**1**. The numbers

Statement #1:

Statement #2:

**2**. Given that

Statement #1:

Statement #2:

**3**. In the diagram above,

Statement #1:

Statement #2:

**4**.

(A)

(B)

(C)

(D)

(E)

Doing math involve both following procedures and recognizing patterns. Three important patterns for algebra on the QUANT are as follows:

**Pattern #1: The Difference of Two Squares**

**Pattern #2: The Squares of a Sum**

**Pattern #3: The Squares of a Difference**

For Quant success, you need to know these patterns cold. You need to know them as well as you know your own phone number or address. The test will throw question after question at you in which you simply will be expected to recognize these patterns. In such a question, if you recognize the relevant formula, it will enormously simplify the problem. If you don’t recognize the relevant formula, you are likely to be stymied by such a question.

You might think I would say: memorize them. Instead, I will ask you to remember them. What’s the difference? Memorization implies a rote process, simply trying to stuff an isolated and disconnected factoid into your head. By contrast, you strengthen you capacity to remember a math formula when you understand all the logic that underlies it.

Here, the logic behind these formulas is the logic of FOILing and factoring. You should review those patterns until you can follow each both ways - until you can FOIL the product out, or factor it back into components. If you can do that, you really understand these, and are much more likely to remember them in an integrated way.

If these patterns are relatively new to you, you may want to revisit the problems at the top with the list handy: see if you can reason your way through them, before reading the explanations below.

1. Let

Statement #1:

From this statement alone, we cannot calculate **insufficient**.

Statement #2:

From this statement alone, we cannot calculate **insufficient**.

2. The prompt tells us that

Statement #1:

Obvious, by itself, this tells us zilch about **insufficient**.

Now, this may be a pattern-recognition stretch for some folks, but this is simply the “Square of a Sum” pattern. It may be clearer if we re-write it like this:

This is now the “Square of a Sum” pattern, with

All we have to do is take a square root. Normally, we would have to consider both the positive and the negative square root, but since the prompt guarantees that

This statement allows us to determine the unique value of **sufficient**.

Answer = B

3. To find the area of the circle, we need to use Archimedes’ formula,

Statement #1:

A major pattern-matching hit! This, as written, is the “Square of a Difference” pattern.

In fact, this statement already gives us **sufficient**.

Statement #2:

We need **insufficient**.

**Answer = A**

4. A tricky one. First of all, notice that the shaded area, quite literally and visually, is the difference of two square - Area =

Area

Well, if a rectangle had this same area, and it had a length of

**Answer = D**