Evidence in Tables and Graphs

CHAPTER SEVEN · INFORMATION AND IDEAS

A weather app tells you it rained on 40 percent of days last month. A friend tells you it rained on 12 days last month. Both can be true about the same month at once, and neither one alone tells you the other: you need to know the month had 30 days to connect the percentage to the count, or vice versa. People navigate this kind of gap constantly, between a share and a number, a level and a change, a total and a rate, usually without noticing they’re doing it. Once a specific claim is being tested, confusing those quantities becomes a direct source of error.

This chapter covers the same skill as the previous one, Command of Evidence, in its quantitative form: a passage states a claim, and beside it sits a table, a bar graph, or a line graph the claim is supposed to draw on. The math involved stays light. The real difficulty is matching the right data relationship to the claim, because a choice that reads the numbers correctly can still answer a different question than the one the claim actually asks. Many quantitative errors begin with labels and units before any arithmetic occurs.

Start With the Claim

Common quantitative-evidence stems ask students to complete a data-based statement, support a conclusion, or evaluate whether the data support a conclusion. That third form asks whether the data actually bear out the conclusion at all, which means a choice that undercuts the conclusion can be the correct answer.

These questions work the same way the textual form does, with the evidence supplied in a graphic instead of a sentence. The passage introduces a subject and usually states a claim, and the question asks which choice draws on the data to carry that claim, complete it, or test it. Your work has two conditions that must both hold at once: the choice has to be true of the graphic, and it has to bear on the claim. A reading that satisfies the first condition while failing the second is one of the most common ways to lose this kind of question.

Read Labels and Units First

Much of what decides these questions sits in the labels rather than in the values themselves. Read them in a fixed order every time, so the order becomes automatic and the actual values arrive last, once you already know what they mean.

Read the title and ask what is being counted, and where; a choice about a different quantity entirely fails before you check a single figure. Read the axis or column heads and ask what runs across and what runs up; time on one axis makes a trend claim possible, while categories alone do not. Read the unit and ask whether you’re looking at counts, percentages, rates, or amounts; percentage and raw number can move in opposite directions at the same time. Read the multiplier and ask whether the numbers are in thousands, millions, or per hundred thousand; a plotted figure of 40 may actually stand for forty thousand cases. Read the groups and check the legend, so you don’t assign a value to the wrong series. Read the range and ask where the data actually starts and stops; nothing outside the plotted range can be claimed from it, no matter how confidently a choice states it.

A graphic can use a term the passage itself defines. A graphic may plot something the passage has just explained, and that explanation is what gives the axis label its meaning. When an axis reads recovery interval or effective range, the sentence defining that exact phrase sits in the passage above it. Read the passage first, then the labels, then the numbers, in that order.

Check Accuracy and Relevance Together

Ecologists tracked four ponds after removing an invasive weed. Records from before the invasion put native cover on these ponds at roughly 60 percent, and the team treated a return to at least half that figure as recovery. They measured cover each autumn for three years.

Native plant cover, percentage of pond surface

Take the claim that native cover returned in most of the ponds within three seasons, with recovery defined as at least 30 percent cover. Weigh four statements against it.

“Three of the four ponds passed the 30 percent threshold by year 2 and exceeded 50 percent by year 3” is true of the data and bears directly on the claim; this is the answer. “Colt Mill held the highest cover in year 1” is true of the data and says nothing about return; a starting figure carries no claim about recovery. “Every pond gained cover in each year measured” is true of the data and bears only weakly on the claim, since Colt Mill gained every year and never came close to recovering. “All four ponds reached the recovery threshold by year 3” is not even true of the data, since Colt Mill reached only 24 percent, so this fails before the claim is ever reached.

Only the first statement clears both tests at once. The third is worth studying closely: every figure behind it is accurate, and it treats a rise from 15 to 24 as though Colt Mill had recovered, when 24 still sits below the threshold the team itself set.

Keep Quantities and Units Separate

The quantities below are genuinely distinct, and a claim built on one of them cannot be carried by another, however closely related they sound. Fixing this vocabulary first makes everything else in this chapter faster to apply.

Count reports how many there were; it cannot report whether that is a lot, without a total to set it against. Share or proportion reports how many out of how many, as a fraction or a percentage; it cannot report a count unless the denominator is actually given. Rate reports events measured against a denominator such as people, exposure, or time; it cannot report an individual’s own probability of being affected, since that depends on exactly what is being counted and whether one person can contribute more than one event to the total. Percentage-point change reports the arithmetic difference between two percentages, such as a move from 41 to 69; it cannot report how large that change was relative to where it started. Percent change reports a change measured against the starting figure, such as a rise of roughly two thirds; it cannot report the size of the gap in points. Level reports where a value stands at one single moment; it cannot report any movement at all.

A share alone will not hand you a count. Two districts can report the identical percentage connected and still differ tenfold in the actual number of households connected, because those percentages rest on entirely different totals. When a choice converts a share into a number of people, households, or cases, check first whether the graphic actually supplies the denominator needed to do that conversion.

Households with home internet, share of all households

Brill gained 28 percentage points and Corby gained 18. Measured against where each district began, Brill grew by roughly two thirds and Corby by a bit under a third. Both readings put Brill first, and the two measures part company just as easily elsewhere: a district climbing from 5 percent to 10 doubles its share while gaining only five points, and one climbing from 60 to 70 gains ten points while growing by only a sixth.

“Rose by 28 percentage points” means the difference between two percentages, and the answer it produces here is Brill, from 41 to 69. “Rose by 68 percent” means the change measured against the starting figure, and the answer is Brill again, though the number itself is different from 28. “Highest in 2023” is a level rather than a change, and the answer it produces is Ashby, the district that actually gained the least. “Narrowed the gap with Ashby” is a comparison of two districts across two dates, and the answer is Brill, whose distance behind Ashby fell from 37 points to 19.

Worked Examples With Tables and Graphs

Read a Table Against the Claim

Ecologists removed an invasive weed from four ponds and measured native plant cover each autumn for three years, treating 30 percent cover as recovery. They report that native cover returned in most of the ponds and that one pond lagged well behind the rest.

Which choice most effectively uses data from the table above to support the ecologists’ report?

