Plug in 2 for a to find 3³⁽²⁾ – 2 or 3⁶ – 2. When in doubt, expand it out. So, (3 × 3 × 3 × 3 × 3 × 3) – 2 = 729 – 2 = 727.

Divide both sides by 8 to get z 4 = 12.Rather than finding the fourth root of 12, try plugging in 2 for z: 24 = 16, so z must be less than 2. Of course, z may be negative, but any negative number is also less than 2.

Try Plugging In. If a = –3, then Quantity A is (–3)² = 9 and Quantity B is 2(–3) = –6. Notice that Quantity A must always be positive because anything raised to an even power is positive. Quantity B must be negative because a positive times a negative is always negative.Thus, Quantity A must always be greater.

10

Here’s the ratio box you can set up. From the ratio with the granola and the actual ounces of granola provided you can solve for the multiplier, which is 2.

Multiplying vertically, the number of peanuts is 18.You have 18 = x + 8, so x = 10.

Plug in your own numbers for c and h. Let’s say Elier can bake 14 cakes in 2 hours; this makes c = 14 and h = 2.That means he can bake 7 cakes per hour. At this rate, it will take him 111 hours to bake 777 cakes.Circle 111 as your target number. When you plug in your values, choices (A) and (D) are way too big.Choices (C) and (E) are way too small. Using your calculator, you can determine that choice (B) matches

As soon as you see variables in the answer choices, set up your scratch paper to Plug In. Start with x = 5, so it takes 1 minute to knit 1 row. Now make y = 2. A scarf 2 feet long means Mariko has to knit 200 rows, which will take 200 minutes; since the problem asks how many hours it will take, your target answer is \(\frac{200}{60}=3\frac{1}{3}\). Now plug your values into the answer choices; only choice (A) hits your target.Choices (C) and (E) are clearly too small, and choice (D) is a fraction, so you may not have to calculate all the choices

\(\frac{22}{9}\)

The common element between both proportions is b, so that’s what you’ll want to start with. However, the numerical value of b does not match from proportion to proportion, so you’ll essentially want to find a common multiple for both values of b.Both 4 and 6 are factors of 12, so use 12 as your common multiple. For the first proportion, you’ll need to double it in order to make b = 12. When you do so, a = 22. For the second proportion, you’ll need to triple it to make b = 12.Therefore, c = 9. Now that the two proportions have the same value for b, you know that a:c equals 22:9, which can be written as a fraction.

A,B, D, and F

For each choice, use a ratio box.The first part of each ratio represents 45 degrees. For choice (A), the multiplier will be 45 divided by 2, or 22.5.The ratio adds up to 8 (2 + 3 + 3), so check that 8 × 22.5 = 180. It does, so choice (A) works. For choice (B), based on 3 representing 45 degrees, the multiplier is 15.The ratio adds up to 12, and 12 × 15 = 180, so this choice works as well. Using this approach, choice (C) does not work:The multiplier is again 15, but 15 × 15 does not equal 180.Choice (D) works, with a multiplier of 5: 5 × 36 = 180. When you test the remaining two choices, neither one produces the 180 degrees you need for the triangle, so eliminate them.

It’s an algebra question with numbers for answer choices, so set up your scratch paper to plug in the answers.The answers represent the number of messages Keith receives from Juan, so label them K, or something similar, and give yourself columns for L, which is K ÷ 3, and M, which is 4.5 × L. Start with choice (C). If K = 16, then L is a fraction; since you can send a fractional message, eliminate choice (C)—and go ahead and eliminate choice (E), since it’s also not divisible by 3. Next, try choice (B), since it’s the middle of the remaining 3 answer choices. If K = 12, then L = 4 and M = 18.That’s the correct number of messages for Missy, so choice (B) is correct.

20

Jenny must complete 3000 gear shafts in 10 hours, which is a rate of 300 gear shafts per hour. Percent change is \(\left (\frac{difference}{original} \right )\times 100\). In this case, the difference is 50 and the original is 250, so the percent change is \(\left ( \frac{50}{250} \right )\).The question asks for percent increase, so be sure to enter 20, and not 0.2