Week 5 · STAY ORGANIZED · 10–15 hrs

Work & rates, RC foundations & tables

Work and rate

Quantitative

Work-rate questions on GMAT Focus are rarely about multiplying rates. They test one habit: rewrite every participant as output per unit time, then add. The rest is bookkeeping.

The stem seldom says "rate". It says a pump fills a tank, a machine stamps parts, a drain leaks. Negative rates are ordinary — a leak is just a rate with a minus sign, and the answer turns on whether you kept that sign.

Two decisions separate correct from almost-correct. First, what counts as one job. If the stem gives counts (widgets, pages, litres), write $W=rt$ and keep the count as $W$. If it gives only times, choose $W$ deliberately — the LCM of those times makes every rate a whole number. Second, the inversion: "A is twice as fast as B" is a claim about rates, so $t_A=t_B\mathrm{/}2$. Rate and time pull in opposite directions, and carrying the 2 straight across into the times is the most common error on this topic.

For simultaneous work, $\frac{1}{t_{\text{together}}}=\frac{1}{t_A}+\frac{1}{t_B}$, valid only while both actually work. Combined time is never the mean of the individual times: for three hours and five hours it is $15\mathrm{/}8$.

The mechanical loss is dropping the reciprocal — computing a combined rate correctly, then offering that rate as the answer to a question that asked for time. Under pressure it goes unnoticed.

When someone joins or leaves mid-job, split the timeline at that point. Work done in each phase adds; average rates do not.

Speed, distance and time

Quantitative

GMAT Focus rarely asks for a bare $d=rt$. It asks you to hold two or three rates in one consistent frame, and the whole question turns on which quantity is held fixed. Distance fixed across legs gives a harmonic average; time fixed gives an arithmetic one. The exam sets up the first and punishes the second.

The disguise is always a story — two cyclists, a train clearing a platform, a tailwind, a return journey. Nothing says "average speed". Your job is to build the table (distance, rate, time; one row per leg; every unit identical) before writing any equation. That organisation is the topic.

Three decisions separate the answer from the trap. First, average speed is $\frac{\text{total distance}}{\text{total time}}$, never the mean of the speeds; for equal distances at $a$ and $b$ it is $\frac{2ab}{a+b}$, and that shortcut only holds when the distances are equal. Second, relative speed is $a+b$ for opposing motion and $a-b$ for chasing. Third, convert before combining: $1\text{ km/h}=\frac{5}{18}\text{ m/s}$.

The mechanical loss is splitting time evenly when the problem split distance evenly, or the reverse. Assign the faster leg the smaller time explicitly, then check the answer sits between the two speeds.

Mixtures and concentration

Quantitative

On GMAT Focus, mixtures are weighted-average questions in costume. The exam will not ask for a chemistry idea; it gives you two stocks at different concentrations and asks for the blend, the amount to add, or the fraction to replace. This is bookkeeping, and the week's theme applies: keep a ledger.

Track solute in absolute units. Percentages don't add; amounts do. Write solute-in + solute-added = solute-final, with volumes alongside, before computing. Final volume is not automatically initial plus added — removals and evaporation shrink it.

Three decisions decide most of these:

• Never average the two concentrations unless the volumes are equal. The unweighted mean is the standard trap.
• In replacement, the portion removed carries the current concentration, and each cycle multiplies the remaining solute by the same factor.
• "Add water" and "evaporate" both leave solute fixed — resist recomputing it.

Formulas: blend concentration is $\frac{V_1{c}_1+V_2{c}_2}{V_1+V_2}$. For a target $c$ between $c_1$ and $c_2$, alligation gives amounts in ratio $V_1:V_2=(c_2-c):(c-c_1)$. After $n$ replacements of volume $x$ from total $V$: $c_n=c_0(1-x\mathrm{/}V{)}^n$ — needs full mixing and solvent-only replacement.

Disguises: alloys, fuel blends, diluting juice, draining a tank of solution, and the "average percentage across two groups" question.

The mechanical way strong candidates lose points: they track volume through a removal but not solute, so they divide the wrong quantity; or they apply the replacement factor once rather than compounding; or they reverse the alligation ratio.

Reading Comprehension: mapping a passage

Verbal

GMAT Focus RC is a location test, not a memory test. Your notes exist to tell you where to look and who is speaking — not what the passage says.

Map for function, not content. For each paragraph, write a few words naming its job: sets up a puzzle, states the orthodox view, offers evidence, concedes, rebuts. Add one marker for the author's stance verb (argues, concedes, merely notes): a passage that reports a theory and one that endorses it look identical until a question asks what the author would accept.

Disguises: "The author implies" and "It can be inferred" name no line, so your map is the only pointer. "According to the passage" questions do name a line, and the trap is answering from your gist instead of rereading that sentence. Watch choices that are true in the world but absent from the text, and choices that quote a view the author cites only to reject.

Two decisions separate answers: whether the claim is the author's or a reported party's, and whether the question's scope is the whole passage or one sentence. A primary-purpose answer must account for every paragraph; a detail answer needs one sentence.

Keep this rule in memory: hinge words (however, therefore, moreover) mark a paragraph's function, and every paragraph gets exactly one label.

The mechanical loss is over-mapping — paraphrasing whole sentences — which burns the time you needed to reread the single sentence that settles the question.

Table Analysis and sorting

Data Insights

GMAT Focus does not test whether you can read a table. It tests whether you can convert a verbal claim into a row filter and a column comparison, then use the sort control to make the relevant rows adjacent. The table is a search space, not a dataset to be averaged.

The statements are disguised queries. 'Every site with capacity above 500 has a vacancy rate below 10%' is a universal claim: sort by capacity, find the first row above 500, then scan the vacancy column for all rows in that block. 'At least one project has both a budget over 2 million and a duration under 6 months' is existential: sort by either condition and look for the first row satisfying both. 'The median of column A exceeds the median of column B' asks you to sort each column separately, not to compute means.

Three decisions separate correct from tempting:

• Universal vs existential: for 'all', one counterexample defeats it; for 'some', one example proves it. Sorting to the extreme is usually the fastest test.
• Within-row vs across-row: the statement may compare two columns in the same row, or aggregate one column across many rows. Do not mix them.
• Strict vs inclusive: 'more than' and 'at least' change which rows qualify after sorting.

The mechanical loss: you answer a nearby question. You verify that the highest value is above a threshold when the statement asks whether every value is. Or you read the top row after sorting but forget the table scrolls, missing rows below.

Formula worth having in memory: for $n$ sorted values, the median is the $((n+1)\mathrm{/}2)$th if $n$ is odd, and the average of the $n\mathrm{/}2$th and $(n\mathrm{/}2+1)$th if $n$ is even.

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