A. Cover at Colt Mill rose from 15 percent to 24 percent, remaining below the 30 percent threshold that the other three ponds exceeded by year 3

B. Cover rose at every pond in every year of the study

C. Ashfield began the study with 12 percent cover

D. No pond reached 70 percent cover by year 3

A captures both parts of the report at once: most ponds recovered by the end of the study, while Colt Mill remained below the threshold. B is true and flattens the exact difference the ecologists went out of their way to report; every pond hides Colt Mill inside the group instead of setting it apart. C is true but irrelevant to the recovery claim; a starting figure alone carries no claim about return. D is true and bears on a ceiling the report never mentions; no pond reports an upper limit rather than a recovery.

Let the Unit Decide the Calculation

A regional authority reports that home internet access rose across all four districts between 2015 and 2023, and that the district furthest behind at the start closed much of the gap.

Which choice most effectively uses data from the chart above to support that report?

A. Ashby recorded the highest share of connected households in 2023

B. Brill rose from 41 percent to 69 percent, cutting its distance behind Ashby from 37 points to 19

C. Dunmow’s share rose by 11 percentage points over the period

D. More households were connected in Ashby than in Brill in both years

B shows the rise and measures the gap at both ends, which directly measures the narrowing the report describes. A is true and describes a level when the report describes a closing gap; highest ranks the finish and ignores the movement. C is true of a district that was never the one furthest behind, the wrong district for this specific claim. D changes a share into a household count the chart never supplies; the chart plots percentages and counts no actual households at all.

Separate Totals From Rates

A county compared library use across four towns. Officials argue that the smaller towns draw more use from their residents than the larger ones do.

Library use by town, 2024

Which choice most effectively uses data from the table to support the officials’ argument?

A. Ashby recorded 240,000 visits, more than any other town

B. Brill and Dunmow recorded 8.0 and 6.0 visits per resident, against 4.0 and 3.0 in the two larger towns

C. Corby recorded 150,000 visits from 50,000 residents

D. Dunmow recorded the fewest visits of the four towns

B puts two small towns above and two large towns below on exactly the measure the argument is built on: use per resident. A is true and argues the opposite of the claim; a raw total is influenced by population size and never answers a per-resident question. C reports both figures for one town with no comparison drawn between towns at all. D is true on total visits, and the argument concerns use per resident; the smallest town can record the fewest total visits while still showing high per-resident use.

Read the Trend and Its Endpoints

Researchers monitored the return of a migratory warbler to one valley. They report that arrival has moved earlier over the period observed.

First recorded arrival, day of the year

Which choice most effectively uses data from the table to support the researchers’ report?

A. The birds arrived on day 106 in 2024, twelve days earlier than in 2019

B. Arrival moved earlier in every year of the study

C. By 2030 the birds will arrive before day 100

D. The birds arrived later in 2021 than in 2020

A gives two endpoints and the distance between them, which directly supports a net earlier arrival across the observed period; a trend across a period does not require every single year to move the same direction. B is false: arrival slipped back by two days in 2021, so every year fails on the data itself. C reaches beyond the table entirely; six years of data cannot reach a claim about 2030. D is true, and it reports the one year that runs against the trend, which undercuts the claim it was meant to support rather than illustrating it.

Separate Final Level From Change

A district can finish at 88 percent after rising 10 points, while another finishes at 69 percent after rising 28 points. Highest at the end and biggest gain are different facts about the same data, and a choice can be completely accurate about one while the claim actually needs the other.

Two towns reported vaccination rates. Elm Town rose from 74 percent to 84 percent. Birchfield rose from 40 percent to 69 percent.

Which choice most effectively supports the claim that Birchfield made the larger gain?

A. Elm Town’s rate is higher than Birchfield’s rate in the most recent year

B. Birchfield rose 29 percentage points, compared with 10 points in Elm Town

C. Elm Town’s rate has always been higher than Birchfield’s

D. Birchfield’s rate is now closer to 70 percent than to 60 percent

B directly compares the two point gains, which is what the claim requires. A reports a final level, the opposite of what a gain claim needs. C restates a level comparison across time, not a measure of how much each one moved. D reports where Birchfield’s level sits now, not how far it traveled to get there.

The same distinction holds for percent change instead of point change: a rise from 41 percent to 69 percent is a 28-point gain and roughly a 68 percent increase relative to the starting value, while a rise from 5 percent to 10 percent is only a 5-point gain and a full 100 percent increase. A claim about the largest point gain and a claim about the largest percent increase can crown two entirely different groups as the leader.

Separate Percentages From Counts

If 70 percent of Town A’s households and 60 percent of Town B’s households have internet access, you cannot know which town has more connected households until you know how many households each town actually has.

Which choice, if true, would allow the claim “Town A has more connected households than Town B” to be evaluated?

A. Town A has 70 percent access and Town B has 60 percent access

B. Town A has 10,000 households and Town B has 40,000 households

C. Town A’s access rate rose faster than Town B’s over the past five years

D. Town B’s households are more spread out geographically

B supplies the missing denominators; with them, Town A’s connected households come to 7,000 and Town B’s come to 24,000, showing why the larger percentage does not imply the larger count. A repeats the percentages themselves, which is exactly the information that cannot answer a question about counts on its own. C concerns a rate of change, not the current count. D is irrelevant to either the percentages or the counts.

Keep Counts, Shares, and Rates Separate

Three hundred students may be a large number at one school and a small fraction at another; without the total enrollment, a count alone does not tell you the proportion it represents. Separately, eight injuries per 1,000 cyclists reports events measured against cyclists, not the chance that any one cyclist was hurt; if a single cyclist can be injured more than once in the same period, the rate is not simply an 0.8 percent chance of injury for an individual rider.

A city reports 450 workplace injuries this year among a workforce of 30,000, compared with 300 injuries last year among a workforce of 15,000.

Which choice most accurately compares the two years?

A. Injuries rose from 300 to 450, so the workplace grew more dangerous

B. The injury rate fell from 20 per 1,000 workers to 15 per 1,000 workers, even though the raw count of injuries rose

C. The workforce grew by 15,000 people

D. Most injuries occurred among workers hired within the past year

B supplies the rate both years actually require, and shows the rate falling even as the count rose, because the workforce itself grew. A reads the count alone and reaches a conclusion the count cannot support without the total workforce behind it. C reports a true fact about workforce growth without translating it into a rate. D introduces a claim about new hires that the numbers given cannot establish either way.

Check the Denominator Before Comparing

Cases per 100,000 people cannot be compared as though they were raw case counts, and events per hour cannot be read as events per participant; each rate carries its own denominator, and swapping which denominator a number is attached to changes what it actually reports.

