Bunuel wrote:
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?
A. 23/24
B. 11/12
C. 7/8
D. 2/3
E. 1/2
This question is not hard, but the language is tricky. Assigning values is efficient.
Break the setup (and hence the language) into two parts: capacity, then actual amount of water in each.
Use the LCM of the denominators for the biggest number: 2*3*4 = 24
CapacityX has \(\frac{1}{2}\) of Y's capacity
Y has twice Z's capacity
Y is the largest
X and Z have equal capacity
Let Y = 24
Let X = 12
Let Z = 12
Amount of water in each bottle(fraction full)*(capacity) = amount of water
Y is \(\frac{1}{2}\) full: \(\frac{1}{2}\) * 24 = 12 units of water in Y
X is \(\frac{2}{3}\) full: \(\frac{2}{3}\) * 12 = 8 units of water in X
Z is \(\frac{1}{4}\) full: \(\frac{1}{4}\) * 12 = 3 units of water in Z
Bottle Y is filled to what fraction of its capacity?All the water in X and Z is poured into Y
X + Z: (8 + 3) = 11 units
Y has 12 units
Y has (11 + 12) = 23 units of water in it
Bottle Y is filled to what fraction of capacity?
\(\frac{Part}{Whole}=\frac{AmtOfWater}{Capacity}=\frac{23}{24}\)Answer A
AlgebraicallyDefine X and Z in terms of Y.
Water in X: \(\frac{1}{2}Y * \frac{2}{3}=\frac{1}{3}Y\)
Water in Z: \(\frac{1}{2}Y*\frac{1}{4}=\frac{1}{8}Y\)
Water in Y: \(\frac{1}{2}Y\)
Bottle Y is filled to what capacity?
\(\frac{1}{3}Y +\\
\frac{1}{8}Y +\frac{1}{2}Y =\)
\((\frac{8}{24}Y +\frac{3}{24}Y+\frac{12}{24}Y) = \frac{23}{24}\\
Y\)
Answer A