Coat colorEye colorDeep blueEye colorLight brownTotalCream-tortoiseshell161632Chocolate12416Total282048The data on the coat color and eye color for 48...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
| Coat color | Eye color Deep blue | Eye color Light brown | Total |
|---|---|---|---|
| Cream-tortoiseshell | 16 | 16 | 32 |
| Chocolate | 12 | 4 | 16 |
| Total | 28 | 20 | 48 |
The data on the coat color and eye color for 48 Himalayan kittens available for adoption were collected and summarized in the table above. What fraction of the chocolate-colored kittens has deep blue eyes?
\(\frac{12}{48}\)
\(\frac{12}{28}\)
\(\frac{16}{32}\)
\(\frac{12}{16}\)
1. TRANSLATE the question carefully
- The question asks: "What fraction of the chocolate-colored kittens has deep blue eyes?"
- This means: out of all the chocolate kittens, what portion has deep blue eyes?
- Key insight: We're looking at chocolate kittens only, not all kittens
2. INFER what numbers to use from the table
- We need to focus on the "Chocolate" row only
- From the Chocolate row: 12 kittens have deep blue eyes, 4 have light brown eyes
- Total chocolate kittens: \(\mathrm{12 + 4 = 16}\) (or read directly from "Total" column)
3. Set up the fraction
- Fraction = (Chocolate kittens with deep blue eyes) ÷ (Total chocolate kittens)
- Fraction = \(\frac{12}{16}\)
Answer: D. \(\frac{12}{16}\)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misread "fraction of chocolate kittens" as "fraction of all kittens" and use the total number of kittens (48) as the denominator instead of just the chocolate kittens (16).
They calculate \(\frac{12}{48}\) instead of \(\frac{12}{16}\), thinking the question asks what fraction of all kittens are chocolate with deep blue eyes.
This leads them to select Choice A (\(\frac{12}{48}\)).
Second Most Common Error:
Poor INFER reasoning: Students get confused about which group forms the denominator and use the total number of deep blue-eyed kittens (28) instead of total chocolate kittens (16).
They calculate \(\frac{12}{28}\), interpreting the question as "what fraction of deep blue-eyed kittens are chocolate" instead of "what fraction of chocolate kittens have deep blue eyes."
This leads them to select Choice B (\(\frac{12}{28}\)).
The Bottom Line:
The key challenge is correctly identifying the reference group (denominator) from the conditional language "fraction of chocolate kittens that..." - the denominator must be the total count of the specified group (chocolate kittens), not all kittens or some other category.
\(\frac{12}{48}\)
\(\frac{12}{28}\)
\(\frac{16}{32}\)
\(\frac{12}{16}\)