A fine-art paints company creates custom paint mixtures according to artists' specifications. An artist has placed an order with the...
GMAT Two Part Analysis : (TPA) Questions
A fine-art paints company creates custom paint mixtures according to artists' specifications. An artist has placed an order with the company for 300 milliliters (ml) of each of two different custom mixtures—Mixtures 1 and 2. By volume, Mixture 1 is \(\frac{1}{6}\) white paint, \(\frac{1}{3}\) magenta paint, and \(\frac{1}{2}\) ultramarine paint. And by volume, Mixture 2 is \(\frac{1}{6}\) ultramarine paint, \(\frac{1}{3}\) cyan paint, and \(\frac{1}{2}\) magenta paint.
Assuming the company uses only as much of each color of paint as is necessary to fill the order, the ratio of the quantity of magenta paint to the quantity of ultramarine paint needed to fill this order is \(\mathrm{M} \_ \text{ to } \mathrm{U}\). Select for \(\mathrm{M}\) and for \(\mathrm{U}\) the values for magenta and ultramarine, respectively, that complete the statement so that it is accurate based on the information provided. Make only two selections, one in each column.
Phase 1: Owning the Dataset
Visualization
Let's create a table to organize the paint compositions:
| Paint Color | Mixture 1 (300 ml) | Mixture 2 (300 ml) | Total Needed |
| White | \(\frac{1}{6}\) = ? | 0 | ? |
| Magenta | \(\frac{1}{3}\) = ? | \(\frac{1}{2}\) = ? | ? |
| Ultramarine | \(\frac{1}{2}\) = ? | \(\frac{1}{6}\) = ? | ? |
| Cyan | 0 | \(\frac{1}{3}\) = ? | ? |
Calculating Amounts
For each 300 ml mixture, let's calculate the volume of each paint:
Mixture 1 (300 ml):
- White: \(300 \times \frac{1}{6} = 50\) ml
- Magenta: \(300 \times \frac{1}{3} = 100\) ml
- Ultramarine: \(300 \times \frac{1}{2} = 150\) ml
Mixture 2 (300 ml):
- Ultramarine: \(300 \times \frac{1}{6} = 50\) ml
- Cyan: \(300 \times \frac{1}{3} = 100\) ml
- Magenta: \(300 \times \frac{1}{2} = 150\) ml
Updating our table:
| Paint Color | Mixture 1 (300 ml) | Mixture 2 (300 ml) | Total Needed |
| White | 50 ml | 0 ml | 50 ml |
| Magenta | 100 ml | 150 ml | 250 ml |
| Ultramarine | 150 ml | 50 ml | 200 ml |
| Cyan | 0 ml | 100 ml | 100 ml |
Phase 2: Understanding the Question
We need to find the ratio M:U where:
- M represents the quantity of magenta paint
- U represents the quantity of ultramarine paint
From our calculations:
- Total magenta needed: 250 ml
- Total ultramarine needed: 200 ml
Phase 3: Finding the Answer
The ratio of magenta to ultramarine is:
\(250 \mathrm{ml} : 200 \mathrm{ml}\)
To simplify this ratio, we divide both numbers by their greatest common divisor (50):
\(250 \div 50 : 200 \div 50 = 5 : 4\)
Therefore:
- M = 5
- U = 4
Phase 4: Solution
Final Answer:
- Select 5 for M (magenta)
- Select 4 for U (ultramarine)
The ratio of magenta paint to ultramarine paint needed is \(5:4\), which accurately reflects the 250 ml of magenta to 200 ml of ultramarine required to fill this order.