Free SAT Command of Evidence (Quantitative) Questions and Answers 2 — Questions and Answers
Question 1: A materials scientist is analyzing the performance of five new polymer blends under varying temperature and pressure conditions. The scientist proposes that for some blends, increasing the pressure has a counterintuitive, inverse effect on the material's tensile strength at higher temperatures. **Tensile Strength (MPa) of Polymer Blends** | Blend | 25°C / 100 kPa | 25°C / 500 kPa | 150°C / 100 kPa | 150°C / 500 kPa | |---|---|---|---|---| | PB-1 | 55 | 65 | 40 | 45 | | PB-2 | 62 | 70 | 48 | 44 | | PB-3 | 58 | 68 | 35 | 39 | | PB-4 | 75 | 85 | 60 | 52 | | PB-5 | 68 | 78 | 55 | 59 | Which choice most effectively uses data from the table to support the scientist's proposal?
- At 150°C, the tensile strength of PB-2 decreased from 48 MPa to 44 MPa as the pressure increased from 100 kPa to 500 kPa.
- At 25°C, the tensile strength of PB-1 increased from 55 MPa to 65 MPa as the pressure was raised from 100 kPa to 500 kPa.
- The tensile strength of PB-4 at 150°C and 500 kPa was 52 MPa, which was lower than its strength of 60 MPa at 150°C and 100 kPa. (Correct answer)
- For PB-5, the tensile strength increased from 55 MPa to 59 MPa at 150°C when the pressure was increased.
Correct answer: The tensile strength of PB-4 at 150°C and 500 kPa was 52 MPa, which was lower than its strength of 60 MPa at 150°C and 100 kPa.
The scientist's proposal is about an inverse relationship between pressure and tensile strength specifically at *higher temperatures*. Choice C provides a direct example of this: for PB-4 at the higher temperature (150°C), increasing the pressure from 100 kPa to 500 kPa resulted in a *decrease* in tensile strength from 60 MPa to 52 MPa. Choices A and D describe an increase in strength with pressure at high temperature, contradicting the proposal. Choice B uses data from the lower temperature, which is not what the proposal is focused on.
Question 2: An ecologist is studying the population dynamics of predator and prey species in a controlled environment over five years. The ecologist claims that a significant drop in the primary food source for the prey species in one year had a delayed, but pronounced, negative effect on the predator population. **Population Sizes in Controlled Environment** | Year | Prey (Species X) | Predator (Species Y) | Food Source Availability (Units) | |---|---|---|---| | 1 | 1,200 | 150 | 10,000 | | 2 | 1,150 | 145 | 9,500 | | 3 | 900 | 140 | 5,000 | | 4 | 850 | 110 | 5,200 | | 5 | 880 | 95 | 5,500 | Which choice best uses data from the table to illustrate the ecologist's claim?
- The predator population of Species Y was at its highest in Year 1 with 150 individuals, while the food source availability was also at its peak of 10,000 units.
- In Year 3, the availability of the food source dropped sharply to 5,000 units, and the prey population (Species X) fell to 900.
- The predator population (Species Y) experienced its most significant single-year decline between Year 3 and Year 4, falling from 140 to 110 individuals, a year after a major drop in the prey's food source. (Correct answer)
- Between Year 4 and Year 5, the prey population began to recover, increasing from 850 to 880, while the predator population continued to decline.
Correct answer: The predator population (Species Y) experienced its most significant single-year decline between Year 3 and Year 4, falling from 140 to 110 individuals, a year after a major drop in the prey's food source.
The ecologist's claim is about a *delayed* negative effect on the predator population following a drop in the prey's food source. The data shows a massive drop in the food source in Year 3. The most pronounced drop in the predator population occurs in the *following* year (Year 4), falling from 140 to 110. This perfectly illustrates the delayed effect. The other options describe related events but do not connect the food source drop to the subsequent, delayed predator decline as effectively.
