Week 6 · STAY STRUCTURED · 15–20 hrs

Sets & sequences, RC purpose & Mock 2

Overlapping sets and the double matrix

Quantitative

GMAT Focus sets questions almost always reduce to two binary attributes plus a total — which is why the 2×2 grid beats a Venn diagram. Set up rows for one attribute, columns for the other, add a total row and a total column, and every cell becomes arithmetic. Venn diagrams earn their place only when three attributes are in play.

The question rarely says "sets". It says employees who passed certification and speak Spanish, patients given the drug and reporting side effects, respondents who read the report or attended the briefing. Translate "or" to the union, "and" to the intersection, "only" to a single cell, "neither" to the bottom-right corner. Given percentages with no counts, set the total to 100.

Three decisions separate the credited answer from the tempting one:

• Whether the stated total includes the "neither" group. "Of 200 surveyed" usually does; "of the 180 who answered" does not.
• Whether "or" is inclusive. In counts it is, unless the question says "but not both" — then you want the union minus the intersection.
• With three attributes, "exactly two" is not the sum of pairwise overlaps. It is that sum minus $3\mathrm{\mid }A\cap B\cap C\mathrm{\mid }$, since each triple-overlap member sits in all three pairwise cells.

The mechanical loss: filling the "only A" cell with A's total instead of subtracting the overlap, then carrying the error down the totals column. The grid stays self-consistent, so it survives a sanity check.

Keep in memory: $\mathrm{\mid }A\cup B\mathrm{\mid }=\mathrm{\mid }A\mathrm{\mid }+\mathrm{\mid }B\mathrm{\mid }-\mathrm{\mid }A\cap B\mathrm{\mid }$, and when a neither group exists, $\mathrm{\mid }A\cup B\mathrm{\mid }=\text{Total}-\mathrm{\mid }\text{Neither}\mathrm{\mid }$.

Sequences and series

Quantitative

On GMAT Focus, sequences are rarely named. The section tests two moves: turning a definition into a specific term, and summing evenly spaced numbers. Most items arrive as word problems — weekly savings that rise by a fixed amount, a population that doubles, a repeating alphabet or digit pattern, "how many multiples of 6 lie between 200 and 500".

Three decisions separate the credited answer from the tempting one:

• Term, sum, or count? The distractors are built from the other two. Computing $a_n$ when the question asked for $S_n$ is the most common trap on offer.
• Where does the index start? A definition like $a_n=a_{n-1}+3$ with $a_1$ given is 1-based; a "0th" term shifts every answer.
• Brute force or cycle? For recursive and repeating sequences, compute $a_1$ through $a_5$ or $a_6$, identify the period, then use $n<mrow><mi\; mathvariant="normal">m</mi><mi\; mathvariant="normal">o</mi><mi\; mathvariant="normal">d</mi></mrow>\text{period}$. Candidates who grind out terms run out of clock and drop a sign.

The mechanical loss is the count. Terms from $p$ to $q$ in steps of $d$: $(q-p)\mathrm{/}d+1$. The $+1$ is where points go. With the count, an evenly spaced sum is count × average, and the average is $(\text{first}+\text{last})\mathrm{/}2$ — valid only when consecutive terms differ by a constant.

For a quantity growing by a fixed percentage, $a_n=a_1{r}^{n-1}$. Not $r^n$. Both exponents will appear among the choices.

Reading Comprehension: primary purpose and structure

Verbal

The GMAT Focus does not ask what a passage says. It asks what the author is doing and how the parts are arranged. Two question families dominate: primary purpose ("The primary purpose of the passage is to...") and structure/function ("The author mentions X in order to...", "Which of the following best describes the organization..."). The subject—astronomy, art, economics—is bait.

Disguises: purpose questions offered as topic summaries. A choice that accurately states the subject but omits the author's stance—evaluate, reconcile, challenge, explain—is wrong. Structure answers often describe one paragraph's move as if it were the whole passage. The reverse also appears: a sweeping abstraction that ignores a crucial qualification.

Three decisions separate correct from tempting. (1) Scope: whole passage, not the most memorable paragraph. (2) Verb: what is the author doing to the material? (3) Stance: endorse, critique, or neutral? If a passage presents a debate and then resolves it, the purpose is usually to adjudicate, not to survey.

Strong candidates lose points mechanically by reading for content, then answering from memory. The fix: after each paragraph, note its function in the margin—"received view," "counterexample," "qualified conclusion." Answer from that skeleton, returning only to verify a contested choice.

Worth having in memory: $\text{primary purpose}=\text{subject}+\text{author’s action}+\text{scope}$. Condition: for argumentative passages, the action must be a stance verb, not "describe."

Multi-Source Reasoning

Data Insights

Multi-Source Reasoning hands you two or three tabs — usually a memo, a table or graph, and a third piece that looks like scenery. It tests triage, not reading speed. The real question is whether you can hold a claim in your head and know which tab can adjudicate it.

Map the tabs before you read the first question: one line each on what it uniquely contains. The third tab is rarely filler. It often sets scope (a policy that applies only above a stated order value) or supplies the join key — a product code, a region name — linking the other two. A definition buried in the prose tab quietly overrides a column heading in the table.

The disguises: a question using a term defined in a footnote; a comparison whose two numbers sit in different tabs; a qualifier column (such as pending) that invalidates a row you would otherwise count.

Two decisions separate right from wrong. First, name the source before you calculate — if lookup answers it, do not compute; most prompts need at most one operation. Second, verify each row of a select-one-per-row item independently; one wrong judgement loses the whole question, and the standard failure is stopping once two rows feel right.

Your mechanical leak: anchoring on Tab 1, then answering a Tab 3 question with Tab 1's numbers. Re-anchor per question, not per stimulus.

No formula worth memorising here, just claim + source = verdict. Of each statement ask: which tab could falsify this?

Mock 2: reading a mid-preparation mock

Exam skills

A mid-preparation mock is a measuring instrument with a sample size of one. The composite is a noisy reading; the answer log is the result. Read the log first, and deliberately delay reading the score until you have written down what the log says.

The thing worth extracting is where accuracy breaks inside each section. Accumulated time debt usually converts into three or four rushed questions in a row; find the question number where your first rushed answer occurs and write it down. That number is more actionable than any section score, and it moves in ways the score hides.

Two decisions carry most of the value. First, classify every miss as content (you did not know), process (you knew, chose badly) or clock (you knew, ran out of time). Content misses send you back to a topic; process and clock misses send you back to a rule, and mid-preparation mocks produce far more of the latter than people want to admit. Second, change strategy only on a pattern seen twice. One mock is an anecdote; the same collapse in two consecutive mocks is a fact.

The mechanical loss: reviewing only the questions you got wrong. Add the ones you got right slowly, and the ones you flagged as a guess. Those are latent misses, and they distort the accuracy picture you are about to base decisions on.

Review at least as long as you tested. For a $2.5$-hour mock, budget $2.5$ hours of review — otherwise you have bought a score, not a diagnosis.

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