Region X reports 40 cases per 100,000 residents. Region Y reports 250 total cases.

Which choice, if true, would allow a valid comparison of case rates between the two regions?

A. Region X has 2,000,000 residents and Region Y has 500,000 residents

B. Region X’s case count has been rising for three years

C. Region Y has more hospitals than Region X

D. Both regions use the same reporting software

A supplies the missing population for Region Y, letting you convert its 250 total cases into a rate of 50 per 100,000, genuinely comparable to Region X’s stated rate of 40. B, C, and D all fail to supply anything that turns a raw count and a rate into numbers built on the same footing.

Carry the Unit Multiplier Through the Calculation

A graph labeled “in thousands” turns a plotted value of 40 into 40,000 actual cases. A choice can quote the number 40 correctly from the graph and still describe the underlying quantity incorrectly if it drops the multiplier along the way.

A chart plots “Annual sales, in thousands of units” and shows a value of 85 for last year.

Which choice accurately reports last year’s sales?

A. The company sold 85 units last year

B. The company sold 85,000 units last year

C. The company’s sales fell by 85 percent last year

D. The company sold more units than any competitor last year

B correctly restores the multiplier the axis label supplies. A quotes the number accurately and drops the multiplier entirely, understating the real total by a factor of a thousand. C invents a percentage the chart never states. D makes a competitive claim the chart, showing only one company, cannot support.

Attach Each Number to the Correct Group

A value may belong to adults rather than adolescents, to the control group rather than the treatment group, to 2024 rather than 2020, or to one site rather than another; a number can be completely real and still be attached to the wrong row or column for the claim being tested.

A table reports that Site B recorded 62 percent satisfaction in 2023, and Site C recorded 71 percent in the same year.

Which choice, if the claim concerns Site C’s improvement since 2019, would be usable evidence?

A. Site B recorded 71 percent satisfaction in 2023

B. Site C recorded 71 percent satisfaction in 2023, up from 58 percent in 2019

C. Site C recorded 62 percent satisfaction in 2023

D. Site B improved by 9 points between 2019 and 2023

B keeps both the correct site and the correct years together. A swaps the value between the two sites. C keeps the right site and imports the wrong site’s 2023 figure. D reports real movement, for the wrong site entirely.

Separate Within-Group Change From Between-Group Level

Treatment can measure higher than control at the end of a study, and that comparison alone does not tell you how much the treatment group actually changed from its own starting value; the two questions, level and change, need different numbers to answer.

A trial reports that the treatment group ended with a score of 78 and the control group ended with a score of 71.

Which choice would be needed to evaluate the claim that the treatment group improved more than the control group?

A. The treatment group’s score at the end of the trial

B. The treatment and control groups’ scores at both the beginning and the end of the trial

C. The number of participants in each group

D. The name of the treatment being tested

B supplies what a claim about improvement actually requires: a starting point for each group as well as an ending point. A gives only a final level, useful for a different claim entirely. C and D are details about the study’s design that do not by themselves measure change in either group.

Track the Gap While Both Groups Change

If Group A rises 10 points and Group B rises 25 points, “both groups improved” is true and may miss the more specific and more useful claim that Group B actually caught up with Group A.

Group A rose from 55 to 65. Group B rose from 30 to 55.

Which choice most exactly describes what happened to the gap between the groups?

A. Both groups improved over the period

B. The gap between the groups narrowed from 25 points to 10 points

C. Group B’s score is now higher than Group A’s score

D. Group A improved less than Group B in absolute terms

B states exactly what changed about the relationship between the two groups, which is the most specific and most useful description available. A is true and says nothing about the gap itself. C is false; 55 is still lower than 65. D is true and, like A, stops short of stating the actual size of the change in the gap.

Distinguish a Narrower Gap From an Overtake

Being 37 points behind and then 19 points behind is a substantial narrowing of a gap. It does not mean the two groups became equal, and it does not mean their order reversed.

Which of these claims does a gap narrowing from 37 points to 19 points support?

A. The two groups are now equal

B. The lower group has now overtaken the higher group

C. The lower group closed roughly half the distance separating it from the higher group

D. The higher group’s value has fallen

C states only what the narrowing itself establishes. A and B both claim more than a narrowed gap can support on its own; a gap can shrink by half and remain a real, substantial gap. D assumes a specific mechanism, a fall in the higher group, that a narrowing gap does not by itself reveal; the higher group could just as easily have risen more slowly than the lower one.

Read the Full Trend Between Endpoints

A value can run 2019 to 2024 showing an overall decrease even if 2021 briefly rises above the 2019 level; overall movement across a period does not require every single interval to move in the same direction.

A city’s crime index ran 100 in 2019, 108 in 2021, and 82 in 2024.

Which choice most accurately describes the change from 2019 to 2024?

A. Crime decreased every year from 2019 to 2024

B. The index fell from 100 to 82 over the period, though it rose temporarily in 2021 before falling again

C. Crime has been rising since 2021

D. The index has never exceeded 100

B reports the actual net change and does not hide the year that moved against it. A is false, since 2021 rose above 2019. C reverses the actual direction of the later years, which fell after 2021. D is false; the index reached 108 in 2021, above the 100 level in 2019.

Use Enough Points to Support a Trend

A value of 80 in 2019 and 60 in 2024 supports a claim about a lower endpoint. It does not by itself show a continuous, year-by-year decline, since the two endpoints alone say nothing about what happened in between them.

Given only a 2019 value of 80 and a 2024 value of 60, which claim can these two data points alone support?

A. The value declined steadily and continuously from 2019 to 2024

B. The value was lower in 2024 than in 2019

C. The value never rose above 80 during the period

D. The value fell by exactly 4 points per year

B is the only claim these two points can actually carry on their own. A requires knowledge of every year in between that two endpoints alone cannot supply. C and D both make claims about the years in between that are not visible from the endpoints alone.

Use Only Thresholds the Passage Defines

A pond rising from 15 percent cover to 24 percent cover has genuinely improved. It has not “recovered” unless the passage or the data actually define what recovery means; without a stated threshold, a choice cannot correctly call an increase a recovery.

A wetland’s water clarity rose from 40 percent to 55 percent over two years. The passage never states a clarity threshold for “restored.”

Which choice can be supported by the data alone?

A. Clarity rose from 40 percent to 55 percent over two years

B. The wetland has been fully restored

C. Clarity now meets the standard for a healthy wetland

D. The wetland has recovered from its earlier decline

A states only what the data show, an increase with no claim about what that increase means. B, C, and D each apply a label, restored, a standard, recovered, that requires a threshold the passage never actually supplies.

