Two-Part Analysis: two linked answers from one problem

What the question type asks

Two-Part Analysis is one of the five question types GMAC lists for Data Insights. As the name says, one problem has two parts to answer, and this lesson practises both numerical and verbal problems of that shape. GMAC states that all parts must be correct to score on Data Insights questions with several parts, so getting one part right earns nothing on its own.

The checks on this page are single-answer multiple choice: each option is a pair, written as (first part, second part), and you pick the pair that is right in both places. That keeps the core skill: a pair that satisfies one condition but not the other is wrong.

First question: are the parts linked?

Every two-part problem is one of two kinds.

• Dependent parts. The two answers are tied together: two unknowns in one situation (how many of each ticket), or a choice in one part that limits the other (workers and days for a fixed job). You usually need both conditions to find either answer.
• Independent parts. Two separate questions share a setting: which finding strengthens a claim and which weakens it, or the maximum and the minimum of a quantity. Each part has its own test.

Decide which kind you face before you start; it tells you whether to solve together or one at a time.

Dependent parts: set up, solve, check

For two unknowns, write one equation per fact.

$$\text{count: } a + c = N \qquad \text{value: } p_a a + p_c c = V$$

A fast way to solve the pair is to imagine every item at the cheaper price: $p_c N$. The shortfall $V - p_c N$ is made up by the items at the dearer price, each adding $p_a - p_c$. So

$$a = \frac{V - p_c N}{p_a - p_c}$$

and $c = N - a$. Then check both equations with the numbers. The check takes ten seconds and catches the commonest slip in this question type: swapping which number belongs to which part.

Constraints and trade-offs

Some dependent problems are about trade-offs: more workers means fewer days, a higher price means fewer buyers. The parts are linked by a fixed product or sum, and extra limits (no more than so many, whole numbers only) cut down the choices. Work from the tightest constraint: it often leaves only one or two candidates, and the other condition then settles the pair.

Independent parts: one test per part

When the parts are separate questions, treat them as two small questions. For a verbal problem such as "which finding would most strengthen the claim, and which would most weaken it", state the claim exactly first, including what causes what. Then run each finding through the strengthen test and the weaken test separately. A finding can be irrelevant to both; do not force every choice into one of the two roles.

Things to watch in verbal two-part problems:

• Causal claims ("X explains Y") are weakened by evidence that Y happened without X, or by another cause that fits better. They are strengthened by evidence that Y changed only where or when X did.
• Swapped pairs. The same two findings may appear in both orders. Decide the role of each finding before you read the pairs.

Test the pair, not the halves

Wrong pairs can be built from plausible halves. A pair that gets the first part right and the second part wrong looks right if you check only the first part. Before you commit, substitute the whole pair into every condition of the problem.

Time

A two-part problem has more to read than a single question, but often less to compute once it is set up. Spend the first moments on the setup: what are the two parts, how are they linked, and what condition must each satisfy. If you can write the two equations or the two tests in a line each, the rest is quick.