We publish practice problems on our social media pages. Here's where you can find the correct answers—and explanations.

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.

*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).

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 = 0.4*x*; 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.

*miles*/60 *minutes* =190 *miles*/*x* *minutes* and 120*x* = 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 60*y* = 5,400 and* y* = 90 *miles*, and the correct answer is (D).

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

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 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.

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.

*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).

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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