GMAT Integrated Reasoning Syllabus

On a scatterplot, what does a positive correlation between two variables look like?

Points trending upward from lower-left to upper-right, so that as the $x$-variable increases the $y$-variable tends to increase as well.

On a scatterplot, what does a negative correlation between two variables look like?

Points trending downward from upper-left to lower-right, so that as the $x$-variable increases the $y$-variable tends to decrease.

What does the 'line of best fit' (trend line) on a scatterplot represent?

The straight line that best approximates the overall relationship between the two variables, minimizing the vertical distances from points to the line; it is used to estimate and predict values.

For a trend line written as $y = mx + b$, what do the slope $m$ and intercept $b$ tell you?

$m$ is the rate of change of $y$ per unit increase in $x$; $b$ is the predicted value of $y$ when $x = 0$.

How do you compute the slope of a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ on a graph?

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

On a line graph, how do you identify the interval of greatest increase?

Find the segment with the steepest positive slope (largest upward change in $y$ over its $x$-interval).

What does each slice of a pie chart represent, and how large is a slice for a category with fraction $f$ of the total?

Each slice represents a category's share of the whole; its central angle is $f \times 360^{\circ}$, and its percentage is $f \times 100\%$.

On a bubble chart, what three variables can a single bubble encode?

Its $x$-position, its $y$-position, and its size (area/diameter), which represents a third quantitative variable.

When drawing a conclusion from visual data, why must you distinguish correlation from causation?

A graph can show that two variables move together (correlation), but that alone does not prove one causes the other; IR answers must not assume causation without support.

When a Graphics Interpretation drop-down asks you to estimate a value between gridlines, what technique should you use?

Interpolate: read the position proportionally between the two nearest labeled gridlines using the known scale.

What is the structure of a Two-Part Analysis question in the GMAT IR section?

A prompt followed by a table with two columns (one per part) and one shared list of answer options; you select exactly one option in each column.

In Two-Part Analysis, can the same answer option be selected for both columns?

Yes—unless the prompt states otherwise, a single option may satisfy both parts, so each column must be evaluated independently.

What is a common relationship tested in Two-Part Analysis involving two quantities that must satisfy one equation?

Selecting two values (e.g., $x$ and $y$) that jointly satisfy a given constraint such as $x + y = k$ or a ratio; each column supplies one of the two quantities.

In a Two-Part Analysis problem asking for a maximum and a minimum value, what is the efficient approach?

Evaluate the answer options against the constraints to find the largest option that still satisfies them (max) and the smallest that does (min), testing candidates rather than solving blindly.

What is the general formula for the relationship 'quantity = rate × time', frequently used in IR two-part and table problems?

$$D = r \times t$$ where $D$ is the amount/distance, $r$ the rate, and $t$ the time.

How is combined work rate computed when two agents work together at rates $r_1$ and $r_2$?

Rates add: $$r_{\text{total}} = r_1 + r_2$$ so time to complete one job together is $\frac{1}{r_1 + r_2}$.

What does the weighted average formula look like when combining groups with sizes $n_1, n_2$ and means $\bar{x}_1, \bar{x}_2$?

$$\bar{x} = \frac{n_1 \bar{x}_1 + n_2 \bar{x}_2}{n_1 + n_2}$$

In IR problems, how do you convert a ratio $a : b$ into the fraction of the whole represented by part $a$?

$$\frac{a}{a+b}$$

What is the compound interest formula that may appear in IR table or two-part finance problems?

$$A = P\left(1 + \frac{r}{n}\right)^{nt}$$ where $P$ is principal, $r$ annual rate, $n$ compoundings per year, $t$ years.

What is the simple interest formula used in IR quantitative reasoning?

$$I = P \cdot r \cdot t$$ where $I$ is interest, $P$ principal, $r$ the rate per period, and $t$ the number of periods.

When an IR statement uses the word 'must be true,' what standard of proof does the correct answer require?

The statement has to be guaranteed by the given data in every case; a single counterexample makes it false. 'Could be true' only requires one possible case.

How should you treat a statement in Multi-Source Reasoning that is supported by one source but contradicted by another?

Reconcile both sources; if they genuinely conflict on the point, the statement cannot be established as true, so it is not a valid inference.

What is the difference between 'inference' questions and 'apply the data' questions in IR?

Inference questions ask what logically follows from the given information; apply-the-data questions ask you to use the information to compute or decide a specific new result.

In Graphics Interpretation, how do you find the value of $y$ predicted by a trend line for a given $x$?

Locate $x$ on the horizontal axis, move vertically to the trend line, then read horizontally to the $y$-axis; or substitute $x$ into $y = mx + b$.

When comparing two quantities in IR, what does it mean for their relationship to be 'directly proportional'?

They satisfy $y = kx$ for a constant $k$, so their ratio $\frac{y}{x}$ is constant and one doubles when the other doubles.

When comparing two quantities in IR, what characterizes an 'inversely proportional' relationship?

They satisfy $y = \frac{k}{x}$ (equivalently $xy = k$), so their product is constant and one halves when the other doubles.

What is the recommended order for tackling IR question parts to manage the 30-minute time limit?

Read the question stem first, identify what is asked, gather only relevant data, and answer; if a question is too time-consuming, make a best estimate and move on since there is no partial credit to protect.

In decision-making IR problems, how do you choose the best option when given a criterion to optimize (e.g., lowest cost)?

Compute the target metric for each candidate option under the stated constraints, then select the option with the optimal (minimum or maximum) value that still satisfies all requirements.

When a Multi-Source Reasoning tab gives a formula or rule, how should it be used with data from another tab?

Apply the rule/formula from one tab to the specific values found in another tab—combining sources—to compute the answer; neither tab alone is sufficient.

Why is estimation often preferable to exact calculation in the IR section?

IR answer choices and drop-downs are usually spaced far enough apart that a rough estimate identifies the correct choice, saving time given the tight $2.5$-minute-per-question pace.