Test - 6 - SAT MCQ

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 = 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).

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).

The quality control expert discovered that 13 out of 1,000 randomly selected tennis balls were defective. 13/1000 = 0.013, which is equivalent to 1.3%. This means that 100 - 1.3 = 98.7% of tennis balls tested were not defective, and this data most supports answer (B).

First, you know the new proportion must be less than the current 0.34 for biofuels (because the total amount spent on alternative energy is increasing, but the amount spent on biofuels is remaining the same), so you can eliminate (D). Next, determine the amount that will be spent on biofuels in 2017 by multiplying 0.34 by the total of $254 million: 0.34 × 254 = $86.36 million. Because 57 million new dollars will be spent on alternative energy, the new total will be 254 + 57 = $311 million. Divide $86.36 million by $311 million to get the new proportion: 86.38/311 = 0.28, which is (C).

The formula for compound interest is A = P(1 + r)^t, where P is the starting principle, r is the rate expressed as a decimal, and t is the number of times the interest is compounded. Melanie received less than 5% interest, so you can eliminate (B) because 1.05 = 1 + 0.05, indicating she was receiving 5% interest. You can also eliminate (C) because over the course of a year the interest is compounded 4 times, not 1/3 of a time. Because Melanie invested $1,100 at what she thought was 5% compounded 4 times (12 months in a year ÷ 3 months per period), she expected 1,100(1 + 0.05)⁴ = $1,337.06 after a year. Instead, she has 1,337.06 - 50 = $1,287.06 after one year. Because t is in years in the answer choices, make t = 1 in (A) and (D) and eliminate any choice which does not equal 1,287.06. Only (A) works.

i^a = 1 when a is a multiple of 4. Using your exponents rules, 413 + x must also be a multiple of 4. Plug in the answers and look for what makes 413 + x a multiple of 4. Only (D) works.

The flu shot is most effective against Strain C, which is least prevalent in March. To determine the overall efficacy of the flu shot at this time, multiply the prevalence of each strain of flu by the efficacy of the flu shot against that strain, and then add those products to get a weighted average of the efficacy of the shot: (0.23 × 0.35) + (0.25 × 0.13) + (0.13 × 0.76) + (0.39 × 0.68) = 0.477 = 47.7%, which is closest to (D).

The zero of g is the value of the variable, in this case x, when the equation is set to 0. This is also called the root or solution of an equation. Set the equation to 0 to get 0 = 2x² - dx - 6. Plug 6 in for x to get 0 = 2(6²) - d(6) - 6. Simplify the equation to get 0 = 72 - 6d - 6, or 0 = 66 - 6d. Solve for d to get -66 = -6d, so 11 = d. Plug 11 in for d and set the quadratic to 0 to get 0 = 2x² - 11x - 6. Factor the equation to get 0 = (x - 6)(2x + 1). The other zero of the equation is when 2x + 1 = 0. Solve for x to get 2x = -1, or x = -1/2. The correct answer is (C).

In quadrant II, the x-coordinate is negative, and the y-coordinate is positive. Therefore, eliminate (C). Whenever the question includes variables and the answers are numbers, think Plugging In the Answers. Of the remaining answers, (B) is easiest to work with. In (B), the x-value is -4 and the y-value is 2. Plug these values into the second equation to get -4 = -2 + 2. Given that this is not a true statement, eliminate (B). Try the values in (A) in the second equation to get 3√2 = -(-3√2) + 2. This is also not true, so the correct answer is (D).

Whenever there are variables in the question and numbers in the answer choices, think Plugging In the Answers. In (A), j = 6, and k = -6. Plug these two values into the first equation to get -24 - 8(6) = 12(-6). Solve for both sides of the equation to get -24 - 48 = -72, or -72 = -72. Therefore, the values work for the first equation. Plug the values into the second equation to get 3 + 5/3(-6) = -7/6(6). Solve both sides of the equation to get 3 + (-10) = -7, or -7 = -7. Since the values given in (A) work in both equations, the correct answer is (A).