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

THE CORRECT ANSWER IS A.

The question asks for a point that does NOT lie on the exterior of a circle, so the correct answer will be on the circle or inside it. Sketch a graph, and then Ballpark. The standard form of the equation of a circle is (*x – h*)^{2}+ (*y – k*)^{2 }= *r*^{2}, where the center of the circle is (*h, k*) and the radius is *r.* Therefore, the center of this circle is at (2, –5) and the radius is 6. Choices (B) and (C) are clearly outside the circle, so eliminate them. Choice (A) is 6 units directly up from the center of the circle, and the circle has a radius of 6. Therefore, the distance from (–1, 1) to the center of the circle is equal to the radius and must be on the circle. The correct answer is (A).

THE CORRECT ANSWER IS C.

The question asks for an equivalent inequality. The inequalities in the choices are in the same form as the original. The only difference is the coefficients. This indicates that factoring is the key. All terms in the original inequality are multiples of 3. Divide both sides by 3 to get *4a *+* 3b *<* 12*. The correct answer is (C).

THE CORRECT ANSWER IS A.

The question asks for the number of *seconds *Andrew waits for the weight rack. Start by converting 30 minutes to seconds by setting up a proportion: 1 minute/60 seconds = 30 minutes/*x* seconds. Cross-multiply to get *x *= 1,800 seconds. Next, take 35% of 1,800 seconds by multiplying 0.35 × 1,800 = 630 seconds. The correct answer is (A).

THE CORRECT ANSWER IS C.

The question asks what the slope represents in the graph of a certain situation. When asked about the meaning of a constant or variable in context, start by reading the full question. In the given equation, the slope is the coefficient on the *x *term: −75. Next, label the information in the equation. The variable *y *represents *amount of money remaining*, and the variable *x *is *days after the start of the fall semester*. Therefore, the equation is *amount of money remaining *= –75(*days after the start of the fall semester*) + 5,000. Next, go through the answer choices using Process of Elimination. Choice (A) references the total amount, which is *y*, not the slope. Eliminate (A). Choice (B) refers to the number 5,000, but the slope of the equation is –75. Eliminate (B). Choice (C) fits the equation; −75 is multiplied by the number of days since the beginning of the semester, so it would be consistent that Bo spent $75 per day. Keep (C). Choice (D) refers to the amount of money Bo earned over the summer. However, that is the starting point and wouldn’t need to be multiplied by the number of days. Also, slope is a rate of change, and the amount he made over the summer is fixed. Eliminate (D). The correct answer is (C).

THE CORRECT ANSWER IS D.

The question asks for a system of equations that models a certain situation. Use Bite-Sized Pieces, translate from English to math, and use Process of Elimination. Start with the most straightforward piece of information. The backpacker uses *a total of 10 granola bars and packets of peanut butter*, and *g *represents granola bars and *p *represents packets of peanut butter. This means that *g *+ *p *= 10. This is not part of any answer choice. In the answer choices, look at the equations that have the number 10. Choices (A) and (B) include the equation *g *– *p *= 10. This equation is definitely not the same as *g *+ *p *= 10. However, (C) and (D) include the equation *g *= 10 – *p*. Add *p *to both sides of the equation to get *g *+ *p *= 10, which matches the translation. Eliminate (A) and (B). Next, compare the remaining answer choices. Choices (C) and (D) only differ by what *g *and *p *are multiplied by; both remaining equations equal 1,660, which is the *total...food calories*. The question states that *a packet of peanut butter has 90 food calories*, so 90 should be multiplied by *p*, not *g*. Eliminate (C). The correct answer is (D).

THE CORRECT ANSWER IS C.

The question asks for the meaning of the number 20 in the context of the function. Label the parts of the function. *C*(*h*) represents *the number of bacteria colonies *and *h *represents *hours*, so the function becomes *number of bacteria colonies *= 3^{hours }– 2(*hours*) + 20. Next, go through the answers and use Process of Elimination. The number 20 is not affected by *hours*, so it cannot rep- resent a rate of growth; eliminate (A) and (B). Next, plug in. Choice (C) asks about the initial number of colonies, so make *h *= 0. The function becomes *C*(0) = 30 – 2(0) + 20, which is *C*(0) = 1 – 0 + 20 or *C*(0) = 21. This fits (C). There’s no way to determine the final number of bacteria colonies because the final time is not given; eliminate (D). The correct answer is (C).

THE CORRECT ANSWER IS D.

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

THE CORRECT ANSWER IS D.

