practice SAT and ACT questions and answers

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1/24/20

THE CORRECT ANSWER IS 7/36 or 0.194.

The question asks what fraction of the circumference is the arc, which translates to (arc/circumference). The length of an arc compared to the circumference of the circle is proportional to the central angle over 360 degrees, so (arc/circumference) = (angle/360o). Plug in the given information to get (arc/circumference) = (70o/360o). The fraction reduces to 7/36. The correct answer is 7/36, or 0.194.

1/20/20

THE CORRECT ANSWER IS A.

The question asks for the relationship between two variables, so Plug In. Use Nickel in the table because it has the most straightforward value for grams. Because y is grams and d is drams, make = 5.00 and d = 2.82. Plug these values into the answer choices and eliminate any choice that is not true. Choice (A) becomes 5.00 = 1.8(2.82), which is 5.00 = 5.08. This is close, so keep (A). Choice (B) becomes 2.82 = 1.8(5.00) which is 2.82 = 9.00. This is false; eliminate (B). Choice (C) becomes (5.00)(2.82) = 1.8, which is 14.1 = 1.8. This is false; eliminate (C). Choice (D) becomes 5.00 = 0.56(2.82), which is 5.00 = 1.58. This is false; eliminate (D). The correct answer is (A).

1/17/20

THE CORRECT ANSWER IS D.

The question asks for the number of peppers the farmer expects...in August. Work in bite-sized pieces. The question states that the percent increase from June to July would be half the percent increase from July to August. First find the percent increase from June to July using the percent change formula: percent change = (difference/original) x 100. Plug the numbers from the table into the formula to original get [(2,640 – 2,200)/2,200] x 100, which is (440/2,200) x 100 = 20%. If this is half the percent increase from July to August, then the percent increase from July to August must be double 20%, or 40%. To find the number of peppers expected in August, find what 40% of July’s amount would be. Multiply 2,640 by 40% to get 1,056. Add this to 2,640 to get 3,696 peppers expected in August. The correct answer is (D).

1/13/20

THE CORRECT ANSWER IS B.

The question asks for the value of x – y given a system of equations. Start by multiplying both sides of the first equation by 3 to get = 12. Next, plug x = 12 into the second equation to get 12 + = 32. Subtract 12 from both sides to get y = 20. The question asks for the value of x – y, which is 12 – 20 = –8, choice (B). 

1/6/20

THE CORRECT ANSWER IS C.

The question asks for a specific value, and there are numbers in the answer choices, so Plug In the Answers. Choice (C) is easier to work with than (B), so start with (C). If the original weight of the steak is 10.00 ounces, then the weight of the fat trimmed off would be 12% of 10.00, which is 1.20 ounces. Subtract this from 10.00 to find the weight after trimming the fat: 10.00 – 1.20 = 8.80 ounces. This matches the information in the question. The correct answer is (C).

12/30/19

THE CORRECT ANSWER IS D.

The question asks for the number of boards needed to cover a certain floor width. Set up a proportion. Be sure to match the labels on the numerators and denominators: 10 boards/7.75 feet = x boards/32 feet. Cross-multiply to get 7.75x = 320. Divide both sides by 7.75 to get x ≈ 41.3. The question asks for the closest answer, so the correct answer is (D).

12/28/19

THE CORRECT ANSWER IS B.

First, use your pencil to label the variables. Then, Plug In! Try p = 2. At $2 a slice, the cafeteria sells 1,265 slices. Try p = 3 next. At $3 a slice, the cafeteria sells 1,261 slices. Next, try p = 4. At $4 a slice, the cafeteria sells 1,257 slices. Now, use POE. As the price of pizza goes up, the cafeteria sells fewer slices of pizza. That means you can eliminate (C) and (D). Choice (A) says that for every $4 the price goes down, the cafeteria sells 1 more slice of pizza. Does your plugging in back that up? No. Now take a look at (B). Does the cafeteria sell 4 more slices of pizza for every dollar the price drops? Yes! You've got the correct answer.

12/23/19

THE CORRECT ANSWER IS A.

Use Bite-Sized Pieces and Process of Elimination to determine the correct answer. Since the question deals with percentages, 30% and 70% must be converted to decimals, 0.3 and 0.7, respectively. Eliminate (C) and (D), since the percentages are not converted to decimals. Trail Mix X is 30% peanuts by volume and is represented by a; therefore, the correct relationship will take 30% of a. Likewise, Trail Mix Y is 70% peanuts by volume and is represented by b; therefore, the correct relationship will take 70% of b. Choice (B) has reversed this relationship, so eliminate it. The correct answer is (A).

12/16/19

THE CORRECT ANSWER IS D.

The question asks for an equivalent expression to the one given. There are variables in the answer choices, so Plugging In is an option. However, the question is straightforward enough to solve without plugging in. Use Bite-Sized Pieces and Process of Elimination. Start with the aterms. Combine the terms: –a2 – (2a2) = –3a2. Eliminate (A) and (B). Next, work the numbers: 4 – (–6), which is 4 + 6 = 10. Eliminate (C). The correct answer is (D).

12/9/19

THE CORRECT ANSWER IS C.

If | | = | 2x – 1 |, either x = 2x – 1 or –x = 2x – 1. The solutions to these equations are 1 and 1/3, respectively. The only thing you need to recognize, however, is that the equation has two different solutions. The correct answer is therefore C.

12/2/19

THE CORRECT ANSWER IS C.

The question states that the corn on the north edge is shorter than the corn on the south edge, which is 50 inches tall. You are asked to find the height of the corn on the north edge, so the correct answer must be less than 50. Eliminate (D), which is too high. Often, at least one of the bad answers on these questions is the result you would get if you applied the percentage to the wrong value. To find the right answer, take 30% of 50 by multiplying 0.3 by 50 to get 15, then subtract that from 50. The corn on the north edge is 35 inches tall, which is choice (C).

11/25/19

THE CORRECT ANSWER IS B.

To find the value of f(3) + f(5), find the values of f(3) and f(5) separately: f(3) = 2(3)2 + 4 = 22 and f(5) = 2(5)2 + 4 = 54. So f(3) + f(5) = 76. You can tell that f(4) will be between 22 and 54, so you can cross out (A). If you Ballpark (C) and (D), putting 10 or 15 in the function will give you a number bigger than 100, and you're looking for 76, so (C) and (D) are too big. That means the answer is (B) by POE (Process of Elimination). 

11/18/19

The correct answer is D.


This is a system-of-equations question in disguise. Here's how to crack it: First, locate a piece of information you can work with. "The sum of three numbers, ab, and c, is 400" translates to a b + c = 400. Here's another piece of info: "One of the numbers, a, is 40 percent less than the sum of b and c ." Translate this to get a = (1 – 0.4)(b c), or a = 0.6(b c). Distribute the 0.6 to get a = 0.6b + 0.6c. Arrange these variables so they line up with those in the first equation as  a – 0.6b – 0.6c = 0. To solve for b c, stack the equations and multiple the second equation by –1:

        a +       b   +    c   = 400
   –1(a – 0.6b – 0.6 c ) = 0(–1)

Now solve:

       a  +     b +      c  = 400
     –a + 0.6b + 0.6c = 0
.             1.6b + 1.6c = 400

Simplify by dividing both sides by 1.6 to get b c = 250.
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