Graduate Record Examinations (GRE) Quantitative Reasoning: Data Analysis and Test Strategy Syllabus

What does it mean for two events to be mutually exclusive (disjoint)?

They cannot occur at the same time: $P(A \cap B) = 0$. Therefore $P(A \cup B) = P(A) + P(B)$.

What is the conditional probability of $A$ given $B$?

$$P(A \mid B) = \frac{P(A \cap B)}{P(B)}, \quad P(B) \neq 0$$

What is the formula for the number of permutations of $n$ distinct objects taken $r$ at a time?

$$P(n,r) = \frac{n!}{(n-r)!}$$ Use permutations when order matters.

What is the formula for the number of combinations of $n$ distinct objects taken $r$ at a time?

$$C(n,r) = \binom{n}{r} = \frac{n!}{r!\,(n-r)!}$$ Use combinations when order does not matter.

What is the key difference between a permutation and a combination?

Permutations count arrangements where order matters; combinations count selections where order does not matter. Always $P(n,r) \geq C(n,r)$ since $P(n,r) = C(n,r)\cdot r!$.

What does $n!$ (n factorial) mean, and what is $0!$?

$n! = n \times (n-1) \times \cdots \times 2 \times 1$, the product of all positive integers up to $n$. By definition $0! = 1$.

What is the fundamental counting principle?

If one task can be done in $m$ ways and a second independent task in $n$ ways, the two together can be done in $m \times n$ ways. This extends to any number of stages by multiplication.

How do you count the number of distinguishable arrangements of $n$ objects when some are identical?

Divide $n!$ by the factorials of the counts of each repeated item: $$\frac{n!}{n_1!\,n_2!\cdots n_k!}$$

What is a set, and what does the empty set denote?

A set is a collection of distinct objects (elements). The empty set, written $\varnothing$ or $\{\}$, contains no elements.

What is the union of two sets versus the intersection?

The union $A \cup B$ contains all elements in $A$, in $B$, or in both. The intersection $A \cap B$ contains only elements in both $A$ and $B$.

State the inclusion-exclusion formula for the size of the union of two sets.

$$|A \cup B| = |A| + |B| - |A \cap B|$$ Subtracting the intersection corrects for double-counting the overlap.

In a Venn diagram with two overlapping circles, what does the overlapping (central) region represent?

The intersection $A \cap B$ — the elements that belong to both sets simultaneously.

What is the complement of a set $A$ within a universal set $U$?

The complement $A^{c}$ (or $A'$) consists of all elements of $U$ that are not in $A$. Thus $|A^{c}| = |U| - |A|$.

What is a subset, and how is it written?

$A$ is a subset of $B$, written $A \subseteq B$, if every element of $A$ is also in $B$. The empty set is a subset of every set.

For the inclusion-exclusion of three sets, what is $|A \cup B \cup C|$?

$$|A \cup B \cup C| = |A|+|B|+|C| - |A\cap B| - |A\cap C| - |B\cap C| + |A\cap B\cap C|$$

When reading a table on the GRE, what should you check before extracting any value?

Read the title, row and column headers, and especially the units and any footnotes (e.g., "in thousands," "percent"). Misreading units is the most common error.

On a pie/circle graph, how do you convert a sector's percentage into the corresponding central angle?

Multiply the percentage (as a fraction of the whole) by 360 degrees: $$\text{angle} = \frac{\text{part}}{\text{whole}} \times 360^{\circ}$$

In a GRE Data Interpretation set, how should you treat the data shared across the multiple questions?

All questions in the set refer to the same display(s). Read the graphs/tables carefully once, note units and scales, and reuse that understanding; answer each question independently since one wrong reading can affect several.

How do you compute the percent change between an old value and a new value?

$$\text{percent change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100\%$$ A positive result is an increase, a negative result is a decrease.

From a frequency table, how do you compute the mean of the data?

Multiply each value by its frequency, sum these products, and divide by the total frequency: $$\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$$

On a bar graph, why must you read the vertical axis scale carefully before comparing bars?

Axes may not start at zero or may use nonstandard increments, which can exaggerate or hide differences. Always read the actual numeric scale rather than judging by bar height alone.

How do you find what percent one quantity is of another from a data display?

$$\text{percent} = \frac{\text{part}}{\text{whole}} \times 100\%$$ Identify which value is the part and which is the whole (the base) from the labels.

On a GRE Quantitative Comparison question, what are the four fixed answer choices?

(A) Quantity A is greater; (B) Quantity B is greater; (C) The two quantities are equal; (D) The relationship cannot be determined from the information given. These never change.

In Quantitative Comparison, when is choice (D) correct?

When the relationship between the quantities can change depending on allowable values (e.g., different signs or ranges of a variable). If even one case gives a different ordering, the answer is (D). Note: (D) is impossible if both quantities are purely numeric.

What is an effective strategy for Quantitative Comparison problems with variables?

Plug in strategic test values — try positive, negative, zero, fractions, and extremes. You may also add, subtract, multiply, or divide both quantities by the same positive amount to simplify, just as with an inequality.

What rule about inequalities must you respect when simplifying both quantities in a Quantitative Comparison?

You may add or subtract anything from both sides, and multiply or divide both by the same positive number, but multiplying or dividing by a negative number reverses the comparison — and you usually do not know a variable's sign, so avoid it.

What is the difference between multiple-choice (select one) and multiple-choice (select one or more) on the GRE Quant section?

Select-one has exactly one correct answer marked with ovals. Select-one-or-more uses square checkboxes and may have one, several, or all options correct; you must select every correct choice and no incorrect ones for credit.

How should you enter answers in a Numeric Entry question, including fractions?

Type the number directly into the box (with a separate box for numerator and denominator if it is a fraction). Fractions need not be reduced. Follow any rounding instruction given; if none, enter the exact value. Include a negative sign when required.

What functions does the GRE on-screen calculator provide, and what is a key limitation?

It performs addition, subtraction, multiplication, division, square root, plus/minus, and has memory keys and a Transfer Display feature. It is a basic four-function-plus-square-root tool: no exponents beyond squaring via multiplication, no parentheses precedence beyond simple use, so manage order of operations yourself.

What does the "Transfer Display" button on the GRE calculator do, and when is it useful?

It transfers the calculator's displayed result directly into a Numeric Entry answer box, reducing transcription errors. It is available only for Numeric Entry questions that accept the answer format.

What are the key mechanics of the GRE Quantitative Reasoning section (timing, navigation, scoring adaptivity)?

It has two sections of roughly 27 minutes each. Within a section you can skip, flag (Mark/Review), and return to questions before time expires. The test is section-level adaptive: performance on the first Quant section affects the difficulty of the second. There is no penalty for wrong answers, so answer every question.