GMAT Problem Solving - 16 Ounces of Fresh Orange Juice Contains 216 Calories

Question - 16 ounces of fresh orange juice contains 216 calories and 16 ounces of fresh grapefruit juice contains 174 calories. If an 8 ounce mixture of these two juices contains 94 calories, what fraction of the mixture is orange juice?

1. 1/3
2. 12/27
3. 1/2
4. 2/3
5. None of these

“16 Ounces of Fresh Orange Juice Contains 216 Calories” - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review". To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills.
In GMAT Problem Solving section, examiners measure how well the candidates make analytical and logical approaches to solve numerical problems. In this section, candidates have to evaluate and interpret data from given graphical representation. In this section, mostly one finds out mathematical questions. Five answer choices are given for each GMAT Problem solving question. 

Solution and Explanation:

Approach Solution 1

It is asked what fraction of the mixture is orange juice when an 8 ounce mixture of these two juices contains 94 calories. It is given that
16 ounces of fresh orange juice contains 216 calories and 16 ounces of fresh grapefruit juice contains 174 calories.
Let us Make the orange juice in the mixture equal to x ounces.
So 8-x ounces of grape juice are required.
Now,
x* (\(\frac{216}{16}\)) + \(\frac{174}{16}\)(8-x) = 94
Let us multiply both sides by 16
We will get
216x + 1392 - 174x = 1504
42x = 112
x –= 2.66 ounces
To find the fraction lets
\(\frac{2.66}{8}\)
\(\frac{1}{3}\)
fraction of the mixture is orange juice is 1/3
Answer is A which is 1/3

Correct Answer: A

Approach Solution 2

There is another approach to answering this question:
Let orange be O
Let grapefruit be G
16 ounces Orange(O) = 216 Calories,
1ounce orange=13.5 Calories
16 ounces grape(G)=174 Calories,
1 ounce grape=10.875 Calories
Solving it further
13.5(O) + 10.875(G) = 94 Calories
O + G = 8 ounces
When we Solve both equations simultaneously,
We get
O=2.67
G=5.33
Ratio of Orange in mixture is \(\frac{2.66}{8}\)
fraction of the mixture is orange juice is 1/3
Answer is A which is 1/3

Correct Answer: A

Approach Solution 3

Let us consider x=orange
Let us consider y=grapefruit
Hence, we get:

216/16(x)+174/16(y)=94/8(x+y)
Now, we will have to multiply right hand side (RHS) by 2/2
We get:

216x+174y=188x+188y
x/y=1/2

Total orange in mixture =1/3
Answer : A

Correct Answer: A

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