, 18:12
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Incase anyone fell into the trap I did and tried to multiply the Vinegar ratio by two...

i.e.

2/ 8 * 2 =
4/8 =
1/2

This is incorrect, this is from the MGMAT staff...

"Doubling the AMOUNT is not the same as doubling the PERCENTAGE.

Think of it this way. Let's say you're making a sandwich. You like your sandwich to be 1/2 peanut butter and 1/2 jelly. If you double the amount of peanut butter, do you have 100% peanut butter? Of course not. You just have a higher % peanut butter than before.

The easiest route for a problem such as this is to pick some real numbers from the outset. Then double the real number you've picked for the AMOUNT of vinegar, and reinsert that into the total to see what new fraction results.
"
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New post 24 Mar 2013, 22:23
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Finally .......guys if you are getting an answer of 5/12, i can help you explain why it is incorrect.

We all know:

Olive Oil-5/8
Vinegar-1/4
Salt-1/24
Pepper-1/24
Sugar-1/24

Now changes done:
Vinegar-2/4=1/2
Sugar-0

Changes not done:
Olive Oil-5/8; it is remaining same, as Manuel is not changing its quantity.
Salt-1/24
Pepper-1/24

Therefore the new quantity becomes = 1/2+0+5/8+1/24+1/24=29/24

Now the question : olive oil is what fraction of new mixture 29/24
i.e. 5/8=x.29/24; calculate x=15/29.

Vola!!!!
Hope that helps.
Please guide in case i m wrong :)
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New post 13 Jun 2013, 03:09
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

All DS Mixture Problems to practice: search.php?search_id=tag&tag_id=43
All PS Mixture Problems to practice: search.php?search_id=tag&tag_id=114
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Re: Miguel is mixing up a salad dressing. Regardless of the  [#permalink]

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New post 17 Sep 2014, 02:36
Bunuel wrote:
noodlesalad wrote:
Hi guys, can you have a go at this question? I'm not getting the one of the available answers.

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


Olive oil = 5/8 = 15/24 --> 15 parts out of 24;
Vinegar = 1/4 = 6/24 --> 6 parts out of 24;
Salt + pepper + sugar = 1-(15/24+6/24)= 3/24, so each = 1/24 --> 1 part out of 24 each;

If vinegar = 12 (instead of 6) and sugar = 0 (instead of 1) then total = 15+12+1+1+0 = 29 parts out of which 15 parts are olive oil --> proportion = 15/29.

Answer: A.

P.S. Took 24 as common denominator so that share of each ingredient to be integer.

Similar questions to practice:
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Hope this helps.


Hi Bunuel,

I still dint get it.

5/8-Oil
1/4-Vinegar
Sugar,Salt and Peppar- 1-7/8(total of oil +vinegar)= 1/8 now this is evenly divided so 1/24 is each.

New formation
Vinegar- 2*1/4=1/2
Sugar is not there so 1/24 each of salt and peppar= 1/24+1/24=2/24=1/12
So now Oil will be according to me 1-(1/12+1/2)= 1-7/12=5/12

Please tell me where am i going wrong.. Thanks
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New post 17 Sep 2014, 05:49
snehamd1309 wrote:
Bunuel wrote:
noodlesalad wrote:
Hi guys, can you have a go at this question? I'm not getting the one of the available answers.

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


Olive oil = 5/8 = 15/24 --> 15 parts out of 24;
Vinegar = 1/4 = 6/24 --> 6 parts out of 24;
Salt + pepper + sugar = 1-(15/24+6/24)= 3/24, so each = 1/24 --> 1 part out of 24 each;

If vinegar = 12 (instead of 6) and sugar = 0 (instead of 1) then total = 15+12+1+1+0 = 29 parts out of which 15 parts are olive oil --> proportion = 15/29.

Answer: A.

P.S. Took 24 as common denominator so that share of each ingredient to be integer.

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Hi Bunuel,

I still dint get it.

5/8-Oil
1/4-Vinegar
Sugar,Salt and Peppar- 1-7/8(total of oil +vinegar)= 1/8 now this is evenly divided so 1/24 is each.

New formation
Vinegar- 2*1/4=1/2
Sugar is not there so 1/24 each of salt and peppar= 1/24+1/24=2/24=1/12
So now Oil will be according to me 1-(1/12+1/2)= 1-7/12=5/12

Please tell me where am i going wrong.. Thanks


WHY are you saying that oil will be 1-(1/12+1/2)??? With this logic why is not salt 1-(1/24+5/8+1/2)???