Separate Threshold Crossing From Maximum Value

Several groups can clear a stated cutoff, and a question may care only about whether they crossed it, not about which group finished highest above it.

Four towns’ recycling rates: Ashford 42 percent, Barrow 58 percent, Colton 51 percent, Drewsbury 39 percent. A program considers 40 percent recycling a “passing” rate.

Which choice most accurately describes how many towns passed?

A. Barrow passed with the highest rate of the four towns

B. Three of the four towns met or exceeded the 40 percent threshold

C. Every town increased its recycling rate this year

D. Drewsbury recycled the least of the four towns

B answers exactly the threshold question: three towns, Ashford, Barrow, and Colton, cleared 40 percent, while Drewsbury did not. A reports a ranking, a different question from a pass/fail threshold. C makes a claim about change over time that this single year of data cannot support. D reports a ranking as well, not a threshold count.

Keep Conclusions Within the Plotted Range

A graph ending in 2024 cannot tell you what happened in 2025. A scale beginning at age 40 cannot establish a pattern among people younger than 40, no matter how strong the trend looks within the range that is actually shown.

A chart plots outcomes for ages 40 to 70 only, showing a steady improvement across that range.

Which choice is supported by the chart?

A. Outcomes improve steadily from age 40 to age 70

B. Outcomes would continue improving past age 70

C. The same pattern holds for people under 40

D. The improvement began before age 40

A stays entirely within the range the chart actually plots. B, C, and D all extend a real pattern past the edges of the data, into ages the chart never displays at all.

Keep Subgroup Results Within the Subgroup

A result for women aged 65 to 74 cannot become a result for all adults without additional data covering those other groups; a subgroup finding stays a subgroup finding until more data says otherwise.

A study reports that a supplement improved bone density among women aged 65 to 74.

Which choice accurately reflects what the study supports?

A. The supplement improves bone density in women aged 65 to 74

B. The supplement improves bone density in all older women

C. The supplement improves bone density in adults generally

D. The supplement is effective for treating bone conditions

A keeps the claim exactly at the group actually studied. B expands to “older women” broadly, beyond the specific age range tested. C expands further still, to adults in general. D drops the age and sex qualifiers entirely and adds a general effectiveness claim the study never makes.

Match the Graphic to the Named Subgroup

An overall average can hide opposite patterns running in opposite directions within the groups that make it up; a claim about a named subgroup needs data from that subgroup, not from the combined sample as a whole.

Overall, patients in a trial showed improved sleep. Within the trial, older patients showed improvement and younger patients showed a decline.

Which choice accurately reflects the data for younger patients specifically?

A. Younger patients showed improved sleep, matching the overall trend

B. Younger patients showed a decline in sleep quality, even as the overall sample improved

C. All patients in the trial showed improved sleep

D. The trial did not measure younger patients

B reports the subgroup pattern accurately, which runs opposite to the overall average. A wrongly assumes the subgroup must match the overall trend. C applies the overall result to a group it does not actually describe. D is false; younger patients were measured, and their result simply moved in the opposite direction.

Separate the Mean From Individual Values

An average of 12 hours does not mean each individual participant actually recorded 12 hours; a mean describes the group as a whole, and individuals can sit far above or far below it.

A survey reports that respondents slept an average of 6.5 hours per night.

Which choice accurately reflects what this average shows?

A. Every respondent slept exactly 6.5 hours per night

B. The average across all respondents was 6.5 hours per night, and individual respondents may have slept more or less

C. No respondent slept fewer than 6.5 hours

D. Sleep did not vary across respondents

B correctly describes what a mean actually reports: a summary of the group, not a claim about every individual member of it. A, C, and D each convert the group average into a claim about every single respondent, which an average alone cannot support.

Separate Totals From Averages

A region with 500 total cases may have a lower per-person rate than a smaller region with only 200 total cases, once population size is taken into account; a raw total says nothing about the rate until it is divided by the right denominator.

Region A reports 500 total flu cases. Region B reports 200 total flu cases. Region A has 1,000,000 residents; Region B has 100,000 residents.

Which choice accurately compares the two regions’ flu rates?

A. Region A has a higher flu burden because it recorded more total cases

B. Region B has a higher rate of flu per resident, despite recording fewer total cases

C. Both regions have identical flu rates

D. Region A’s population is irrelevant to its case count

B correctly divides each total by its own population: Region A’s rate comes to 0.5 cases per 1,000 residents, while Region B’s comes to 2.0 cases per 1,000, meaningfully higher despite the smaller total. A compares totals alone, ignoring the very different populations behind them. C is false once the rates are actually calculated. D dismisses the exact variable, population, that a per-resident comparison requires.

Convert Cumulative Values to Interval Values

A line showing total sales to date cannot be read as sales during any one specific month unless the graphic explicitly defines it that way; a running total and an interval value answer different questions.

A chart plots cumulative sales: 200 units by March, 350 units by April, 600 units by May.

Which choice accurately describes sales during May alone?

A. 600 units were sold in May

B. 250 units were sold in May

C. Sales in May exceeded sales in April

D. Total sales reached 600 units by the end of May

B correctly isolates the interval by subtracting April’s cumulative total from May’s: 600 minus 350. A mistakes the running total for the single month’s figure. C is imprecise about what exactly is being compared, monthly totals versus cumulative totals. D restates the cumulative figure accurately without answering a question about the interval at all.

Check the Base of Every Percentage

Thirty percent of all voters and 40 percent of young voters have different denominators entirely; the two percentages can be compared as shares in their own right, and neither one converts into a count of people without its own matching total.

A survey reports 30 percent support among all voters (2,000 surveyed) and 45 percent support among voters under 30 (500 surveyed).

Which choice accurately compares the two groups?

A. Support is higher among voters under 30 than among voters overall, as a share

B. More voters under 30 support the measure than voters overall, in raw numbers

C. The two percentages can be added together to find total support

D. Voters under 30 make up 45 percent of all voters surveyed

A compares the two groups correctly, as shares built on their own separate totals. B converts the shares into a raw-number comparison the different sample sizes cannot support; 45 percent of 500 is fewer actual people than 30 percent of 2,000. C treats two percentages built on different bases as though they could simply be summed. D confuses the support percentage for the under-30 group with that group’s share of the overall sample, two entirely different figures.