Because there is a lot of information in the question, solve in bite-sized pieces. Start with the easiest piece. The question states that Heinrich *must buy at least 20 shares of Stock X. *The term *at least *translates to ≥. Since *a *represents the number of shares of Stock X, the correct answer must include *a *≥ 20. Eliminate the answer choices that do not include this inequality, which are (A) and (B). Look at the two remaining choices and find the difference between them. The only difference between (C) and (D) is that (C) includes the inequality *a *+ *b *≤ 100, while (D) includes the inequality *a *+ *b *≥ 100. According to the question, Heinrich must buy at least 100 total shares. Therefore, the total number of shares must be ≥ 100. Eliminate (C). The correct answer is (D).

THE CORRECT ANSWER IS B.

The question asks for the least number of photographs, so Plug In the Answers, starting with the least choice. Try (A). According to the question, Juliet sells the first 20 photographs for $10 each. Therefore, she takes in a total of 20 x $10 = $200. If Juliet sells an additional 18 photographs for $15 each, she will bring in an additional 18 x $15 = $270. Therefore, she brought in a total of $200 + $270 = $470. She earns a profit of 80% of her revenue, so she earns 80/100 x $470, which is 4/5 x 470. This can be simplified to 4 x $94, which equals $376. She must earn at least $400 in profit, so this answer is too small. Eliminate (A). Try (B). She still makes $200 on the first 20 photographs. If she sells 20 additional photographs, she takes in an additional 20 x $15 = $300, for a total of $200 + $300 = $500 in revenue. She earns a profit of 80% of the revenue, which is 80/100 x $500 = 4/5 x $500 = $400. This matches the goal of at least $400. Therefore, the correct answer is (B).

THE CORRECT ANSWER IS B.

Start by reading the full question. The question asks what the variable *b *represents. Next, label the parts of the equation. The variable *a *represents *the number of hours...doing homework each week*, and the number 15 represents *hours doing homework and watching television each week*. This makes the equation *number of hours doing homework *+ *b *= *hours doing homework and watching television each week*. Next, go through the answers and use Process of Elimination. Choice (A) relates doing homework and watching television to each other, but no information is given about the specific number of hours spent on each activity. Eliminate (A). Choice (B) fits the labeling of the equation; keep (B). Choice (C) can be eliminated because the question states that this is represented by *a*. Choice (D) can be eliminated because the question states that this is 15. The correct answer is (B).

THE CORRECT ANSWER IS C.

Start by determining the population of Toronto in 2001 by subtracting the increase from the 2011 population: 2.615 – 0.134 = 2.481 million people. To find the number of residents served per hospital, divide the population by the number of hospitals: 2,481,000/43 = 57,697.67, which is approximately equal to 57,700. The correct answer is (C).

THE CORRECT ANSWER IS C.

There are numbers in the choices, so Plug In the Answers, starting with one of the middle choices. The question asks how many days the First Opium War lasted. Start with (B). If the First Opium War lasted 1,180 days and was 218 days shorter than the second, then the Second Opium War lasted 1,180 + 218 = 1,398 days. Therefore, the two together lasted a total of 1,180 + 1,398 = 2,578 days. This is too small, so eliminate (A) and (B). Try (C). If the first war lasted 1,260 days, then the second lasted 1,260 + 218 = 1,478 days, and the two together lasted 1,260 + 1,478 - 2,738 days. This is consistent with the information in the question, so the correct answer is (C).

THE CORRECT ANSWER IS B.

The sample of the survey was made up of students who play a sport. These students would be more likely than the average student to want increased funding to the athletic department, so the sampling does not likely reflect the preference of the student body as a whole. Go through each choice one at a time. Choice (A) would only further the problem. Eliminate (A). Choice (B) reflects the problem discussed above. Keep (B). Choice (C) appears to be the result of the survey. However, the results may be skewed because of the sample chosen, so this conclusion cannot necessarily be reached. Eliminate (C). Choice (D) would be unrepresentative for a different reason: These students would be less likely than the average student to support increased funding to the athletic department. Eliminate (D). The correct answer is (B).

THE CORRECT ANSWER IS B.

The key to finding the correct system of equations or inequalities is to translate the information using Bite-Sized pieces, and then use the Process of Elimination at each step. Choose a piece of straightforward information to translate first, such as that each pound of potatoes,* p*, costs $3.25 and each pound of carrots, *c*, costs $2.47 Eliminate (C) and (D), since those answers do not relate the coefficients to the correct variables. To determine the correct inequality that relates to the number of pounds of vegetables, refer to the statement* the owner needs to buy at least three times as many pounds of potatoes as carrots.* Translate this statement into an inequality. The owner needs more potatoes than carrots. Whatever number of pounds of potatoes she buys, that number needs to be at least 3 times more than the number of pounds of carrots. Therefore, the correct inequality is* p ≥ *3*c*. The correct answer is (B).

THE CORRECT ANSWER IS A.

