Solve this one by Plugging In values for a and b.Try making a = ¹⁄₄ and b = ¹⁄₂ :The value in Quantity B is now. Quantity A is greater, so eliminate choices (B) and (C).Because b is bigger than a, (a − b) will always be negative, so any other allowable values for a and b will yield the same results; thus, Quantity A is greater.

To solve this one, plug in for a and b, but don’t forget your restrictions:Try a = 1 and b = −2. In Quantity A, the sum is 1 + (−2) = −1, and in Quantity B the difference is 1 − (−2) = 3; Quantity B is greater, so eliminate choices (A) and (C). Now try other allowable values for a and b; any acceptable value gives the same outcome, so select choice (B).

To solve this question, Plug In a value for the race’s distance. Here, you want a number that is divisible by 3, 4, 8, and 10, such as 120. If the race is 120 miles, then since Jan completes ³⁄₄ × 120 = 90 miles in 2 hours, and her speed is 45 miles per hour. Now for Marko’s rate. Since Jan’s rate is 45 miles per hour, and the race is 120 miles, you can set up a proportion to find her time: \(\frac{45 miles}{1 hour}=\frac{\frac{90}{100}\times 120 mile}{xhour}or\frac{45miles}{1hour}=\frac{108miles}{xhour}\); x = ¹²⁄₅, so it takes Jan ¹²⁄₅ hours to complete of the race. Marko thus completes ²⁄₃ × 120= 80 miles in ⁵⁄₈ × ¹²⁄₅ = ³⁄₂ hours.This means that Marko’s rate, expressed as hours, is \(\frac{80}{\frac{3}{2}}=\frac{80}{1}\times \frac{2}{3}=\frac{160}{3}=53.\bar{33}\) miles per hour.

Marko has the higher rate, so the correct answer is choice (B).

The minute you see variables, make your set-up. Start with something easy but interesting with exponents, such as 1. When a = 1, Quantity A is 3 and Quantity B is something much larger than 3. Don’t take the time to bother calculating; just eliminate choices (A) and (C). When you try another basic integer, you get the same result. Fractions less than 1 get smaller when multiplied, so try . Quantity B is still bigger.Check ZONEF to see if there is anything you haven’t tried yet.There is, so plug in 0 for a. In this case, both quantities are equal.Eliminate choice (B) and select choice (D).

Algebraically, both a and b + c are equal to 180 minus the unnamed angle in the triangle. Like most relationships that involve both algebra and geometry, though, this is most easily seen by Plugging In values for the angles. If a = 110, for instance, the unnamed angle in the triangle must be 70°.You have no specific information for b or c, so plug in 60 for b: c must now be 50, and because a equals the sum of b and c, select choice (C). Plugging In numbers may also make it easier to notice that choices (B) and (E) are identical and, therefore, can be eliminated.

It’s a little difficult to Plug In on this one because you have to pick numbers that make 7(q − r) = ¹⁰⁄₇ true. First divide both sides by 7 to find q − r = ¹⁰⁄₇.Then add r to both sides to find q = ¹⁰⁄₇ + r or q = r + ¹⁰⁄₇.

The minute you see variables, make your set-up. Start with something easy like x = 2 and y = 1. Quantity A is bigger, so eliminate choices (B) and (C). Use ZONEF to figure out what to plug in next. Zero is out, you tried 1, and negative numbers are out.Try extremely large numbers, such as 100 and 101. When you do this Quantity B becomes bigger, so the answer is choice (D).You could also have used a non-integer such as 1.1.

The minute you see variables, make your set-up.This problem looks suspiciously simple.Clearly x = 3 and y = 4.Eliminate choices (A) and (C).Your set-up, however, tells you to Plug In more than once. Is there anything else you could plug in? Yes, the square root of 16 could be either 4 or −4. Go through the motions to make sure you don’t miss any options.Because y could be negative, eliminate choice (B), leaving you with choice (D) for the answer.

The minute you see variables, make your set-up.You’re dealing with exponents, so try starting with 1. When a = 1, Quantity A is equal to 1 and Quantity B is one.Both quantities are equal so eliminate choices (A) and (B). Now see if you can screw it up by Plugging In a fraction. If you plug in ¹⁄₂, Quantity A will still equal 1.You’re not allowed to plug in 0, so try a regular old integer to see what it does. If you plug in 4 you end up with ¹⁄₄ for Quantity A. Since B is now greater than Quantity A, you have inconsistent results and must choose (D).

The minute you see variables, make your set-up. Plug in something happy for y to start with, such as 2. Quantity A is 4 × 6 = 24 and Quantity B is 16(2) – 4 = 28. Quantity B is greater, so eliminate choices (A) and (C) on your scratch paper. Use ZONEF to try fractions, large numbers, and one. No matter what you plug in, choice (B) is greater.The answer is choice (B).