Live east of the riverLive west of the riverTotalLess than 40 years old171128At least 40 years old1889107Total35100135The table summarizes members...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
| Live east of the river | Live west of the river | Total | |
|---|---|---|---|
| Less than 40 years old | 17 | 11 | 28 |
| At least 40 years old | 18 | 89 | 107 |
| Total | 35 | 100 | 135 |
The table summarizes members of a local organization by age and whether they live east or west of the river. If a member of the organization is selected at random, what is the probability that the selected member is at least 40 years old?
\(\frac{28}{135}\)
\(\frac{35}{135}\)
\(\frac{100}{135}\)
\(\frac{107}{135}\)
1. TRANSLATE the problem information
- Given information:
- A two-way table showing 135 organization members
- Categories: age (less than 40 vs at least 40) and location (east vs west of river)
- Question asks: probability of selecting someone at least 40 years old
- What "at least 40 years old" means: This includes everyone who is 40 or older (the bottom row of the table)
2. INFER the approach
- This is a basic probability problem requiring: \(\mathrm{P(event)} = \frac{\mathrm{favorable\,outcomes}}{\mathrm{total\,outcomes}}\)
- I need the count of people at least 40 years old as my favorable outcomes
- The total number of members becomes my denominator
3. TRANSLATE the specific numbers from the table
- People at least 40 years old: 18 (east) + 89 (west) = 107
- Total members: 135 (given in bottom-right corner)
4. Apply the probability formula
- \(\mathrm{P(at\,least\,40\,years\,old)} = \frac{107}{135}\)
Answer: D. 107/135
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misinterpret what the question is asking for and use the wrong numbers from the table.
They might focus on location instead of age, thinking the problem asks about geography rather than age. This leads them to select Choice B (35/135) for people living east of the river, or Choice C (100/135) for people living west of the river.
Second Most Common Error:
Poor table reading: Students correctly identify that age matters but read the wrong row.
They might use the "Less than 40 years old" row instead of "At least 40 years old," leading them to select Choice A (28/135).
The Bottom Line:
Two-way tables contain lots of numbers, and the key challenge is identifying exactly which numbers answer the specific question being asked. Always start by clearly identifying what condition you're looking for, then trace that condition through the table systematically.
\(\frac{28}{135}\)
\(\frac{35}{135}\)
\(\frac{100}{135}\)
\(\frac{107}{135}\)