The minute you see variables, make your set-up. Start with happy numbers for p and q such as p = 1 and q = 2. Quantity A will equal 27 while Quantity B will equal 9.Cross off (B) and (C).Try some fractions such as p = ¹⁄₂ and q = ¹⁄₄. Quantity A will equal \(\frac{27}{64}\) while Quantity B will equal \(\frac{27}{64}\). Quantity A is still bigger. Use ZONEF and try some negative numbers such as p = –3 and q = –2. Quantity A will equal –125 and Quantity B will equal –35. –35 is bigger.Cross off choice (A).The answer is choice (D).

The minute you see variables, make your set-up. When you draw your shape, label the third angle of the triangle z. In general, when you have 2 angles of a triangle, go ahead and find the third angle, because it is likely to come in handy. For this problem, it might be easier to Plug In for angle z. When you have geometry on Quant Comp, you usually need to draw your shape in different ways and really exaggerate the differences. In this case, make z something really small, like 2. Quantity A will be 2 and Quantity B will also be 2.Eliminate choices (A) and (B). Now exaggerate the difference between possible triangles and make z a really large value, like 178. Quantity A will be 354 and Quantity B will be 178.Eliminate choice (C) and select choice (D).

The minute you see variables, make your set-up.The question here is what to plug in.You could start with any integer between 130 and 150.You are looking for the greatest factors, so you might as well start with the greatest integer which is 149.The largest factor of 149 is 149, which is odd. If you use 148, the largest factor is 148, but that is smaller than 149. If you use 147, the largest factor is 147, still smaller. 149 is the largest factor of the largest number in your set, so you are done.The answer is choice (A).

In the left triangle, you have x + x + 5y = 180, and in the right triangle, you have 2x + 2x + y = 180.Because both these sums equal 180, they must be equal to each other: x + x + 5y = 2x + 2x + y.This equation simplifies to become x = 2y, choice (A).

Variables in the question and the answer choices tell you this is a Plug In question.Try plugging in x = 2.The diagonal of this rectangle makes a 30-60-90 triangle. We know this because we have a right triangle with a side of x and another side of 2x.The hypotenuse therefore must be x√3.d = 2√3 .The area of the rectangle is 8.This is your target number. Write it down and circle it. Now check all of the answer choices. Anywhere you see a d, plug in 2√3. Only answer choice (D) works.

Variables in the question and the answer choices tell you this is a Plug In question. Since it represents a circumference, pick something that makes it easy to find the radius.Try x = 8π.That means that the radius of the circle is 4 and the area is 16π.This is your target number. Write it down and circle it. Now check all of the answer choices. Anywhere you see an x, plug in 8π.You’re looking for 16π. Only choice (A) works.

Plug in 100 for z: now, Wanda’s number is 50 and 20 percent of her number is 10. Now plug in 100 for z in the answer choices; only choice (D) hits your target answer of 10.

First, try plugging in some easy numbers for the length and width that obey the restrictions, such as 6 and 10.The area of the rectangle is 60, so the two columns are equal.Eliminate choices (A) and (B). Now try plugging in different numbers, such as 12 and 20.This time, column A is greater, so the answer must be choice (D).

The minute you see variables, make your set-up. Plug in some nice easy numbers to start.Try w = 1, x = −2, and y = 1. Quantity A works out to and Quantity B works out to ¹⁄₂.Eliminate choices (A) and (C).You’ve been given a rule for what you can plug in for x and y, but no rules for w.The question addresses positive versus negative numbers, so plug in a negative number for w.Try w = −1, x = −2, and y = 4. When you do this Quantity A is −¹⁄₂ and Quantity B is −4. −¹⁄₂ is bigger, so eliminate choice (B).The answer is choice (D).

The minute you see variables, make your set-up.The first thing to do is to clean up the expression and isolate the variable. When you do this, you end up with ⁴⁄₉ > y. Now you can start Plugging In.Try something nice and easy for y. Quantity B is 2, so start by Plugging In 2, making Quantity A 1⁷⁄₈, while Quantity B is 2.Eliminate choices (A) and (C).Can you beat 2 in Quantity A? Plug in something larger than 2 for y, but remember that you can’t go above ⁹⁄₄.Try ¹⁷⁄₈.This gets you closer but doesn’t close the gap. How about ? Closer still, but you’re still running a losing race. As long as you can only use of y, you’ll never make it back to 2, so select choice (B).