Consider this: to make a salad dressing we need 15 grams of oil, 6 grams of vinegar, 1 gram of salt, 1 gram of pepper and 1 gram of sugar.

Vinegar is doubled and sugar is omitted, so we have 15 grams of oil, 6*2=12 grams of vinegar, 1 gram of salt, and 1 gram of pepper --> oil/total = 15/(15+12+1+1) = 15/29.

Hope it's clear.
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New post 13 Nov 2014, 16:06
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Let's start by looking at the recipe it calls for 5/8 olive oil and 1/4 (2/8) vinegar, with the remaining 1/8 split evenly between salt pepper and sugar. which means 1/24 is salt, 1/24 is sugar and 1/24 is pepper.

So if we put it all together, it is 15 parts olive oil, 6 parts vinegar, 1 part salt, 1 part sugar and 1 part pepper as a total recipe

If we double the vinegar and forget the sugar we get 12 parts vinegar, 15 parts olive oil, 1 part salt and 1 part pepper and 0 parts sugar

so the total for the olive oil is 15/(12+15+1+1) or 15/29 (A)
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New post 10 Jun 2017, 19:38
noodlesalad 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?

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

1. The proportion is 5/8 olive oil, 1/4 vinegar, 1/24 salt, 1/24 pepper and 1/24 sugar
2. Let there be 24 units of the mixture. That would mean 15 units olive oil, 6 units vinegar 1 unit each of salt, sugar and pepper.
3. Doubling the vinegar and forgetting sugar would give 15 units olive oil, 12 units vinegar, 1 unit each of pepper and salt.
4. In the botched up dressing proportion of olive oil is 15/29
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Re: Miguel is mixing up a salad dressing. Regardless of the  [#permalink]

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New post 02 Mar 2018, 11:26
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Hi All,

This question can be solved with TEST IT or with Arithmetic. Here's how you can solve this problem with just arithmetic.

We're told to work with the following ingredients (and their respective fractions of the WHOLE):

5/8 olive oil
1/4 = 2/8 vinegar
The rest is an equal mix of salt, pepper and sugar…

5/8 + 2/8 = 7/8
1/8 = Salt + pepper + sugar

Since it's EQUAL amounts of salt, pepper and sugar, we have…
1/24 salt
1/24 pepper
1/24 sugar

Overall mixture:
5/8 olive oil
2/8 vinegar
1/24 salt
1/24 pepper
1/24 sugar

We're told to DOUBLE the vinegar and eliminate the sugar, which leaves us with…
5/8 olive oil
2/8 x 2 = 4/8 vinegar
1/24 salt
1/24 pepper

Total NOW equals….
5/8 + 4/8 + 1/24 + 1/24 =
15/24 + 12/24 + 1/24 + 1/24 = 29/24

We're asked what proportion of this new total is olive oil….
Total = 29/24
Olive oil = 15/24

(15/24)/(29/24) =
15/29

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

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New post 18 Aug 2018, 04:50
noodlesalad 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?

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


Official Solution (Credit: Manhattan Prep)



This problem can be solved most easily by picking smart numbers and assigning values to the portion of each ingredient in the dressing. A smart number in this case would be one that enables you to add and subtract ingredients without having to deal with fractions or decimals. In a fraction problem, the ‘smart number’ is typically based on the least common denominator among the given fractions.

The two fractions given, 5/8 and 1/4, have a least common denominator of 8. However, we must also consider the equal parts salt, pepper and sugar. Because 1/4 = 2/8, the total proportion of oil and vinegar combined is 5/8 + 2/8 = 7/8. The remaining 1/8 of the recipe is split three ways: 1/24 each of salt, pepper, and sugar. 24 is therefore our least common denominator, suggesting that we should regard the salad dressing as consisting of 24 units. Let’s call them cups for simplicity, but any unit of measure would do. If properly mixed, the dressing would consist of

5/8 × 24 = 15 cups of olive oil
1/4 × 24 = 6 cups of vinegar
1/24 × 24 = 1 cup of salt
1/24 × 24 = 1 cup of sugar
1/24 × 24 = 1 cup of pepper

Miguel accidentally doubled the vinegar and omitted the sugar. The composition of his bad salad dressing would therefore be

15 cups of olive oil
12 cups of vinegar
1 cup of salt
1 cup of pepper

The total number of cups in the bad dressing equals 29. Olive oil comprises 15/29 of the final mix.

The correct answer is A.
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Re: Miguel is mixing up a salad dressing. Regardless of the   [#permalink] 13 Sep 2019, 05:40
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