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Miguel is mixing up a salad dressing. Regardless of the [#permalink]
 20 Feb 2011, 12:44
Question Stats:
52% (03:07) correct
47% (01:53) wrong based on 108 sessions
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
Last edited by Bunuel on 03 Feb 2012, 05:30, edited 1 time in total.
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Re: PS - Salad Dressing Mix Problem [#permalink]
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]
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 = 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 question to practice: papayaya-a-popular-soft-drink-contains-only-four-ingredien-135672.html
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Re: PS - Salad Dressing Mix Problem [#permalink]
20 Feb 2011, 13:01
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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Re: PS - Salad Dressing Mix Problem [#permalink]
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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Re: PS - Salad Dressing Mix Problem [#permalink]
20 Feb 2011, 13:38
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]
20 Feb 2011, 20:04
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]
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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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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Re: mixture problem [#permalink]
28 Nov 2011, 09:35
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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Miguel is mixing up a salad dressing. Regardless of the [#permalink]
21 Oct 2012, 18:12
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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Re: Miguel is mixing up a salad dressing. Regardless of the [#permalink]
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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Re: Miguel is mixing up a salad dressing. Regardless of the [#permalink]
13 Jun 2013, 03:09
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Re: Miguel is mixing up a salad dressing. Regardless of the
[#permalink]
13 Jun 2013, 03:09
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