Question: Bottle X is 2/3 full of water and has half the capacity of Bottle Y. Bottle Y is 1/2 full of water and has twice the capacity of Bottle Z, which is 1/4 full of water. If Bottle X and Bottle Z were poured into Bottle Y, Bottle Y would then be filled to what fraction of capacity?

1. 23/24
2. 11/12
3. 7/8
4. 2/3
5. 1/2

Correct Answer: A
Solution and Explanation:
Approach Solution 1:

The problem statement states that:

Given:

• Bottle X is 2/3 full of water and has half the capacity of Bottle Y.
• Bottle Y is 1/2 full of water and has twice the capacity of Bottle Z, which is 1/4 full of water.

Find out:

• The fraction of capacity of Bottle Y, if Bottle X and Bottle Z were poured into Bottle Y.

To solve the question, it is required to use the LCM of the denominators for the biggest number: 2*3*4 = 24.
The capacity of each bottle as per the question:

X has ½ of Y's capacity
Y has twice Z's capacity
Y is the largest
Therefore, we can say X and Z have equal capacity
Let Y = 24
Let X = 12
Let Z = 12

Therefore, the amount of water in each bottle is:
(fraction full)*(capacity) = amount of water
Y is ½ full, it implies ½ * 24 = 12 units of water in Y
X is ⅔ full, it implies ⅔ * 12 = 8 units of water in X
Z is ¼ full, it implies ¼ * 12 = 3 units of water in Z

All the water in X and Z is poured into Y
X + Z= (8 + 3) = 11 units
Y has initially 12 units
Now, Y has (11 + 12) = 23 units of water in it

Therefore, the fraction of capacity in bottle Y is filled
= Part/Whole = Amount of Water/Capacity= 23/24

Approach Solution 2:

The problem statement informs that:

Given:

• Bottle X is 2/3 full of water and has half the capacity of Bottle Y.
• Bottle Y is 1/2 full of water and has twice the capacity of Bottle Z, which is 1/4 full of water.

Find out:

• The fraction of capacity of Bottle Y, if Bottle X and Bottle Z were poured into Bottle Y.

Let’s express X and Z in terms of Y.
Water in X= ½ Y∗ ⅔ = ⅓ Y
Water in Z= ½ Y∗ ¼ = ⅛ Y
Water in Y= ½ Y

Therefore, the fraction of capacity Bottle Y is filled

= ⅓ Y+ ⅛ Y+ ½ Y
= \((\frac{8}{24}Y+ \frac{3}{24}Y+ \frac{12}{24}Y)\)

=\(\frac{23}{24}Y\)

Hence, \(\frac{23}{24}\) capacity is filled in Bottle Y if Bottle X and Bottle Z were poured into Bottle Y .

“Bottle X is 2/3 full of water and has half the capacity of Bottle Y”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “GMAT Official Guide 2021”. GMAT Problem Solving questions help the candidates to enhance their skills in arithmetic, geometry and algebra. GMAT Quant practice papers assist the candidates to go through varieties of questions that will improve their mathematical knowledge.

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