A biomanufacturing facility operates two harvesting lines, Line A and Line B, to collect a… — GRE General Test

A biomanufacturing facility operates two harvesting lines, Line A and Line B, to collect a refined protein compound suspended in a liquid growth medium into a single storage tank.

- Line A processes liquid at a constant rate of $120\text{ liters per hour}$ , and its output contains protein and medium in a volume ratio of $1 : 4$ .
- Line B processes liquid at a constant rate of $180\text{ liters per hour}$ , and its output contains protein and medium in a volume ratio of $1 : 9$ .

Both lines run simultaneously for exactly $5\text{ hours}$ into the empty storage tank. Which of the following statements about the resulting liquid mixture in the storage tank must be true? Indicate all such statements.

The total volume of protein collected in the storage tank is $210\text{ liters}$ .Answer
Protein accounts for exactly $14\%$ of the total liquid volume in the storage tank.Answer
The ratio of total protein to total medium in the storage tank is $7 : 43$ .Answer
D
The total volume of protein collected in the storage tank is $250\text{ liters}$ .
E
Protein accounts for exactly $15\%$ of the total liquid volume in the storage tank.

Answer

The correct statements are those asserting that the total volume of protein collected is 210 liters, that protein accounts for exactly 14% of the total liquid volume, and that the ratio of total protein to total medium is 7 to 43.

The total protein collected is

210\text{ liters}

(

120\text{ L}

from Line A and

90\text{ L}

from Line B). Dividing this by the overall volume of

1500\text{ liters}

gives

14\%

. Subtracting protein from total volume gives

1290\text{ liters}

of medium, yielding a protein-to-medium ratio of

210 : 1290 = 7 : 43

. Therefore, the three statements asserting

210\text{ liters}

of protein, a

14\%

concentration, and a

7:43

ratio are all correct.

Step-by-Step Solution

Calculate the total liquid volume produced by each line in 5 hours.

Line A volume =

120\text{ L/hr} \times 5\text{ hr} = 600\text{ liters}

. Line B volume =

180\text{ L/hr} \times 5\text{ hr} = 900\text{ liters}

. Total combined volume =

600 + 900 = 1500\text{ liters}

Total volume per line is the product of its constant flow rate and duration.

Convert the part-to-part ratios to part-to-whole fractions to find the protein volume from each line.

Line A ratio

1:4

means protein is

\frac{1}{1+4} = \frac{1}{5}

of the volume. Protein A =

\frac{1}{5} \times 600 = 120\text{ L}

. Line B ratio

1:9

means protein is

\frac{1}{1+9} = \frac{1}{10}

of the volume. Protein B =

\frac{1}{10} \times 900 = 90\text{ L}

. Total protein =

120 + 90 = 210\text{ liters}

Ratios of

a:b

correspond to a component fraction of

\frac{a}{a+b}

of the total mixture.

Determine the percentage concentration of protein in the final mixture.

\text{Percentage} = \frac{210\text{ L}}{1500\text{ L}} \times 100\% = 14\%

The overall concentration is total protein volume divided by overall mixture volume.

Determine the simplified ratio of total protein to total medium.

Total medium volume =

1500 - 210 = 1290\text{ L}

. Ratio of protein to medium =

210 : 1290 = 7 : 43

Dividing both parts of

210 : 1290

by their greatest common divisor (

30

) yields

7 : 43

Key Concept

Combining rates and converting part-to-part ratios to part-to-whole fractions

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