practice SAT and ACT questions and answers

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10/3/20

THE CORRECT ANSWER IS E.

First, determine the value of x, which is 32, or 9. The problem asks for the value of xx, so substitute 9 for x, which makes the expression 99. This is not an answer choice. In fact, all the answer choices are written with a base of 3, so convert 99 to a base of 3. This yields 99 = (32)9, or 318. This matches (E), which is the correct answer.

9/29/20

THE CORRECT ANSWER IS A.

The quantities are already represented as the product of prime factors: 72 = (7)(7), so the least prime factor of Quantity A is its only prime factor, 7. Similarly, 27 = (2)(2)(2)(2)(2)(2)(2), so Quantity B is 2. The answer is (A). 

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9/26/20

THE CORRECT ANSWER IS D.

There are variables in the quantities, so Plug In. Begin with something that impacts exponents in a unique way, such as 1. When a = 1, Quantity A is 3 and Quantity B is something greater than 3. Eliminate (A) and (C). Now Plug In again using FROZEN numbers. Try a = 0. In this case, both quantities are equal. Eliminate (B) and the correct answer is (D). 

9/22/20 

THE CORRECT ANSWER IS D.

This problem has variables in the question stem and quantities, so Plug In. This problem looks suspiciously simple. Clearly x = 3 and y = 4. Eliminate choices (A) and (C). However, remember to Plug In more than once using FROZEN numbers for Quant Comp problems. Plug In again. Because y2 = 16 could represent either y = 4 or y = –4. If y equals –4, then Quantity A is greater. Eliminate (B) and the correct answer is (D). 

9/19/20

THE CORRECT ANSWER IS 9.

This problem provides a ratio, so draw a ratio box. With a ratio of 5 : 7 : 3, the total number of singers is at least 15. If you double the number, and keep the ratio, there are 30 singers. To have at least 40 singers with the same ratio, the actual total is 45, or 3 times 15, which means there are three times the number of basses (3) in the ratio, or 9.

9/15/20 

THE CORRECT ANSWER IS D.

There are variables in the question stem and quantities, so Plug In. Start with easy numbers for p and q such as p = 1 and q = 2. In this case, Quantity A is 27 and Quantity B is 9. Eliminate (B) and (C). Plug In again using FROZEN numbers. Try fractions such as p = 1/2 and q = 1/4. In this case, Quantity A is still greater. Plug In one more time, this time with negative numbers such as p = –3 and q = –2. Now, Quantity A is –125 and Quantity B is –35. Because –35 is greater than –125, Quantity B is greater than Quantity A. Eliminate (A). The correct answer is (D). 

9/12/20

THE CORRECT ANSWER IS A.

A computer manufacturer builds 1,000 computers and sells all of them, yielding a profit of $20,000. The amount of $20,000 is 40% of the cost of production, so the total cost of production is $20,000 = 0.4x; therefore, x = $50,000. Determine the cost of one computer at the retail store to find the value for Quantity A. All computers are sold for the same amount of money, so determine the total amount of money spent at the retail store. If the total profit is $20,000 and the total cost of production is $50,000, then the total amount of money spent on the computers at the retail store is $70,000. The cost of one computer is $70. So, Quantity A is $70 and Quantity B is $50, which means that Quantity A is greater and the correct answer is (A). 

9/8/20 

THE CORRECT ANSWER IS D.

Together, Rachel and Rob cover 120 of the 190 miles in one hour. Set up a proportion to find out how long the whole trip takes, so 120 miles/60 minutes =190 miles/x minutes and 120x = 11,400. Therefore, x = 95 minutes for the whole trip. Since the whole trip takes 95 minutes, a separate proportion can be set up to figure out how many miles they cover in 45 minutes. 120 miles/60 minutes = y miles/45 minutes, so 60y = 5,400 and y = 90 miles, and the correct answer is (D). 

9/5/20

THE CORRECT ANSWER IS 4.

To solve this question, write it out. Since there are fewer numbers that yield a remainder of 2 when divided by 7, start there. The first such number is 2, and thereafter they increase by 7; the rest of the list is thus 9, 16, 23, 30, 37, 44, 51, 58, 65, 72, 79, 86, and 93. Rather than list out all the numbers that yield a remainder of 1 when divided by 3, just select the numbers that meet the requirement from the list you already have: only 16, 37, 58, and 79 do, so there are 4 values for x.

