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by j_shreyans » Wed Oct 22, 2014 10:36 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?

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

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by GMATGuruNY » Wed Oct 22, 2014 10:38 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?
A. 15/29
B. 5/8
C. 5/16
D. ½
E. 13/27
Let total mixture = 24.
Oil = (5/8)*24 = 15.
Vinegar = (1/4)*24 = 6.
Remainder = 24-15-6 = 3.
Since the remainder is divided equally among the salt, the pepper, and the sugar:
Salt = 1, Pepper = 1, Sugar = 1.
Vinegar doubled = 2*6 = 12.
New total without sugar = Oil+Vinegar+Salt+Pepper = 15+12+1+1 = 29.
Oil/Total = 15/29.

The correct answer is A.
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by [email protected] » Wed Oct 22, 2014 10:23 pm
Hi j_shreyans,

Mitch's explanation, which uses a combination of TESTing VALUES and arithmetic, is great. Here's how you can solve this problem with just arithmetic though.

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

Final Answer: A

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