Keep Numerator and Denominator Straight

Twenty patients among 100 participants is 20 percent of participants. It is not “100 participants per 20 patients” in whatever sense a claim might seem to need; reversing which figure sits on top changes the meaning of the fraction entirely.

A trial enrolled 100 participants; 20 experienced a side effect.

Which choice correctly states the side-effect rate?

A. 20 percent of participants experienced the side effect

B. Five participants experienced the side effect for every one who did not

C. 100 percent of participants experienced 20 side effects

D. Participants experienced side effects at a rate of 100 to 20

A states the rate the right way around: the affected group over the total. B inverts the relationship into an unsupported ratio. C and D both garble the numerator and denominator into statements the original numbers do not actually support.

Match Each Number to the Correct Variable

A table may show temperature and survival side by side; quoting the temperature figure correctly does not support a claim about survival unless the data actually state that specific relationship.

A table shows: at 15 degrees, survival was 40 percent; at 25 degrees, survival was 72 percent.

Which choice, if the claim concerns survival at 25 degrees, correctly uses the table?

A. The temperature was 25 degrees

B. Survival was 72 percent at 25 degrees

C. The temperature ranged from 15 to 25 degrees

D. Survival improved as temperatures rose from 15 to 40 degrees

B connects the correct variable, survival, to the correct condition, 25 degrees. A quotes a real number from the table and reports the wrong variable, temperature instead of survival. C reports a range without connecting it to any outcome. D extends the claim to 40 degrees, a temperature the table never actually shows.

Preserve Association Language in Graph Questions

Treatment and outcome can move together in a chart without the chart alone showing why; stronger causal language needs justification from the passage or the study’s design, not from the shape of the data alone.

A chart shows that regions with more parks also report higher average life expectancy.

Which choice most accurately reflects what the chart alone supports?

A. More parks cause longer life expectancy

B. Regions with more parks tend to have higher life expectancy, though the chart alone does not establish why

C. Building more parks will extend residents’ lives

D. Life expectancy has no relationship to park access

B stays at the level the chart itself supports: an association, without a claimed mechanism. A and C both assert causation the chart’s design, a simple comparison across regions, cannot establish on its own. D denies a relationship the chart plainly shows.

Compare Against a Control Before Attributing Change

Scores rising after a program began is consistent with the program working; without an appropriate comparison or other design information, other changes occurring over the same period may also explain the rise.

Test scores at a school rose from 68 to 76 in the year after a new curriculum was introduced.

Which choice would most directly strengthen the claim that the curriculum caused the rise?

A. Scores rose from 68 to 76 after the curriculum began

B. A comparable school that did not adopt the curriculum showed no similar rise over the same year

C. Teachers reported liking the new curriculum

D. The curriculum took a semester to fully implement

B supplies the comparison the before-and-after figures alone cannot: a similar school without the change, tracked over the same period, that did not see the same rise. A restates the timing, which is consistent with an effect and does not by itself rule out other causes. C reports opinion, not outcomes. D reports a detail about implementation, not evidence of impact.

Use the Control Group to Estimate Additional Change

If a treatment group improves 15 points and a control group improves 13 points, the treatment group’s raw gain looks impressive on its own; the comparison between the two groups may tell a much smaller story than the treatment number alone suggests.

A treatment group’s score rose from 60 to 75. A control group’s score rose from 58 to 71.

Which choice most accurately reflects the difference in changes between the two groups?

A. The treatment group improved by 15 points

B. The treatment group improved by 15 points, only 2 points more than the control group’s 13-point improvement

C. The treatment was highly effective, given its large improvement

D. The control group’s results are irrelevant to evaluating the treatment

B reports the treatment group’s gain alongside the control group’s own gain, showing a much smaller difference in changes than the raw 15-point figure suggests on its own. A is true and, read alone, invites exactly the overstatement the full comparison corrects. C draws a conclusion the modest 2-point difference does not support. D dismisses the exact comparison needed to evaluate the differential change between groups.

Use Numbers That Address the Claim

The highest 2023 value in a table can be perfectly accurate while the claim actually asks which district closed the most ground since 2015; an accurate number answers nothing if it answers the wrong question.

Four districts’ 2023 levels: Ashby 88, Brill 69, Corby 80, Dunmow 66. The claim concerns which district closed the most ground since 2015.

Which choice is actually usable evidence for this claim?

A. Ashby recorded the highest level in 2023

B. Brill’s 2015 level was 41 percent, and its 2023 level was 69 percent

C. Corby’s 2023 level was 80 percent

D. Dunmow’s 2023 level was the lowest of the four districts

B is the only choice supplying both a starting and an ending point, which is what a “closed the most ground” claim actually requires. A, C, and D each report only a single 2023 level, accurate figures that cannot by themselves show how much any district changed.

Verify Every Numerical Statement in the Answer

A sentence can quote the correct starting value and then misstate the change, the ranking, the denominator, or the comparison that follows it; each clause of a numerical choice has to be checked on its own.

A city’s population rose from 40,000 in 2010 to 52,000 in 2020.

Which choice accurately describes this change?

A. The population rose from 40,000 in 2010, a 30 percent increase, to 52,000 in 2020

B. The population rose from 40,000 in 2010, a 12 percent increase, to 52,000 in 2020

C. The population fell from 52,000 in 2010 to 40,000 in 2020, a 23 percent decrease

D. The population rose from 45,000 in 2010 to 52,000 in 2020, a 30 percent increase

A gets both the raw figures and the percent change correct: a rise of 12,000 on a base of 40,000 is a 30 percent increase. B keeps the correct starting and ending values and mislabels the percent change. C reverses which year had which value, turning a rise into a fall. D changes the starting figure itself while correctly stating the percent change that would have gone with the true figure, an error easy to miss if only the final clause is checked.

Satisfy Every Numerical Demand in the Claim

Some claims are really two claims joined together, and the correct evidence has to satisfy both halves at the same time. A choice that nails one half while ignoring the other is incomplete, even when every number inside it is accurate.

Before opening the choices on a claim like this, underline each separate demand the claim is making. A claim recommending small amounts of an additive while warning against large amounts is making two demands: the small-amount condition should perform acceptably, and the large-amount condition should perform worse. Evidence addressing only one half leaves the claim only half supported.

A materials report recommends adding a fiber reinforcement to concrete only in small proportions, citing test data on compressive strength.

Which finding best supports this recommendation?