9/1/20 

THE CORRECT ANSWER IS 480.

Make lists of the multiples for each number. Work on 240 first; then list the multiples of 160 until you find one on the list for 240. 

240:         160: 
240          160 
480          320 
720          480  

8/29/20 

THE CORRECT ANSWER IS C.

Rather than listing out all of the prime numbers up to 43, stay focused on the unique number, 2, the only even prime number. All of the choices are odd, and two odd numbers would yield an even sum, so you’ll be able to eliminate answers only by adding 2 to an odd number. Each of the incorrect answers, therefore, is the sum of 2 and the previous prime number: Choice (A) is 2 + 5; (B) is 2 + 17; (D) is 2 + 29; and (E) is 2 + 41. The answer is (C).

8/25/20 

THE CORRECT ANSWER IS C.

The question asks for a specific value, and the answer choices represent that value, so Plug In the Answers. Start with (C). If Brian’s paycheck is $924, and he spends 1/4 on the repair, then he spends $231, which leaves $693. The insurance and registration each cost 1/3 of the balance, or $231, so he spends another $462, leaving him with $693 – $462 = $231. This matches the information in the question, so (C) is correct. 

8/22/20

THE CORRECT ANSWERS ARE A, D.

This question asks for a specific value and that value is represented by the answer choices, so Plug In the Answers. Because this is an All That Apply question, it is acceptable to start with (A). Plug In the values in the answer choices for x . Choices (A) and (D) do not result in an integer, while (B) and (C) do. The correct answers are (A) and (D). 

8/18/20

THE CORRECT ANSWERS ARE A, D.

First, use an Average Pie. Multiply 4 by 120 and to find a total of 480 points for the first 4 games. Now, Plug In the Answers to figure out which answers give an overall average that is divisible by 7. Start with (A), because on All That Apply questions, there’s no reason to start in the middle if many answers might work. Choice (A) yields 480 + 80 = 560, and 560 ÷ 5 = 112. That is divisible by 7. Choice (B) is 480 + 110 = 590, and 590 ÷ 5 = 118. This is not divisible by 7, so eliminate (B). Continue checking all the answer choices, looking for any that result in an integer divisible by 7. The correct answers are (A) and (D). 

8/15/20

THE CORRECT ANSWER IS D.

This question has numbers in the answer choices, so Plug in the Answers, starting with (C). 25% of $110,000 is $27,500, and $100,000 plus $27,500 equals $137,500. Since this is too small, choose a bigger number, such as (D), $112,000. In this case, 25% of $112,000 is $28,000, and $112,000 plus $28,000 is $140,000, which is the total stated in the problem, so (D) is the correct response.

8/11/20

THE CORRECT ANSWER IS D.

There are variables in the question stem and answer choices, so Plug In. Plug In a value for z that is easy to work with, such as z = 100. If z =100, then Wanda’s number is 50 and 20 percent of 50 is 10. So, 10 is the target number. Plug In 100 for z in all the answer choices looking for one that equals 10. Choice (D) is the only choice that equals 10, so the correct answer is (D). 

8/8/20

THE CORRECT ANSWER IS B.

This question asks for a specific value, and that value is represented by the answer choices, so Plug In the Answers. Start with (C). If Reservoir A contains 700 million gallons of water, then Reservoir B has 450 million gallons less, or 250 million gallons. When 100 million gallons are drained from Reservoir A to Reservoir B, then the reservoirs hold 600 million and 350 million gallons of water, respectively. The problem states that Reservoir A has twice the water that Reservoir B has, so this choice is incorrect. Eliminate (C). It is hard to tell if the number needs to be larger or smaller, so pick a direction. Try (B). If Reservoir A contains 600 million gallons of water, then Reservoir B has 450 million gallons less, or 150 million gallons. When 100 million gallons are drained from Reservoir A to Reservoir B, then the reservoirs hold 500 million and 250 million gallons of water, respectively. Because Reservoir A has twice the amount of water as Reservoir B, this is the appropriate relationship. The correct answer is (B).

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