FREE SAT Command of Evidence (Quantitative) Questions and Answers 2

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?

Accepted 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.

Answer

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.

Answer

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.

Answer

For PB-5, the tensile strength increased from 55 MPa to 59 MPa at 150°C when the pressure was increased.

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?

Accepted 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.

Answer

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.

Answer

In Year 3, the availability of the food source dropped sharply to 5,000 units, and the prey population (Species X) fell to 900.

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.

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?

Accepted 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.

Answer

The Cloud division saw its revenue increase from $50 million to $300 million and its profit increase from $15 million to $120 million.

Answer

The Software division's profit margin remained stable at 30% in Year 1 and increased to 36% in Year 5.

Answer

Overall company revenue, the sum of all divisions, grew substantially from Year 1 to Year 5.

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?

Accepted 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).

Answer

For Crop Y, the yield was highest at an initial soil pH of 7.0, reaching 2,300 kg/hectare.

Answer

The yield for the control group without fertilizer remained relatively stable across all pH levels, ranging from 1,750 to 1,800 kg/hectare.

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).

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?

Accepted 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%).

Answer

In the Southern branch, the rate of change between 500-1000 CE was 9%, and it was 8% in the following period.

Answer

The Western branch shows a consistently higher rate of change in later periods compared to the Northern branch.

Answer

Between 1500-2000 CE, the rate of lexical change for all branches was relatively low, ranging from 5% to 7%.

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?

Accepted 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.

Answer

The mean commute time for public transit users dropped by 4 minutes, from 62 to 58 minutes, between Year 1 and Year 5.

Answer

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.

Answer

The total number of daily commuters in the city increased by 2,000 from Year 1 to Year 5.