A. At a 10 percent fiber ratio, compressive strength matched the unreinforced control

B. At a 10 percent fiber ratio, compressive strength matched the control, while 20 and 40 percent ratios both reduced strength below the control

C. At a 40 percent fiber ratio, compressive strength dropped well below the control

D. Fiber-reinforced concrete costs less to produce than unreinforced concrete

The recommendation makes two demands: small amounts should work, and larger amounts should not. B is the only choice that reports both the acceptable low-ratio result and the poorer higher-ratio results. A reports only the small-amount condition, leaving the warning against larger amounts unsupported. C reports only the large-amount failure, leaving the case for small amounts unsupported. D addresses cost, a variable the strength-based recommendation never raises.

Read Ranges as Ranges

A reported value is not always a single number. Ranges, minimums, maximums, and open-ended bounds each license a specific, narrower conclusion than a point estimate would, and each also rules out specific conclusions that feel tempting but go beyond what the notation actually states.

A claim that one material’s fiber diameter can be finer than another’s often turns on the minimum of a reported range, not its average. A fiber reported as ranging from 10 to 28 microns in diameter can be finer at the low end than a fiber that never drops below 15 microns, regardless of either fiber’s typical or average diameter. Reading past the minimum and reaching for an average the passage never reports is one of the most common ways a range-based claim gets misjudged.

Filter the Table Before Calculating

A wide table can track several categories at once: instrument, location, year, treatment, and outcome all inside the same grid. A common error is comparing the full table before filtering to the category named in the claim.

The filter sequence: identify the exact category the claim restricts itself to. Remove every row outside that category before comparing anything. Only then apply the requested operation, earliest, highest, lowest, or largest change. Finally, check that the answer choice reattaches the correct category label to the value, not just the correct number.

A table logs ocean-temperature readings from four instruments, mixing satellite, buoy, and shipboard measurements across four decades, with each row labeled by instrument type and year.

Which choice identifies the earliest buoy-based temperature reading in the table?

The table’s overall earliest reading, several decades before any buoy was deployed, belongs to a shipboard measurement, and a student who compares every row without filtering first will find that value and select it. The correct move is to remove every row that is not a buoy reading first, then find the earliest year remaining among only the buoy rows, whatever year that turns out to be. The globally earliest value in a table is frequently not the answer to a claim restricted to one category. Filtering by category before comparing years prevents that error.

Translate the Claim Into a Numerical Pattern

A passage’s claim is often a concept, not a number: heterogeneity, a trade-off, a threshold, a plateau, an incomplete general measure. None of these words appears directly in a chart’s axis labels. Before scanning any values, translate the concept into the specific numerical shape that would actually demonstrate it.

One version of this pattern deserves its own caution. When two groups both change over time, comparing changes to changes, not endpoints to endpoints and not one group’s raw gain in isolation, is the correct arithmetic comparison. A treatment group improving by eighteen points while an untreated comparison group improves by twelve points on its own supports a difference in changes of roughly six points. Whether that six-point difference reflects a genuine treatment effect or some other factor that happened to affect the two groups unequally depends on the study’s design, not on the arithmetic alone.

Separate Differences in Means From Differences in Spread

Two different means being reported tells you the two groups differ on average. It tells you nothing at all about how spread out the individual values inside either group actually were, and a choice claiming wide variation within a group needs its own separate evidence, a range, error bars, or individual data points, not simply two different averages sitting side by side.

Error bars carry the same discipline. Read what the bars actually represent before drawing any conclusion from them: standard deviation, standard error, and a confidence interval are three different things, and a passage that states its own rule for statistical significance should be followed exactly as stated. Unless the passage explicitly tells you what the error bars represent and how to interpret them, do not infer statistical significance from overlap alone; treat visual overlap as suggestive at most, and let the passage’s own stated rule, not an imported statistical convention, decide the rest.

Check for Subgroup-Specific Effects

An overall average can hide a subgroup’s different pattern. A harder version goes one step further: the direction of an effect itself can differ by subgroup, not just its size.

A treatment can genuinely help one age group while measurably harming another, with the overall average landing somewhere in between and concealing both real effects entirely. An overall average can conceal subgroup effects that differ sharply in size or direction. A statement about the combined average may describe neither subgroup well, so subgroup-specific claims must be checked against subgroup-specific data. Whenever a passage reports results broken out by subgroup, check whether every subgroup actually moved in the same direction before accepting a claim that generalizes across all of them, since a shared overall trend and a shared subgroup-level trend are two different, separately verifiable facts.

Use This Method

1. Read the passage and find the claim the question will make you carry.

2. Read the labels: title, axes or columns, units, multiplier, groups, and range.

3. Say what the data actually show in one sentence before you open the choices.

4. Test each choice twice: is it true of the graphic, and does it actually touch the claim?

5. Recheck the unit before you select an answer. A choice that turns counts into people, or shares into numbers, fails however well it otherwise reads.

Compare Close Quantitative Statements

Many hard choices in this chapter use the exact same numbers. The difference sits entirely in the sentence built around them. Before choosing, identify what the claim actually requires: a level, a change, a share, a rate, a comparison, a threshold, or an overall pattern.

Practice

1. A school district introduced free breakfast at four schools and tracked attendance. Administrators report that attendance rose by the largest number of percentage points at the school where it had been lowest.

Average daily attendance, percentage of enrollment

Which choice most effectively uses data from the table to support the administrators’ report?

A. Ellery recorded the highest attendance after the program began

B. Fairlop began at 81 percent and rose 9 points, more than any other school

C. Every school recorded higher attendance after the program began

D. Girton rose by 3 percentage points

2. An agency compared cycling injuries in two cities. It notes that City A recorded more injuries in total while City B recorded the higher injury rate per thousand regular cyclists.

Cycling injuries, 2024

Which choice most effectively uses data from the table to support the agency’s note?

A. City A recorded 540 injuries and City B recorded 280

B. City B recorded 7.0 injuries per 1,000 regular cyclists against 3.0 in City A, though City A recorded more injuries overall

C. City A has more than four times as many regular cyclists as City B

D. City B recorded fewer injuries than City A

3. Conservators tested four cleaning solvents on soiled canvas samples. They conclude that one solvent removed the most soil while causing the least fading of pigment.

Solvent performance on test samples

Which choice most effectively uses data from the table to evaluate the conservators’ conclusion?

