Week 7 · DECIDE YOUR APPROACH · 10–15 hrs

Probability, RC details & MSR

Combinatorics: counting without listing

Quantitative

GMAT Focus rarely asks 'how many ways'. It hides counting inside a scenario — seating, codes, committees, grid paths, schedules — and expects you to name the structure and compute. The topic contains factorials and binomial coefficients; the exam tests whether you can decide which structure applies before calculating.

Three decisions separate the correct count from the tempting one:

• Order: would swapping two chosen items create a new outcome? If yes, it is a permutation; if no, a combination. A committee with named roles is ordered; a committee without roles is not.
• Distinctness: are the objects distinct? Repeated letters or identical items mean you must divide by the factorial of each repeat. This is where careful candidates double-count.
• Restriction: 'at least one' almost always means total minus none. 'Not adjacent' means arrange the free items, then place the restricted ones in the gaps.

The formula worth carrying: $\left(\genfrac{}{}{0px}{}{n}{k}\right)=\frac{n!}{k!(n-k)!}$, valid when order is irrelevant, the $n$ objects are distinct, and no object is reused. For ordered selections, multiply by $k!$.

The mechanical way strong candidates lose points is listing: they build cases by hand under time pressure, or they set up overlapping cases and count an outcome twice. Decide the structure first; list only to verify a small residual.

Probability

Quantitative

GMAT Focus probability is rarely a formula test. It tests whether you pick the smallest sample space before computing — and the exam rewards deciding the approach first: complement, symmetry, a two-way table, sequential multiplication, in that order of preference.

The giveaways for complement are at least one, not all, some. $P(\text{at least one})=1-P(\text{none})$, and the 'none' product needs independence — verify it rather than assume it. The giveaways for a table are of those who, given that, any two-way breakdown. Conditionals are almost always cheaper as a restricted denominator than as $P(A\cap B)\mathrm{/}P(B)$.

Two decisions separate the answer from the trap. First: are the outcomes you are counting equally likely? $\{HH,HT,TT\}$ is not a valid sample space; $\{HH,HT,TH,TT\}$ is. Second: did removal change the denominator? Without replacement, re-check every later fraction — but first look for symmetry, because the probability that the third card drawn is a heart is $13\mathrm{/}52$: positions are exchangeable. Strong candidates lose points here by grinding out a sequential product that symmetry settles in one line.

Keep $P(A\cup B)=P(A)+P(B)-P(A\cap B)$; subtract the overlap unless the events are genuinely disjoint.

Reading Comprehension: detail and inference

Verbal

On GMAT Focus, detail questions are location tasks with a paraphrase attached, not comprehension tasks. The stem names something in the passage; one line settles it. Read that line completely — the answer usually turns on the qualifier you skimmed (usually, until the 1890s, except in France) rather than on the main clause.

Inference stems ("suggests", "would most likely agree with") are not licences to reason freely. The credited answer is forced by the text, almost always by a single sentence and occasionally by two adjacent ones. Anything you know about the subject from outside the passage exists in the options as a trap.

Three decisions separate correct from tempting:

• Scope. If the option introduces a cause, mechanism, or comparison the passage never draws, it fails however sensible it sounds.
• Degree. Only, all, never, primary and the first need explicit warrant; hedged options usually match hedged prose.
• Subject. The classic trap is accurate about the wrong entity, period, or group.

Strong candidates lose points mechanically in two ways: answering from the first read and then defending the pick from memory, and re-reading the whole passage when the stem's keyword was a single searchable phrase.

Worth memorising: for a "must be true" inference, negate the candidate answer — if the passage survives the negation, the answer is unsupported. That test does not apply to "suggests" stems, where the bar is merely consistency with the author's stated attitude.

Multi-Source Reasoning: synthesising across tabs

Data Insights

MSR hands you two to four tabs — typically a prose scenario, a table, and a chart or second table — and either three statements to classify or one question whose options each need a different cross-tab join. The tabs are deliberately insufficient individually. Every answer lives at an intersection.

The disguise is that nothing says "combine". A statement reads like a plain fact check — "Lyon exceeded its 2021 quota" — but quota is defined in the prose tab, output sits in the table, and the year must be filtered in both. Work from a single tab and you will still find a number that appears to settle the statement. That is the trap.

Three decisions separate the correct answer from the tempting one:

1. Which tabs does the stem name or imply? Read the stem first, then read only those tabs.
2. What is the join key — the entity, period, or category that must match across tabs?
3. Which tab has authority? A prose definition ("net revenue is stated after returns") overrides a column header you would otherwise read at face value.

The mechanical loss for strong candidates: they read all tabs thoroughly in order, then answer from whichever tab is freshest in memory. Thorough reading is not synthesis. Before computing, you should be able to say in one clause, "this statement needs tabs 1 and 3".

Worth keeping: where tabs conflict, the prose tab governs unless the question says otherwise.

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