Intro to Quantitative Section

Question 1

What do Quantitative Comparison (QC) questions ask you to do?

Answer 1

They present you with two quantities – Quantity A and Quantity B – and you must determine the relationship.

Question 2

What are the important things to consider with QC questions?

Answer 2

• You only need to determine the relationship
• You want to do as little calculation as possible
• Avoid the Black Swan trap
• Record all important info given (i.e., don’t neglect the stem)

Question 3

What are the ways of approaching QC questions?

Answer 3

1. Restate & simplify your stem info
   (e.g., x^2 = 49? x is 7 or -7)
   or
   Simplify first, then test strategic numbers
   (e.g., FOIL (x+y)^2 and (x-y)^2 before comparing)
2. Use the Inequality Technique
   (We can always use a > or < between A or B)
3. Substitute given info into the quantities if necessary
   (If x=2y, and comparing (A) x and (B) y, you can set as 2y > y and solve)

Question 4

What are the 5 types of strategic numbers we can test QC questions with?

Answer 4

1. Positive integers
2. Positive proper fractions
3. Zero
4. Negative proper fractions
5. Negative integers

Question 5

True or false:
If Quantity A and Quantity B are unique values, we will never have an answer of D, “the relationship cannot be determined”

Answer 5

True.
There is always a relationship between two unique values.

Question 6

What is the AC Method for reverse FOILing when our leading coefficient is not 1?
e.g., 6x^2 + 7x + 2

Answer 6

1. Find what multiplies to the first and last coefficients.
   e.g., 6 x 2 = 12
2. Find what multiplies to this product, but sums to the term in the middle.
   e.g., 3x + 4x = 7x
3. Break out the middle terms, then separate them by grouping.
   e.g., 6x^2 + 3x + 4x + 2
   –> 3x(2x + 1) + 2 (2x + 1)
4. Break them out by factors.
   e.g., (3x + 2)(2x + 1)

Question 7

What is the Korean method for reverse FOILing binomials when the leading coefficient is not 1?
e.g., 6x^2 - 5x -4

Answer 7

1. Multiply the first term by the last term and replace the last term with this product.
   e.g., 6 x (-4) = -24, so 6x^2 - 5x - 4 becomes x^2 - 5x - 24
2. Solve as you would a normal binomial.
   e.g., x^2 - 5x - 24 FOILs to (x - 8)(x + 3)
3. Divide the second term of each expression by the original leading coefficient, then simplify.
   e.g., (x - (8/6)) (x + (3/6))
   –> (x - (4/3)) (x + (1/2))
4. Multiply each x by the respective denominators, which removes the denominators.
   e.g., (3x - 4) (2x + 1)