A. Solvent 4 removed the most soil, and Solvent 3 caused the least fading, so no solvent led on both measures

B. Solvent 2 removed 88 percent of soil with a fading score of 2

C. Solvent 3 caused the least fading of the four

D. Every solvent removed more than 70 percent of the soil

Answers and Explanations

This last item asks you to evaluate a conclusion rather than simply support one, and that single verb changes the entire task. A conclusion claiming a single leader is directly contradicted by this table, because the two best values occur in two different rows.

Final Checks Before You Answer

This is where the last point on this question type is usually won or lost. Check the noun sitting around the number, not only the number itself: households or share of households, injuries or injuries per 1,000 cyclists, final level or change from baseline, percentage points or percent change. Each check below comes with its own worked item.

Before trusting a choice, verify it in a fixed order: does the number match the graph, does the unit match, does the group match, and does the year or condition match? A choice can pass the first test and fail any of the next three.

A table reports “Enrollment by grade, 2023” showing 340 students in Grade 9 and 310 in Grade 10. A separate column shows 2024 figures: 355 in Grade 9 and 298 in Grade 10.

Which choice accurately reports Grade 10 enrollment in 2023?

A. 355 students

B. 310 students

C. 298 students

D. 340 students

B passes all four checks: 310 is the number in the table, the unit is students, the group is Grade 10, and the year is 2023. A takes the right kind of figure from the wrong year. C takes a real number from the wrong year and, coincidentally, the wrong grade’s later value. D takes a real number from the right year and the wrong grade entirely. Running through the sequence, number, unit, group, year, catches each of these on a different step.

A choice can convert a percentage into “more people” without the denominators to support that conversion, and separately, a single set of numbers can be honestly described as a change in percentage points, a percent increase, or simply the highest level, and each description answers a different question.

The share of District X students enrolled in a regional program rose from 20 percent to 35 percent. District X has 4,000 students; the share of District Y students enrolled in the same program rose from 30 percent to 38 percent, and District Y has 10,000 students.

Which choice most accurately compares the two districts?

A. District X now has more students in the program than District Y, since its share grew more

B. District X’s share rose 15 percentage points, compared with 8 points in District Y, though District Y still enrolls more students in the program overall

C. District X’s share is now higher than District Y’s

D. District X’s share grew by 75 percent, the largest percent increase of the two, so District X’s program is now the largest

B keeps the percentage-point comparison honest and adds the actual enrollment comparison rather than assuming one from the other; District X’s growth comes to 1,400 students in the program, District Y’s to 3,800, so Y still leads on the raw count despite X’s larger percentage-point gain. A converts a percentage-point lead into a count lead the numbers do not support. C states a level, and it is false besides; 35 percent is still lower than 38 percent, so this choice fails both as the wrong kind of statement and on the numbers themselves. D correctly computes a 75 percent relative increase, the largest of the two by that specific measure, and then illegitimately converts “largest percent increase” into “now the largest program,” a claim about size that a percent-increase figure cannot support on its own.

A choice claiming the largest improvement, a narrowed gap, or a doubling all commit to a specific, checkable arithmetic relationship, and each one fails if that specific relationship isn’t actually what the numbers show.

Program A’s score rose from 50 to 68. Program B’s score rose from 30 to 54.

Which choice most accurately describes what happened to the gap between the two programs?

A. Program A improved most, since it ended with the higher score

B. Program B’s gain, 24 points, was larger than Program A’s gain of 18 points

C. Program B’s score doubled during the study

D. The gap between the programs narrowed from 20 points to 14 points

D is the only choice that actually answers what was asked: the distance between the two programs, 20 points at the start narrowing to 14 at the end. B reports a true and useful fact, that Program B gained more in absolute terms, and it answers a different question than the one asked, which concerned the gap itself rather than either program’s individual gain. A confuses ending level with amount of improvement. C is false; 30 to 54 is not a doubling, which would require reaching 60.

A choice claiming one figure is half as large as another, a rate per 1,000, or a risk each commit to a specific kind of quantity, and swapping one of these for another changes what the claim actually asserts.

City P recorded 40 injuries among 20,000 cyclists. City Q recorded 25 injuries among 5,000 cyclists.

Which choice most accurately compares the two cities?

A. City P’s injury rate, 2.0 per 1,000 cyclists, is less than half of City Q’s rate of 5.0 per 1,000

B. City P recorded more injuries than City Q

C. A cyclist in City Q has a 5 percent chance of being injured

D. City P is safer because it recorded 40 injuries compared to City Q’s 25

A keeps both figures as rates per 1,000, correctly computed, and correctly compares them as a ratio rather than a raw difference. B compares raw counts, which the different cyclist populations make misleading here. C converts a rate into an individual’s risk, which is not automatically valid, especially if a single cyclist could be counted more than once. D compares raw counts again and draws a safety conclusion the rates directly contradict.

A choice can misuse the word average by applying it to every individual, misuse recovered by skipping a stated threshold, or misuse all groups by failing to check every single one.

Four towns’ pollution levels, with recovery defined as 15 units or lower: Ashcombe 12, Brindle 18, Corvale 9, Dunmore 22.

Which choice most accurately describes the towns?

A. The average pollution level across the four towns is below the recovery threshold

B. Every town has recovered, since pollution levels dropped this year

C. Two of the four towns, Ashcombe and Corvale, have recovered according to the stated threshold

D. All four towns recorded pollution levels below 20 units

C applies the actual stated threshold correctly to each individual town. A is false: the four-town average is 15.25, which is above the 15-unit recovery threshold, not below it. More importantly, the question asks which individual towns have recovered, a claim the average cannot settle even when computed correctly. B claims recovery for every town without checking any of them against the threshold; Brindle and Dunmore both remain above it. D is false; Dunmore recorded 22, above 20.

A choice claiming “most groups” has to actually count how many groups satisfy the condition, a choice claiming a change “over the period” only needs the endpoints, and a choice claiming a change happened in “each year” needs every single interval checked.

Five regions’ recycling rates crossed a 50 percent target as follows: three regions crossed it, two did not.

Which choice accurately describes the group of regions?

A. Most regions crossed the 50 percent target

B. All regions crossed the 50 percent target

C. Recycling rose in each region every year of the study

D. The overall regional average crossed 50 percent

A is the only choice that correctly counts: three out of five is a majority, matching most. B is false on the actual count. C makes a year-by-year claim the passage, which reports only whether the target was crossed, cannot support. D computes a different quantity, an average, that was never asked about and is not established by the threshold data given.

A choice claiming a treatment caused a change has to rule out the possibility that the control group changed too, and a choice merely describing an association is not automatically wrong just because it stops short of claiming causation.

