2024 SAT Standardized Test Math Practice Paper 27

6. In the 1990s, the park rangers at  Yellowstone National Park implemented a program aimed at increasing the dwindling coyote population in Montana. Results of studies of the coyote population in the park are shown in the scatterplot below.

Sat math 27 3

Based on the line of best fit in the scatterplot above, which of the following is the closest to the average annual increase in coyotes in  Yellowstone Park between 1995 and 2000 ?

A. 22
B. 24
C. 26
D. 28

Correct Answer: B

Answer Explanation:

According to the line of best fit, in 1995 there were 20 coyotes in the park. In 2000, there were 140 coyotes in the park. This is an increase of 120 coyotes over a period of 5 years, so ​\( \frac{120}{5} \)​= an average increase of 24 coyotes per year, which is (B).

7.

In the 1990s, the park rangers at  Yellowstone National Park implemented a program aimed at increasing the dwindling coyote population in Montana. Results of studies of the coyote population in the park are shown in the scatterplot below.

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According to the data in the scatterplot, which of the following best represents the percent increase between the median of the results of the studies from 1995 and the median of the results of the studies from 1996 ?

A. 50%
B. 100%
C. 150%
D. 200%

Correct Answer: D

Answer Explanation:

The median number of coyotes in the park in 1995 was 20, and the median number of coyotes in the park in 1996 was 60. (Be careful to RTFQ: the question wants median, NOT line of best fit!) In order to calculate the percent increase, it is necessary to use the percent change formula: ​\( \frac{difference}{original} \)​× 100. The calculation here will be ​\( \frac{60-20}{20} \)​× 100 = ​\( \frac{40}{20} \)​× 100 = 2 × 100 = 200%, which is (D).

8. Bailey’s Boutique Clothing is having a 20% off sale during which shirts cost $30.00 and pants cost $60.00. On the day of the sale, Bailey’s sells ​\( \frac{2}{3} \)​a total of 60 shirts and pants and earned a total of $2,250. On a regular day, Bailey’s sellsthe number of shirts and pants sold during the sale and earns a total of $1,875. Solving which of the following systems of equations yields the number of shirts, s, and the number of pants, p, sold during a regular day?

A. s + p = 40
37.5s + 75p = 1,875
B. s + p = 40
30s + 60p = 2,250
C. s + p = 60
30s + 60p = 2,250
D. s + p = 2,250
30s + 60p = 60

Correct Answer: A

Answer Explanation:

Start with the easier equation and use Process of Elimination. The easier equation is related to the total number of shirts and pants, s + p, sold on a regular day. The question states that on a regular day Bailey’s sells \( \frac{2}{3} \)the number of pants and shirts sold during a sale. \( \frac{2}{3} \)(60) = 40. Therefore, one of the equations in the correct answer should be s + p = 40. Eliminate (C) and (D) since neither of these answers include this equation. The other equation is related to themoney Bailey’s earns on a regular day. According to the question, Bailey’s earns a total of $1,875 on a regular day, so the equation must equal $1,875. Eliminate (B) because the total in the money equation is incorrect. The correct answer is (A).

9. Bryan, who works in a high-end jewelry store, earns a base pay of $10.00 per hour plus a certain percent commission on the sales that he helps to broker in the store. Bryan worked an average of 35 hours per week over the past two weeks and helped to broker sales of $5,000.00 worth of jewelry during that same two-week period. If Bryan’s earnings for the two-week period were $850.00, what percent commission on sales does Bryan earn?

A. 1%
B. 2%
C. 3%
D. 4%

Correct Answer: C

Answer Explanation:

There are a few different ways to approach this question. In any approach, the best first step is to figure out how much income Bryan earned during the two-week period without the commission. Since he worked an average of 35 hours per week for two weeks, he worked a total of 70 hours. At a rate of $10.00 per hour base pay, this would add up to $700.00 (70 × 10 = 700). Since Bryan’s earnings were actually $850.00, that means he must have earned $150.00 of commission (850 – 700 = 150). At this point, you can calculate the percent commission algebraically or simply work backwards from the answers. Algebraically, you know that $150.00 is equal to a certain percent of $5,000.00 in sales, which can be represented as follows: 150 = \( \frac{x}{100} \)(5,000). Solve for x, and you get 3, which is (C). If instead you wish to work backwards from the answers, you can take the answers and calculate what 1%, 2%, etc. of $5,000.00 would be, and then add that back to $700.00 to see which choice matches your target of $850.00: (C).

10. Lennon has 6 hours to spend in Ha Ha Tonka State Park. He plans to drive around the park at an average speed of 20 miles per hour, looking for a good trail  to hike. Once he finds a trail he likes, he will spend the remainder of his time  hiking it. He hopes to travel more than 60 miles total while in the park. If he hikes at an average speed of 1.5 miles per hour, which of the following systems of inequalities can be solved for the number of hours Lennon spends driving, d, and the number of hours he spends hiking, h, while he is at the park?

A. 1.5h + 20d > 60
h + d ≤ 6
B. 1.5h + 20d > 60
h + d ≥ 6
C. 1.5h + 20d < 60
h + d ≥ 360
D. 20h + 1.5d > 6
h + d ≤ 60

Correct Answer: A

Answer Explanation:

Start with the easiest piece of information first, and use Process of Elimination. Given that h is the number of hours spent hiking and d is the number of hours driving, the total number of hours Lennon spends in the park can be calculated as h + d. The question states that Lennon has up to 6 hours to spend in the park-“up to” means ≤. So, h + d ≤ 6. Eliminate (B), (C), and (D). The correct answer is (A).


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