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7/10/20

THE CORRECT ANSWER IS D.

This question requires evaluating both equations to determine the values of a and b. You can begin by solving either of the two equations for a or b, and then substituting the solution into the other equation. But note that the question asks for the value of a + b, so check to see if there's a faster way: Can you stack and add (or subtract) the equations? If you stack and add the equations, you get 7a + 7b = 77. Now divide both sides of the equation by 7, resulting in a + b = 11. This is (D).

7/6/20

THE CORRECT ANSWER IS B.

When there are variables in the answer choices, Plugging In is an option. However, since there are 3 variables in the question, it is probably easier to just do algebraic manipulation. The answer choices indicate that the equation must be solved for m. The variable m is multiplied by both 10 and h, so to isolate m, divide both sides by 10h: E/10= 10mh/10h. The 10 and the h on the right side of the equation cancel, leaving E/10h = m. The correct answer is (B).

7/3/20

THE CORRECT ANSWER IS C.

Everett’s dogs weigh 35 + 55 = 90 pounds. Set up the following proportion to determine the lowest amount of water the dogs need per day: 8.5 ounces / 10 pounds = x / 90 pounds. Cross-multiply to get 10x = 765, so x = 76.5. Multiply by 7 days to get the weekly amount of water the dogs need: 76.5 x 7 = 535.5 ounces, or approximately 536 ounces. Only (C) includes 536 as the low-end amount. Therefore, the correct answer is (C).

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6/29/20

THE CORRECT ANSWER IS B.

The goal here is to isolate x. Since the right-hand side of the equation is –2x + 1, you will want to subtract 1 from both sides, so eliminate (A) and (C). To get x by itself, you will want to divide by –2, not 2, so eliminate (D) and choose (B). Remember that when you multiply or divide across an inequality sign using a negative number, you need to flip the inequality sign in the opposite direction, as reflected in (B).

6/26/20

THE CORRECT ANSWER IS B.

Since the question asks for a specific value, it can be solved by Plugging in the Answers; however, because the question involves roots, it may be easier to solve instead. Since √4 = 2 and √36 = 6, rewrite the expression to read √t + 2 = 6. Isolate t by first subtracting 2 from both sides to get √t = 4. Next, square both sides to clear the radical: t =42, which is 16. The correct answer is (B).

6/22/20

THE CORRECT ANSWER IS D.

When there are numbers in the answer choices, try Plugging in the Answers. These choices represent possible values of z. Start with (C), which is 4. If z is 4, then the right side of the equation becomes (4y + r)(4y –  r). Expand this expression using FOIL to find the first term, which will be 16y2. Since this doesn't match 9y2 from the left side of the equation, eliminate (C). Since 16 is bigger than 9, the correct answer needs to be smaller than the one in (C). Therefore, eliminate (A) and (B). Choice (D) must be the correct answer. Test this by plugging in 3 for z. Notice that the first term of (3y + r)(3y – r) is 9y2. The correct answer is (D).

6/19/20

THE CORRECT ANSWER IS C.

The vertex of a parabola is always on the axis of symmetry, which is located halfway between the roots of the parabola. To find the roots, set g(x) = 0 to get (− 2)(− 4) = 0. Set both factors equal to 0 to get − 2 = 0 and − 4 = 0. If − 2 = 0, then = 2. If − 4 = 0, then = 4. Since the axis of symmetry is halfway between the roots, it is = (2 + 4)/2 = 3. Therefore, the x-coordinate of the vertex is 3. Select the choice that includes = 3. The correct answer is (C). 

6/15/20

THE CORRECT ANSWER IS B.

The question asks for a specific value, so Plug In the Answers. It is easy to plug in a value of 0, so start with (C). The value of y is given in the question, so if k = 0, the equation becomes 25 = [(0)(–2) – 1]2. Multiply in the parentheses to get 25 = (0 – 1)2, which is 25 = (–1)2 or 25 = 1. This is not true, so eliminate (C). It might not be clear if a larger or smaller number is needed, so pick a direction to go in. Try (B). If k = –3, the equation becomes 25 = [(–3)(–2) – 1]2. Multiply in the parentheses to get 25 = (6 – 1)2, which is 25 = 52 or 25 = 25. This is true. The correct answer is (B).

