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

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20 Feb 2011, 11:44

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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?

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.

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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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:

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.

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:

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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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:

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

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21 Oct 2012, 17:12

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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. "

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

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17 Sep 2014, 01:36

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.

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

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.

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.

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

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13 Nov 2014, 15:06

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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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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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