SAT
Practice Test 5
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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.

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 ?

  • Solution

    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: \(\frac{difference}{original} \times 100\).

    The calculation here will be \(\frac{60 - 20}{20} \times 100 = \frac{40}{20} \times 100 = 2 \times 100 = 200\%\), which is (D).

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.

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 ?

  • Solution

    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).

Luciano measured the amount of water that evaporated over a period of time from a container holding w ounces of water, where w is greater than 12. By the end of the first day, the cup had lost 2 ounces of water. By the end of the 7th day, the cup had lost an additional 8 ounces of water. By the end of the 11th day, the cup had lost half of the water that remained after the 7th day. Which of the following represents the remaining amount of water, in ounces, in Luciano’s container at the end of the 11th day?

  • Solution

    Whenever there are variables in the problem and in the answer choices, plug in.

    If w = 20, then Luciano's cup has 20 - 2 = 18 ounces at the end of day 1.

    At the end of 7 days, Luciano's cup would have 18 - 8 = 10 ounces.

    After 11 days, Luciano's cup would hold 10 - 5 = 5 ounces.

    Plug in 20 for w in the answer choices to see which answer is equal to the target number of 5.

    Choice (A) becomes \(\frac{20 - 2}{8} = \frac{18}{8} = 2.25\).

    This does not match the target number of 5, so eliminate (A).

    Choice (B) becomes \(\frac{20 - 2}{2} - 10 = \frac{18}{2} - 10 = 9 - 10 = -1\).

    Eliminate (B).

    Choice (C) becomes (1⁄2)(20) - 10 = 10 - 10 = 0.

    Eliminate (C).

    Choice (D) becomes \(\frac{20 - 10}{2} = \frac{10}{2} = 5\).

    This matches the target number; therefore, the correct answer is (D).

Priya is planning to send her favorite dry rub recipe to a friend who lives in France. Before sending the recipe, Priya wants to convert the American customary units in the instructions into metric units so that her friend will easily be able to understand the measurements. If the recipe calls for a ratio of four ounces of paprika to every seven ounces of chili powder, and if Priya’s friend is planning to make a large batch of dry rub with 91 total ounces of chili powder, approximately how many total grams of paprika and chili powder will the recipe require? (1 ounce = 28.3 grams)

  • Solution

    In order to answer this question, you need to deal with the ratio as well as the unit conversion.

    For the large batch of dry rub, Priya's friend is planning to use 91 ounces of chili powder.

    Since the paprika and the chili powder must be used in a ratio of 4 to 7, you can set up a proportion to determine how much paprika is needed: \(\frac{4}{7} = \frac{x}{91}\).

    Cross-multiply and solve for x to determine that x (i.e., paprika) = 52 ounces.

    So you have 52 ounces of paprika and 91 ounces of chili powder for a total of 143 ounces.

    Multiply that by your conversion number, 28.3, to determine that this is equivalent to 4,046.9 grams, which is closest to (A).

Dogs need 8.5 to 17 ounces of water each day for every 10 pounds of their weight. Everett has two dogs-Ringo is a 35-pound black lab mix, and Elvis is a 55-pound beagle. Which of the following ranges represents the approximate total number of ounces of water, w, that Elvis and Ringo need in a week?

  • Solution

    Taking the two dogs together, Everett has 35 + 55 = 90 pounds of dog.

    Set up the following proportion to determine the lowest amount of water the dogs need per day: \(\frac{8.5 \; ounces}{10 \; lbs} = \frac{x}{90 \; lbs}\).

    Cross-multiply to get 10x = 765, so x = 76.5.

    Multiply by 7 days to get the weekly amount of water the dogs need: 76.5 × 7 = 535.5 ounces, or approximately 536 ounces.

    Only (C) includes 536 as the low-end amount.

    Therefore, the correct answer is (C).

(1⁄2)t + 4 = (1⁄2)t – 5

In the equation above, what is the value of t ?

  • Solution

    Use a calculator to translate the fractions into decimals.

    (1⁄2)t + 4 = (1⁄2)t - 5 becomes 0.5t + 4 = 0.75t - 5.

    Subtract 0.5t from both sides to get 4 = 0.25t - 5, and then add 5 to both sides.

    This results in 9 = 0.25t.

    Use a calculator to divide! t = 36; therefore, the correct answer is (D).

An advertisement for Royal Rat Rations states: “7 out of 8 veterinarians recommend Royal Rat Rations for your fancy rat.” No other information about the data is provided by the company.

Based on this data, which of the following inferences is most valid?

  • Solution

    You do not know how the survey is conducted, nor do you know how many veterinarians were surveyed (it may be the case that only 8 were surveyed).

    Therefore, you cannot infer that the survey accurately measures all veterinarians' beliefs about Royal Rat Rations.

    Choice (A) is not supported.

    First, you do not know what veterinarians believe in general, and second veterinarians may be recommending Royal Rat Rations for a reason other than its nutrition.

    Choice (B) is similarly not supported.

    Besides not knowing veterinarians' beliefs, this choice assumes that no other rat food is acceptable.

    Choice (C) is not supported because you do not know the sample size of the survey, nor is there any indication that there is only one veterinarian who does not recommend Royal Rat Rations.

    Choice (D) is the credited response.

    You know the opinions only of the veterinarians surveyed by Royal Rat Rations.

Which of the following is equivalent to (12x2 + 4x + 5y) + (3x2 – 2x + 3y) ?

  • Solution

    Because the operation between the parentheses is addition, the parentheses can be removed, and the resulting expression becomes 12x2 + 4x + 5y + 3x2 - 2x + 3y.

    Reorder the terms so that like terms are next to each other: 12x2 + 3x2 + 4x - 2x + 5y + 3y.

    Combine like terms to get 15x2 + 2x + 8y.

    The correct answer is (D).

Once a certain plant begins to grow, its height increases at a linear rate. After six weeks, the plant is 54 centimeters tall. Which of the following functions best models the relationship between h(w), the height, in centimeters, of the plant, and w, the number of weeks that the plant has been growing?

  • Solution

    The question states that after 6 weeks the plant is 54 centimeters tall.

    Therefore, when w = 6, h(w) = 54.

    Plug in 6 for w in the answers to see in which answer h(w) equals the target number of 54.

    In (A) h(w) = 6(6) = 36.

    Eliminate (A).

    In (B), h(w) = 9(6) = 54.

    The correct answer is (B).

Hannah placed an online order for shirts that cost $24.50 per shirt. A tax of 7% is added to the cost of the shirts, before a flat, untaxed shipping rate of $6 is charged. Which of the following represents Hannah’s total cost for s shirts, in dollars?

  • Solution

    Whenever the question includes variables, plug in.

    If s = 2, the shirts cost 2($24.50) = $49.

    The tax on the shirts is 0.07($49) = $3.43.

    So, the shirts with tax and the $6 shipping fee cost $49 + $3.43 + $6 = $58.43.

    Plug in 2 for s in the answers to see which answer equals the target number of $58.43.

    In (A), 0.07[24.50(2) + 6] = 3.85.

    This is not the target number, so eliminate (A).

    In (B), 1.07(24.50 + 6)(2) = 65.25.

    Again, this is not the target number, so eliminate (B).

    In (C), 1.07[24.50(2)] + 6 = 58.43.

    This is the target number, so keep it, but be sure to check the remaining answer choice.

    In (D), 1.07(24.50 + 2) + 6 = 34.355, which is not the target number.

    Therefore, the correct answer is (C).

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