As soon as you see the phrase “how much” write your answer choices in a column and label it “Cost to the School” (Column 1). If the $120 the school pitched in represents ¹⁄₅ of the cost of the trip, then the trip must have cost $600 (Column 2). Subtract $20 for the processing fee, then 10% for the discount, then add the processing fee back on.This gives you the actual cost of $542 (Column 3) and the students a surplus of $58 (Column 4). Subtract the $18 they had left over and divide the rest by 200; this will give you the price per cookie (Column 5), $0.80.This is way too much per cookie.To pay less per cookie you need to have more left over, so the school must have chipped in more money.Cross off choices (C), (B), and (A). Don’t be afraid of lots of columns.Combining steps means that you are doing work in your head, and this is where mistakes happen.Keep each step simple and methodical. Limit yourself to one operation per step.This will help prevent errors. Plug $160 into your new spreadsheet. It works.You’re done.

List your answer choices in a column on your scratch paper and label it “Shirley’s hourly.” Assume Shirley’s hourly is $25; Melinda’s hourly (Column 2), therefore, must be twice that, or $50. Shirley worked at that rate for 1.75 hours and earned $43.76 (Column 3). Melinda worked for ³⁄₄ of an hour and earned $37.50 (Column 4).The two together, therefore, earned $81.25 (Column 5), which is almost double what it should be.Cross off choices (C), (D), and (E) and try jumping to Choice (A).Choice (A) is the correct answer.

Plug in each of the answer choices to see which value cannot work. If 1 goal for 3 points is scored, then the team scored 45 points on unassisted goals (because the team had 48 points and 1 goal was worth 3 points, that leaves 48 − 3 = 45) To score 45 points, the team would need 9 assisted goals (9 goals at 5 points each gives us 9 × 5 = 45), so choice (A) cannot be correct. If 6 goals for 3 points are scored, then there are 18 points scored on unassisted goals and 30 points remain to be accounted for. 30 points can be achieved by 6 goals scored with assistance, so choice (B) cannot be correct. If 11 goals for 3 points are scored, there are 33 points scored and 15 left over, so that equals 3 goals scored without assistance, making choice (C) incorrect. If 12 goals for 3 points are scored, then 36 points have been scored and there are 12 points remaining.This is not divisible by 5, so choice (D) does not work and is the correct answer.

The problem wants you to figure out “five less than five times the number.” When the question asks for “the number,” plug in the answers and work backwards. Start with choice (C) and carefully work through the problem, one step at a time.Remember to write out the steps on your scratch paper to make things easier to follow.Choice (C) is −5.This number is “5 less” than “5 times the number,” so first add 5 to −5.That yields 0. 0, then, is “5 times the number” you’re looking for.The only number you can multiply by 5 to get 0 is 0 itself, so that’s the number you want.But does 0 work in the problem? No, because “three less than two times” 0 is just 2(0) − 3, or −3.This doesn’t equal “two more than three times the number,” which is 3(0) + 2, or 2. For a problem like this, it’s tough to figure out if you need a bigger or smaller number, so just pick one and go.Try choice (A), which is −30. −30 is 5 less than the number you want, so you need to add 5.That gives you −25. And −25 is five times the number you’re looking for, so what number times 5 yields −25? It’s −5 (because 5 × −5 = −25, so −25 is five times −5). Now check −5 in the first part of the question. 2(−5) − 3 = −13. And 3(−5) + 2 is also −13, so they’re equal and the best answer is choice (A).

The minute you see the phrase “what value of d,” list the answer choices on your scratch paper and label the first column. In this case, the answer choices, (Column 1) represent the price of a new release, d. If you assume choice (C) to be the correct answer, a new release costs $5.25.That means that a standard release (Column 2) costs $2.25.Carl rented two new releases for five days (Column 3), at a cost of $50.50 (2[$5.25 + (4)$5.00]). His standard release cost him $9 (Column 4), for a total of $59.50. It’s too low, so the initial price of the DVD must be too low.Cross off choices (C), (B) and (A).You now have instructions for exactly what to do with each of the remaining answer choices. Start with $6 and follow the exact same process.The answer is choice (D).

B,C, and D

Variables in the answer choices mean Plug In, and don’t worry if you don’t immediately see easy values to use for n. Try plugging a number into the given requirement and solve for n:\(\frac{n+7}{2}\) = 4, so n = 1. You already know choice (B) can be true, but Snd a few more values:\(\frac{n+7}{2}\) yields n = 9, so now you know choice (D) can be true; note, however, that \(\frac{n+7}{2}\) ≠ 12, since 12 is a multiple of 3, so n ≠ 17. You can try more, but the 3 values you now have—1 and 9, but not 17—are enough to establish a pattern: Increase by 8, but eliminate every third term. The rest of the list is thus 25 and 33, but not 41; 49 and 57, but not 65; 73 and 81, but not 89; and 97. Since 73 and 97 are both prime, choice (C) can be true as well.

625

Combine Plugging In and percent translation to attack this difficult problem. Meet the first requirement by making a = 60 and b = 100. Since b is 40% of c,\(\frac{40}{100}\times c\), and c = 250; c is 20% of d, so 250 =\(\frac{20}{100}\times d\) and d = 1250. Now use your assigned values to translate the last part of the question: 6(1250)= \(\frac{x}{100}\) × 20(60), so 7500 = \(\frac{x}{100}\) × 1200, 7500 = 12x, and x = 625.

It’s an algebra question with numbers for answer choices, so set up your scratch paper to Plug In the Answers. Start with choice (C). If Brian’s paycheck was $924, and he spent ¹⁄₄ on the repair, then he spent $231, leaving him with $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 choice (C) is correct.

B and E

This looks like a good opportunity to Plug In the Answers and see which ones work, but you’ll want to start with some algebra to get rid of the huge exponents in the numerator. First, get rid of the denominator by multiplying both sides by 2x. Now, notice that the term under the radical can be simpliSed to 6x², which—thankfully—is exactly what is on the other side of the equation.Cancel them, and now you have 8x²¹ + 12x²⁰ − 108x¹⁹ = 0. What are the common factors of each of the three terms? 4 and x¹⁹. Factoring them out yields: 4x¹⁹(2x² + 3x − 27) = 0. It may appear that x = 0 is one of your solutions; however, x = 0 would make the denominator on the left side of the original equation equal to zero, and thus undeSned, so x = 0 is not an acceptable solution. Eliminate choice (D). However, you also have a quadratic equation, which, if it can be made to equal zero, renders the other term meaningless. If you’re good at factoring quadratics, you might notice that this one factors to (2x + 9)(x − 3), giving choices (B), −4.5, and (C), 3. If you’re not comfortable factoring—or just don’t feel like it—use your on-screen calculator to start Plugging In the Answers. Don’t worry about the 4x² term: As long as what’s inside the parentheses is zero, it doesn’t matter what it gets multiplied by.

³⁄₁₀

Plug In for the total number of employees in the company. If there are 60 employees, then the number of employees who take the bus to work equals 60 × ¹⁄₅ = 12, and the number of employees who drive to work equals 60 × ¹⁄₃ = 20 . 60 – 12 – 20 = 28 left who neither take the bus nor drive to work.¹⁄₄ of these employees take the subway, so there are 28 × ¹⁄₄ = 7 employees who ride the subway. 28 − 7 = 21, so there are 21 employees remaining.¹⁄₇ of those employees ride a bicycle, so there are 21 × = 3 employees who ride a bicycle. 21 − 3 ¹⁄₇ = 18, so there are 18 employees who walk to work.\(\frac{18}{60}=\frac{3}{10}\), which is the correct answer.