Treatment group: rose from 40 to 58. Control group: rose from 38 to 50.

Which choice most accurately reflects what this comparison shows?

A. The treatment caused an 18-point improvement

B. The treatment group improved by 18 points and the control group by 12 points, a 6-point difference in changes; whether that difference was caused by the treatment depends on how the groups were formed and what else differed between them

C. The chart shows the treatment is associated with improvement

D. The treatment and the outcome are completely unrelated

B is the only choice that actually uses the comparison the question asks about, reporting the treatment group’s gain against the control group’s own gain rather than crediting the full change to treatment or stopping at a bare association. A commits the exact error this check warns against, crediting the full 18-point gain to treatment while ignoring the 12-point gain the control group posted on its own. C is true and less complete than B; it describes a relationship without using the control comparison the data actually make possible. D denies a real relationship the data plainly show.

A choice claiming “no effect” has to distinguish an actual measured zero from a difference that simply wasn’t detected.

A twelve-week trial found no statistically significant difference in yield between a new fertilizer group and an untreated group.

Which choice most accurately reflects this finding?

A. The fertilizer has no effect whatsoever

B. The trial found no statistically significant difference, which is not the same as proving the fertilizer has zero effect

C. The fertilizer’s effect was measured at exactly zero

D. The untreated group outperformed the fertilizer group

B is the only choice that stays at the level the trial actually supports: a result not detected, not a settled zero. A and C both convert “not detected” into a certainty the trial cannot deliver. D invents a directional result the passage never reports. A nonsignificant comparison can still have a point estimate favoring one group; “no statistically significant difference” does not by itself tell which group’s observed mean was higher.

A claim about what a graph shows cannot outrun where the graph’s own axis actually begins.

A bar chart’s y-axis begins at 40, not zero, and two bars reach 52 and 58.

Which choice most accurately reflects what the chart shows?

A. The two bars represent values of 52 and 58

B. The chart shows values starting from zero

C. The shorter bar represents a value close to zero

D. The visual gap between the bars means one value is many times larger than the other

A reads the labeled values directly, regardless of where the axis happens to start. B misstates the axis, which the chart states begins at 40. C misreads a bar’s height as though the axis started at zero, when it starts at 40. D draws a multiplicative comparison from bar heights alone, ignoring that a non-zero axis can make two close values, 52 and 58, look far more different than they actually are.

When two lines cross on a graph, or two bars look almost equal, or error bars overlap, resist the temptation to draw a conclusion the visual impression alone cannot support.

A line graph shows Group A above Group B until 2020, when the lines cross; Group B is above Group A from 2020 onward.

Which choice most accurately describes the two groups across the whole period shown?

A. Group A was higher than Group B throughout the period

B. Group A was higher before 2020, and Group B was higher from 2020 onward

C. The two groups were always roughly equal

D. Group B was higher than Group A throughout the period

B identifies the actual crossing point and describes both segments correctly. A and D each describe only one segment as if it covered the whole period. C mistakes a crossing for constant near-equality, which the crossing itself contradicts; a crossover marks a change in ordering, it does not imply the groups were approximately equal throughout the period.

A table using decimal values, an answer that rounds a figure, and a choice combining two separate numerical facts all require the same discipline: check the exact value against the exact claim, not an impression of it.

A table reports a rate of 0.42 cases per 100 people. A passage states the region’s rate “rounds to slightly less than half a case per hundred people.”

Which choice most accurately reflects the table?

A. The rate is 4.2 cases per 100 people

B. The rate is 0.42 cases per 100 people, consistent with the passage’s description of “slightly less than half a case per hundred”

C. The rate is exactly 0.5 cases per 100 people

D. The rate cannot be determined from a decimal value

B keeps the decimal exactly as the table states it and checks that the rounded description in the passage is a reasonable, non-distorting simplification of that exact figure. A misplaces the decimal point by a factor of ten. C rounds too far, past what “slightly less than half” actually describes. D treats a decimal as though it were unreadable, which it is not.

A blank cell is not the number zero, two bars that look almost equal are not necessarily numerically equal, and overlapping error bars do not automatically prove or disprove a difference on their own.

A table has no entry for Region C in 2021, marked “not reported.” A bar chart shows Region A and Region D with bars of nearly identical height, labeled 41 and 43. A separate chart shows two groups’ results with overlapping error bars, and the passage does not explain how to interpret that overlap.

Which choice most accurately reflects these three graphics?

A. Region C recorded zero cases in 2021

B. Region A and Region D recorded identical results, since their bars look the same height

C. Region A recorded 41 and Region D recorded 43, values that are close but not identical

D. The overlapping error bars prove there is no real difference between the two groups

C reads the two bars by their labeled values rather than by visual impression, correctly noting they are close without calling them the same. A converts a missing report into a measured zero, which the table never states. B mistakes visual closeness for numerical equality, ignoring the labeled values entirely. D draws a firm conclusion from the error-bar overlap that the passage supplies no rule for; overlap alone, without stated guidance, proves neither equality nor difference.

When both surviving choices are numerically true, when scientific language makes a passage feel dense, or when a graph itself is too dense to read cell by cell, return to the claim, strip the passage to plain nouns, and isolate only the rows, columns, or series the claim actually needs.

A biochemical assay recorded enzymatic activity, in nanomoles per minute per milligram of protein, across six substrate concentrations. Activity rose as substrate concentration increased up to 4 millimolar and then remained approximately flat at higher concentrations.

Stripped to plain language, the claim says: the reaction sped up as more substrate was added, up to a point, after which adding more substrate stopped making a difference.

Which choice, if the claim is that the reaction has a maximum speed it does not exceed, most directly supports it?

A. Activity was measured at six different substrate concentrations

B. Activity increased steadily up to 4 millimolar, then remained essentially flat at higher concentrations

C. The units were nanomoles per minute per milligram of protein

D. Activity was highest at the lowest concentration tested

B matches the stated rise-then-plateau pattern. A restates the method without addressing the pattern the claim is about. C restates a unit, useful context that answers nothing about the shape of the trend. D contradicts the pattern already established; if activity increased up to 4 millimolar, the lowest concentration is not where it peaked. The identical technique, strip the claim to plain nouns first, works whether the density in front of you comes from technical vocabulary or from a table with more rows and columns than the question actually requires; once the claim is clear, isolate only the specific rows, columns, or series needed to test it, and set the rest aside.