A group of paleobotanists collected samples of sediments containing pollen and spores from various plant species. Each sample was analyzed...
GMAT Two Part Analysis : (TPA) Questions
A group of paleobotanists collected samples of sediments containing pollen and spores from various plant species. Each sample was analyzed to determine the number of spores in the sample, the number of pollen grains in the sample, and the species to which those spores and pollen grains belong. Samples S1 and S2 were collected and analyzed in this way. For these two samples: S1 had the greater total number of spores, and it contained pollen grains from Species P as well as spores from Species Q. S2 had the greater total number of species represented, and all of the spores it contained were from Species Q.
Statement: Among these two samples, S1 had the greater ratio of total number of \(\mathrm{1\_}\) to total number of \(\mathrm{2\_}\). Select for 1 and for 2 the options 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 Selection
We'll use a comparison table since we're comparing properties of two distinct samples.
Creating Our Visual
| Property | Sample S1 | Sample S2 |
| Total Spores | ** (greater) | (less) |
| Pollen from Species P | ✓ (present) | not stated |
| Spores from Species Q | ✓ (present) | ✓ (all spores) |
| Total Species | (fewer) | ** (greater) |
Phase 2: Understanding the Question
Breaking Down the Statement
We need to complete: "S1 had the greater ratio of total number of 1 to total number of 2"
This means we're looking for: \(\frac{\mathrm{Something\ in\ S1}}{\mathrm{Something\ else\ in\ S1}} > \frac{\mathrm{Same\ something\ in\ S2}}{\mathrm{Same\ something\ else\ in\ S2}}\)
Key Insight
For S1 to have a greater ratio than S2:
- The numerator (position 1) should be something S1 has MORE of than S2
- The denominator (position 2) should be something S1 has LESS of than S2
- OR a combination that makes S1's ratio larger
What We Know for Certain
From our visualization:
- S1 has MORE total spores than S2 ✓
- S1 has FEWER species represented than S2 ✓
- S1 has pollen from Species P (S2's pollen status not mentioned)
Phase 3: Finding the Answer
Applying Our Logical Framework
Let's check which combination gives S1 a definitively greater ratio:
For position 1 (numerator): We need something S1 has more of
- "spores" - S1 has more ✓
- "pollen grains from Species P" - S1 has these, S2 not mentioned to have any
For position 2 (denominator): We need something S1 has less of
- "species represented" - S1 has fewer ✓
The Winning Combination
\(\mathrm{Ratio} = \frac{\mathrm{total\ spores}}{\mathrm{species\ represented}}\)
For S1: \(\frac{\mathrm{Many\ spores}}{\mathrm{Few\ species}} = \mathrm{Large\ ratio}\)
For S2: \(\frac{\mathrm{Few\ spores}}{\mathrm{Many\ species}} = \mathrm{Small\ ratio}\)
This perfectly satisfies our requirement that S1 has the greater ratio!
Phase 4: Solution
Position 1: spores
Position 2: species represented
This gives us: "S1 had the greater ratio of total number of spores to total number of species represented."
This answer emerges naturally from our data - S1 has both more spores (making the numerator larger) AND fewer species (making the denominator smaller), guaranteeing a greater ratio.