The question asks for an inference that can be made from a given survey. For questions like this, stick closely to the results of the survey and use Process of Elimination. Choice (A) concludes that few people who like working alone will be unhappy doing this task, which closely matches the group chosen (*a group of people who indicated that they preferred to work alone*) and the results (*5% stated they were unhappy while doing the task*)*. *This answer sticks closely to the survey; keep (A). Choice (B) makes an inference about people who do not like working alone; however, the survey collected data only on those who do like working alone, so there is no support for (B); eliminate it. Choices (C) and (D) are about people in general and whether they are working alone, but the survey considered only those people who like working alone; eliminate (C) and (D). The correct answer is (A).

THE CORRECT ANSWER IS C.

The question asks for the fraction of the students in Dr. Soper’s class that chose to be graded on the lab report and final exam. A fraction is defined as part/whole. For this question, the “part” is the number of Dr. Soper’s students who chose to be graded on the lab report and final exam, which is 3. The “whole” is Dr. Soper’s class total, which is 20. Therefore, the fraction of Dr. Soper’s class that chose to be graded on the lab report and final exam is 3/20.

THE CORRECT ANSWER IS B.

To solve the quadratic equation, first set the equation equal to 0. The equation becomes *x*^{2} + 12*x *– 64 = 0. Next, factor the equation to get (*x *+ 16)(*x *– 4) = 0. Therefore, the two possible solutions for the quadratic equation are *x *+ 16 = 0 and *x *– 4 = 0, so *x *= –16 or 4. Since the question states that *x *> 0, *x *= 4 is the only possible solution. Another way to approach this question is to Plug In the Answers. Start with (B), *x *= 4. Plug 4 into the equation to get 4^{2} + 12(4) = 64. Solve the left side of the equation to get 16 + 48 = 64, or 64 = 64. Since this is a true statement, the correct answer is (B).

THE CORRECT ANSWER IS C.

Use Process of Elimination. According to the question, *P *represents the population, so the outcome of the entire equation has something to do with the population. Therefore, eliminate both (A) and (B) because 1.0635 can’t represent the population if *P *does. In the given equation, the only operations are multiplication and addition, which means that over time the population would increase. Therefore, eliminate (D). The correct answer is (C).

THE CORRECT ANSWER IS C.

The question asks for the meaning of 14 in the equation. C represents the *total cost*, and *h* represents *hours of work*. Next, use Process of Elimination. 14 is not associated with hours of work, so eliminate (A) and (D). 14 is added to 9*h* to determine the total cost, so it cannot be the total cost for any amount of work; eliminate (B). The correct answer is (C).

THE CORRECT ANSWER IS B.

The correct answer is B. The question asks for an expression equivalent to 4*w* – 100, and it states that both formulas give the same value for *BMI*. Therefore, the left sides of each equation are equal, so set the right sides equal and solve for 4*w* – 100. The equation becomes *w */ *h*^{2} = (4*w* – 100) / 5. Isolate 4*w* – 100 by multiplying both sides by 5 to get 5*w */ *h*^{2} = 4*w* – 100. Be sure to read the full question, which asks for 4*w* – 100, so the correct answer is (B).

THE CORRECT ANSWER IS A.

To find the sum of complex numbers, just add them together, treating *i* like a variable. The sum is 6 + 2*i* + 3 + 5*i*. Combine like terms to find the answer. Add 6 and 3 to get 9. Then, add the imaginary terms, 2*i* and 5*i*, to get 7*i*. The correct answer is (A).

THE CORRECT ANSWER IS C.

The question asks for *w*, and the answer choices are all equations solved for *w*, so isolate *w* in Formula

B. Start by multiplying both sides by 5 to get 5*BMI* = 4*w* – 100. Next, add 100 to both sides to get 5*BMI* + 100 = 4*w*. Divide both sides by 4 to get (5*BMI* + 100)/4 = *w*. The correct answer is (C).

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/360^{o}). Plug in the given information to get (arc/circumference) = (70^{o}/360^{o}). The fraction reduces to 7/36. The correct answer is 7/36, or 0.194.

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 *y *= 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).

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).

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 *x *= 12. Next, plug *x* = 12 into the second equation to get 12 + *y *= 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).

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).

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 7.75*x* = 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).

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.

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).

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 *a*^{2 }terms. Combine the terms: –a^{2} – (2*a*^{2}) = –3*a*^{2}. Eliminate (A) and (B). Next, work the numbers: 4 – (–6), which is 4 + 6 = 10. Eliminate (C). The correct answer is (D).

THE CORRECT ANSWER IS C.

If | *x *| = | 2*x* – 1 |, either *x* = 2*x* – 1 or –*x* = 2*x – *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.

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).

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).

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,

–1(

Now solve:

. 1.6

Simplify by dividing both sides by 1.6 to get

***

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