6/12/20

THE CORRECT ANSWER IS B.

To solve this question, simply subtract y from both sides of the equation to get 2y = 2, which is (B).

6/8/20

THE CORRECT ANSWER IS A.

There are 162 games in the season, so the team needs a total of 162 x 45,500 = 7,371,000 ticket purchases to have a mean of 45,500 ticket purchases per game for the season. The 60 games with an average total ticket purchase of 43,000 gives a total of 2,580,000 ticket purchases, leaving 4,791,000 ticket purchases left for the team to reach its goal. Dividing 4,791,000 by 102 makes (A) the closest value to the average of 46,971 ticket purchases per game the team needs to make.

5/29/20

THE CORRECT ANSWER IS D.

Because the operation between the parentheses is addition, the parentheses can be removed, and the resulting expression becomes 12x+ 4+ 5+ 3x– 2+ 3y. Reorder the terms so that like terms are next to each other: 12x+ 3x+ 4– 2+ 5+ 3y. Combine like terms to get 15x2 + 2+ 8y. The correct answer is (D).

5/25/20

THE CORRECT ANSWER IS A.

In order to answer this question, you need to deal with the ratio as well as the unit conversion. For the large batch of dry rub, Priya's friend is planning to use 91 ounces of chili powder. Since the paprika and the chili powder must be used in a ratio of 4 to 7, you can set up a proportion to determine how much paprika is needed: 4/7 = x/91. Cross-multiply and solve for x to determine that x (i.e., paprika) = 52 ounces. So you have 52 ounces of paprika and 91 ounces of chili powder for a total of 143 ounces. Multiply that by your conversion number, 28.3, to determine that this is equivalent to 4,046.9 grams, which is closest to (A).

5/22/20

THE CORRECT ANSWER IS C.

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 x 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 answer choices. 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 answer choices, you can take each choice 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).

5/18/20

THE CORRECT ANSWER IS B.

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

5/15/20

THE CORRECT ANSWER IS C.

You can Plug In to make sense of this equation. Say that x = $100. The amount of the keg would then be $107 + $17. The $17 must be the untaxed deposit, since it is a flat fee rather than percentage-based. Therefore, the tax is $7, which is 7% of the original $100 base price. The answer is (C).

5/11/20

THE CORRECT ANSWER IS A.

The vertex form of a parabola is y = a(xh)2+ k, where (h, k) denotes the vertex. Plug in the point (3, –3) into the vertex form to get y = a(x – 3)2 – 3. The correct answer is (A).

5/8/20

THE CORRECT ANSWER IS 24.

Distribute the 5 on the left side to get 15y – 60 – (23 + 11y) = 13. Distribute the negative sign to get 15y – 60 – 23 – 11y = 13. Combine like terms on the left side to get 4y – 83 = 13. Add 83 to both sides to get 4y = 96. Divide both sides by 4 to get y = 24. The correct answer is 24.

5/4/20

THE CORRECT ANSWER IS D.

The question asks for the equation for which the solutions are both points that are 2 units away from –5. Determine the two points. The point that is 2 to the left of –5 is –5 – 2 = –7. The point that is 2 to the right of –5 is –5 + 2 = –3. Plug these points into the equations in the answer choices, and eliminate any choice for which one of the points is not a solution. Start with (A). Plug x = –7 into (A) to get |–7 – 2| = 5. This is false, so eliminate (A). Try (B). Plug x = –7 into (B) to get |–7 + 2| = 5. This is true, so try x = –3. Plug x = –3 into (B) to get |–3 + 2| = 5. This is false, so eliminate (B). Try (C). Plug x = –7 into (C) to get |–7 – 5| = 2. This is false, so eliminate (C). Only (D) is left, so it must be correct. Plugging x = –7 and x = –3 into (D) results in two true statements, so the correct answer is (D).

5/1/20

THE CORRECT ANSWER IS C.

