GRE Vocabulary and Quantitative Reasoning Fundamentals

Exam Tip: When tackling sentence equivalence questions, look for the "charge" of the word. Is the missing word positive, negative, or neutral? This can help you eliminate half of the options immediately.

Frequency, Scope, and Change

The exam frequently uses words to describe how widespread a phenomenon is. Ubiquitous, pervasive, and rife all suggest that something is widespread or prevalent. If something is scarce, it is characterized by a paucity.

Finally, understand the stability of a concept. An immutable fact is unchangeable, while a provisional arrangement is temporary. If a situation deviates from the norm, it is anomalous.

Quantitative Reasoning: Geometry and Area

Mathematical reasoning on the GRE often requires you to recall geometric properties quickly to solve for unknown variables.

Calculating Area

Area measures the space inside a two-dimensional shape. You must be comfortable with several different formulas:

• Rectangle: The area is the product of length ($L$) and width ($W$). $A = L \times W$
• Triangle: The area is half of the base ($B$) multiplied by the height ($H$). $A = \frac{1}{2} B \times H$
• Square: Since all sides ($s$) are equal, the area is the side squared. $A = s^2$

For more complex shapes like circles, remember that the area is related to the radius ($r$): $A = \pi r^2$

Percentage Changes and Proportions

Percentage problems are a staple of the GRE Quantitative section. The key is to distinguish between an increase and a decrease, as the denominator (the base) changes depending on the direction of the movement.

Percentage Increase and Decrease

To find the percentage increase, you subtract the original amount from the new amount, divide by the original amount, and multiply by 100: $\text{Percentage Increase} = \frac{\text{new amount} - \text{original amount}}{\text{original amount}} \times 100$

To find the percentage decrease, you subtract the new amount from the original amount, divide by the original amount, and multiply by 100: $\text{Percentage Decrease} = \frac{\text{original amount} - \text{new amount}}{\text{original amount}} \times 100$

Common Pitfall: Always divide by the original amount, not the new amount. This is the most frequent error students make in percentage change problems.

Probability, Motion, and Logic

The final pillar of GRE math involves understanding the likelihood of events and the relationship between rate, time, and distance.

Probability and Distance

The probability of an event is the ratio of the number of successful outcomes to the total number of possible outcomes: $P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total possible outcomes}}$

In motion problems, you will often need to solve for distance ($d$). The relationship between distance, rate ($r$), and time ($t$) is expressed as: $d = r \times t$

By mastering these vocabulary nuances and mathematical foundations, you will build the versatility required to tackle the diverse question types presented on the GRE.