Fractions | Mixtures

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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?

• 15/29
  
  5/8
  
  5/16
  
  1/2
  
  13/27

Please explain the solution in a tabular form for mixtures described in the MGMAT Books instead of the LCM method of picking numbers.

[GMATGuruNY]

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

Please explain the solution in a tabular form for mixtures described in the MGMAT Books instead of the LCM method of picking numbers.

I don't recommend using a table for this problem.

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.

[Brent@GMATPrepNow]

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

To summarize: the dressing contains 5/8 olive oil, 2/8 vinegar, and the remaining 1/8 is and even mixture of salt, pepper and sugar.

If we rewrite the fractions with a denominator 24, we get the following:
The correct dressing contains 15/24 olive oil, 6/24 vinegar, and the remaining 3/24 is and even mixture of salt, pepper and sugar.

In other words:
The dressing contains 15/24 olive oil, 6/24 vinegar, 1/24 salt, 1/24 pepper and 1/24 sugar.

So for example, one correct mixture could have the following:
15 cups of olive oil, 6 cups of vinegar, 1 cup of salt, 1 cup of pepper and 1 cup of sugar.

So, if Miguel doubles the vinegar and forgets to sugar all together, then the above combination of ingredients becomes:
15 cups of olive oil, 12 cups of vinegar, 1 cup of salt, and 1 cup of pepper.

So we have a total of 29 cups of ingredients, and 15 cups are olive oil.
So, 15/29 of the botched dressing is olive oil

Answer: A