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PS 2

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PS 2

by dmateer25 » Wed Dec 24, 2008 6:02 am
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

A
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Re: PS 2

by parallel_chase » Wed Dec 24, 2008 6:39 am
let the actual mixture be 1

olive oil = 5/8

vinegar = 1/4

remainder is divided among salt, pepper & sugar

1-5/8 - 1/4 = 1/8

now 1/8 is to be divided in equal quantities among salt, pepper & sugar

Therefore, 1/8*3 = 1/24 = salt = pepper = sugar

Miguel's mistake

doubles vinegar = 2*(1/4) = 1/2
forgets sugar = 1/24 --eliminate

total mixture = 5/8 + 1/2 + 1/24 + 1/24 = 29/24

required answer = olive oil / total = 5/8 / 29/24 = 15/29

Hence A

Hope this helps.
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by ronniecoleman » Wed Dec 24, 2008 8:03 am
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

Let x be the serving size=

olive oil will be 5/8 x
Vinegar = 1/4 *2 ( condition says that it is doubled )
salt = 1/24x
sugar = 1/24x
Pepper = 1/24 x

But sugar is missing so...

Total dressing is (5/8+ 1/2+ 1/12 )x

Propotion of oliver oil (5/8 )/ ( 29/24)

= 15/29
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by Mozartain » Wed Dec 24, 2008 8:43 am
Thought i'd share a slightly different approach -

sugar =1/3 of (1-5/8-1/4)=1/24

let's consider there are 24 parts in the mix.
sugar is 1 part
vinegar is 1/4 of 24, ie 6 parts
olive oil is 5/8 of 24, ie 15 pars

he adds 6 parts and forgets 1 part. so olive oil/total = 15/(24+6-1) = 15/29
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by hsharif » Sun Oct 21, 2012 5:14 pm
I messed up and fell into an illogical trap...

I assumed that doubling the vinegar simply meant taking Vinegar's ratio and multiplying by 2, WHICH 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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