Question 3: A financial analyst asserts that while the overall revenue of a company has grown, the profitability of its various divisions has diverged significantly, with some legacy divisions experiencing a decline in their profit margins despite revenue growth. **Company Divisional Performance (in millions USD)** | Division | Year 1 Revenue | Year 1 Profit | Year 5 Revenue | Year 5 Profit | |---|---|---|---|---| | Software | 120 | 36 | 250 | 90 | | Hardware | 200 | 40 | 220 | 33 | | Cloud | 50 | 15 | 300 | 120 | | Consulting | 80 | 24 | 90 | 25 | *Profit Margin is calculated as (Profit / Revenue) * 100.* Which choice most effectively uses data from the table to support the analyst's assertion?
- The Cloud division saw its revenue increase from $50 million to $300 million and its profit increase from $15 million to $120 million.
- The Hardware division's revenue increased from $200 million to $220 million, but its profit margin decreased from 20% in Year 1 to 15% in Year 5. (Correct answer)
- The Software division's profit margin remained stable at 30% in Year 1 and increased to 36% in Year 5.
- Overall company revenue, the sum of all divisions, grew substantially from Year 1 to Year 5.
Correct answer: The Hardware division's revenue increased from $200 million to $220 million, but its profit margin decreased from 20% in Year 1 to 15% in Year 5.
The analyst's assertion has two parts: overall growth but diverging profitability, specifically a *decline* in profit margin for some divisions *despite* revenue growth. Choice B perfectly encapsulates this by showing that the Hardware division's revenue grew ($200M to $220M), but its profit margin, which must be calculated, actually fell (from 40/200=20% to 33/220=15%). Choices A and C show divisions with improving profitability, and Choice D only addresses the overall growth, not the divergence.
Question 4: Researchers are investigating the effect of a new fertilizer on crop yield and soil pH. They hypothesize that the fertilizer is most effective in boosting yield for a specific crop, Crop Z, but only when the initial soil pH is neutral (around 7.0), and that its effectiveness diminishes in more acidic or alkaline soils. **Crop Yield (kg/hectare) with New Fertilizer** | Crop | Initial Soil pH 5.5 (Acidic) | Initial Soil pH 7.0 (Neutral) | Initial Soil pH 8.5 (Alkaline) | |---|---|---|---| | Crop X | 1,500 | 1,600 | 1,550 | | Crop Y | 2,200 | 2,300 | 2,250 | | Crop Z | 1,800 | 2,500 | 1,900 | | Control (No Fertilizer) | 1,750 | 1,800 | 1,780 | Which choice best uses data from the table to support the researchers' multifaceted hypothesis?
- For Crop Y, the yield was highest at an initial soil pH of 7.0, reaching 2,300 kg/hectare.
- The yield for the control group without fertilizer remained relatively stable across all pH levels, ranging from 1,750 to 1,800 kg/hectare.
- For Crop Z, the yield in neutral soil (2,500 kg/hectare) was substantially higher than its yield in acidic soil (1,800 kg/hectare) and alkaline soil (1,900 kg/hectare). (Correct answer)
- At a pH of 5.5, the yield of Crop Z (1,800 kg/hectare) was higher than the yield of the control group (1,750 kg/hectare).
Correct answer: For Crop Z, the yield in neutral soil (2,500 kg/hectare) was substantially higher than its yield in acidic soil (1,800 kg/hectare) and alkaline soil (1,900 kg/hectare).
The hypothesis has two key parts: 1) the fertilizer is most effective for Crop Z, and 2) its effectiveness is highest in neutral soil and lower in acidic/alkaline soils. Choice C addresses both parts by focusing on Crop Z and showing the stark contrast in its yield. The 2,500 kg/hectare yield in neutral soil is a massive increase compared to the yields in acidic (1,800) and alkaline (1,900) conditions, demonstrating the peak effectiveness in neutral soil. The other choices are true statements but do not capture the full scope of the hypothesis as effectively as C.
Question 5: A linguist studying language evolution posits that in a certain family of languages, the rate of lexical change (the replacement of core vocabulary) is not constant. Instead, the linguist suggests the rate of change was significantly higher between 500 CE and 1000 CE than in the periods immediately preceding and following. **Percentage of Core Vocabulary Replaced per 500-Year Period** | Language Branch | 1-500 CE | 500-1000 CE | 1000-1500 CE | 1500-2000 CE | |---|---|---|---|---| | Northern | 6% | 14% | 7% | 5% | | Southern | 5% | 9% | 8% | 6% | | Eastern | 7% | 15% | 8% | 5% | | Western | 6% | 10% | 9% | 7% | Which choice most effectively uses data from the table to support the linguist's suggestion?