Whenever there are variables in the question and the answer choices, think Plugging In. If 2 purchases were made, then p = 2, and the number of bonus points can be calculated as 4(2) + 7 = 8 + 7 = 15. If the number of purchases was then increased by 3, the new p equals 5 and the number of bonus points can be calculated as 4(5) + 7 = 27. The bonus points increased by 27 – 15 = 12. The correct answer is (C).

4/27/20

THE CORRECT ANSWER IS A.

The survey was conducted on fourth-grade girls in the county, so restrict the conclusion to that group. Choice (A) restricts the conclusion to fourth-grade girls, so keep (A). Choices (B), (C). (D) all refer to all fourth-graders in general, not just fourth-grade girls, so eliminate these choices. The correct answer is (A).

4/24/20

THE CORRECT ANSWER IS B.

To find the solutions to an equation in factored form, set each of the factors equal to 0. If x + 5 = 0, subtract 5 from both sides to get x = –5. If x – 0.4 = 0, add 0.4 to both sides to get x = 0.4. Therefore, the two solutions are –5 and 0.4, so the sum of the solutions is –5 + 0.4 = –4.6. The correct answer is (B).

4/20/20

THE CORRECT ANSWER IS B.

The question asks for the percent decrease. For percent difference, use the formula difference/original x 100. The difference is $91.94 – $86.53 = $5.41. Because it is a percent decrease, the larger value is the original. Therefore, the percent decrease is $5.41/$91.94 x 100 ≈ 5.884. The question asks to round to the nearest tenth of a percent, so the correct answer is (B).

4/17/20

THE CORRECT ANSWER IS A.

Because the question asks for the value of x, Plug In the Answers, starting with one of the middle choices. Start with (B). If the monthly fee is $55, then it costs $55 x 18 = $990. This is already too high, even without the installation fee, so eliminate (B). Choices (C) and (D) will be greater still, so eliminate those answers as well. Only (A) is left, so it must be correct. If the monthly fee is $45, then 18 months costs $45 x 18 = $810. Add the $150 installation fee to get $810 + $150 = $960. This is the correct total charge, so the correct answer is (A).

4/13/20

THE CORRECT ANSWER IS D.

When subtracting polynomials, use Bite-Sized Pieces. Combine like terms one at a time, eliminating choices at each step. Use the choices to help decide where to start. There are three possibilities for the constant term and only two possibilities for each of the other two terms, so start with the constant. The –11 in the second polynomial must be subtracted from the –5 in the first polynomial to get –5 – (–11) = –5 + 11 = 11 – 5 = 6. Eliminate (A), (B), and (C), which do not include 6. Only one choice remains. The correct answer is (D).

4/10/20

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)= r2, 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).

4/6/20

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).

4/3/20

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). 

3/30/20

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). 

3/27/20

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). 

3/23/20

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 = 3hours – 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). 

3/20/20

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. 

3/16/20

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). 

3/13/20

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). 

3/9/20

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). 

3/6/20

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). 

3/2/20

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). 

2/28/20

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). 

2/24/20

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 ≥ 3c. The correct answer is (B). 

2/21/20

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). 

2/17/20

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.

2/14/20

THE CORRECT ANSWER IS B.

To solve the quadratic equation, first set the equation equal to 0. The equation becomes x2 + 12x – 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 42 + 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). 

2/10/20

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). 

2/7/20

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 9h to determine the total cost, so it cannot be the total cost for any amount of work; eliminate (B). The correct answer is (C).

2/3/20

THE CORRECT ANSWER IS B.

The correct answer is B. The question asks for an expression equivalent to 4w – 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 4w – 100. The equation becomes h2 = (4w – 100) / 5. Isolate 4w – 100 by multiplying both sides by 5 to get 5h2 = 4w – 100. Be sure to read the full question, which asks for 4w – 100, so the correct answer is (B).

1/31/20

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 + 2i + 3 + 5i. Combine like terms to find the answer. Add 6 and 3 to get 9. Then, add the imaginary terms, 2i and 5i, to get 7i. The correct answer is (A).

1/27/20

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

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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