- In the Southern branch, the rate of change between 500-1000 CE was 9%, and it was 8% in the following period.
- For the Eastern branch, the rate of lexical change peaked at 15% in the 500-1000 CE period, which is more than double the rate from the preceding period (7%) and nearly double the rate of the subsequent period (8%). (Correct answer)
- The Western branch shows a consistently higher rate of change in later periods compared to the Northern branch.
- Between 1500-2000 CE, the rate of lexical change for all branches was relatively low, ranging from 5% to 7%.
Correct answer: For the Eastern branch, the rate of lexical change peaked at 15% in the 500-1000 CE period, which is more than double the rate from the preceding period (7%) and nearly double the rate of the subsequent period (8%).
The linguist's suggestion is that the rate of change was *significantly higher* in the 500-1000 CE period compared to the periods before and after. Choice B provides the most dramatic evidence for this. For the Eastern branch, the 15% rate is a massive spike compared to the 7% before and 8% after. This strong contrast directly supports the idea of a non-constant rate with a specific period of accelerated change. Choice A shows a higher rate but the difference isn't as significant. Choices C and D make other comparisons that are not central to the linguist's specific temporal claim.
Question 6: An urban planner is analyzing commuter data to argue that while a new express bus service has reduced average commute times for those who use it, it has had a negligible impact on the median commute time for the city's overall population, suggesting it has not eased general congestion. **City Commute Time Data (in Minutes)** | Metric | Year 1 (Before Service) | Year 5 (After Service) | |---|---|---| | Mean, Car Commuters | 45 | 44 | | Mean, Public Transit | 62 | 58 | | Mean, Express Bus Users | N/A | 40 | | Median, All Commuters | 42 | 41.5 | | Total Daily Commuters | 250,000 | 252,000 | Which choice most effectively uses data from the table to complete the urban planner's argument?
- The mean commute time for public transit users dropped by 4 minutes, from 62 to 58 minutes, between Year 1 and Year 5.
- The new express bus service offers a mean commute time of 40 minutes, which is faster than the mean for car commuters in Year 5.
- While the mean commute time for public transit users decreased, the median commute time for all commuters only fell by 0.5 minutes, from 42 to 41.5 minutes. (Correct answer)
- The total number of daily commuters in the city increased by 2,000 from Year 1 to Year 5.
Correct answer: While the mean commute time for public transit users decreased, the median commute time for all commuters only fell by 0.5 minutes, from 42 to 41.5 minutes.
The planner's argument has two parts: 1) the new service helped its users, but 2) it had a negligible impact on the city's overall commute time, as measured by the median. Choice C directly supports both parts of this nuanced argument. It acknowledges an improvement for one group (public transit users, which includes the new bus) but immediately contrasts it with the very small change in the median time for *all* commuters. This supports the conclusion that the service's overall impact on congestion was minimal. The other options state true facts but fail to connect the specific success of the new service with the lack of broad, city-wide improvement.
Free SAT Command of Evidence (Quantitative) Questions and Answers 2
A materials scientist is analyzing the performance of five new polymer blends under varying temperature and pressure conditions.
The scientist proposes that for some blends, increasing the pressure has a counterintuitive, inverse effect on the material's tensile strength at higher temperatures.
**Tensile Strength (MPa) of Polymer Blends**
| Blend | 25°C / 100 kPa | 25°C / 500 kPa | 150°C / 100 kPa | 150°C / 500 kPa |
|---|---|---|---|---|
| PB-1 | 55 | 65 | 40 | 45 |
| PB-2 | 62 | 70 | 48 | 44 |
| PB-3 | 58 | 68 | 35 | 39 |
| PB-4 | 75 | 85 | 60 | 52 |
| PB-5 | 68 | 78 | 55 | 59 |
Which choice most effectively uses data from the table to support the scientist's proposal?
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