EliteGMAT
Multi Source Reasoning, Section 5.3
elitegmat.com · Practice, not timed exam conditions

Chapter 5: Multi Source Reasoning

Section 5.3, Note Where Different Types of Information Appear
Teaching Mode
Locating information quickly across tabs, reading tab labels and titles as clues, and combining a passage, a memo, and a chart or table under time pressure. 5 question sets
Worked Example Medium Reading Comprehension Table Analysis Problem Solving
Trial Details · Riverbend Coffee Co., flavor sampling event

Riverbend Coffee Co. ran a one day sampling event across four of its branches, Riverside, Downtown, Harbor, and Uptown, to see how customers responded to three new syrup flavors.

The average weekly customer traffic across the four branches was 20,000 customers, and each branch's actual weekly traffic was within 200 customers of that average.

The trial ran in three stages. First, 1 kilogram of Vanilla Bean syrup was set out for all four branches to sample from. Four hours later, 1 kilogram of Caramel Drizzle syrup was added. Four more hours after that, 2 kilograms of Hazelnut Swirl syrup was added.

At each stage, the four branches used up the entire amount of syrup provided to them.

Usage Charts · share of each syrup flavor used, by branch

The charts show what share of each syrup flavor was used by each of the four branches.

we_pies_main.png
According to the information provided, which of the following values is the greatest?
AThe greatest amount of Vanilla Bean syrup used by any one branch.
BThe total amount of Vanilla Bean and Caramel Drizzle syrup used by the Harbor branch.
CThe greatest amount of Caramel Drizzle syrup used by any one branch.
DThe amount of Hazelnut Swirl syrup used by the Uptown branch.
EThe total amount of Vanilla Bean and Caramel Drizzle syrup used by the Uptown branch.

Full Walkthrough

Before touching any of the five choices, let's get straight on what each tab is actually giving us. Tab 1, Trial Details tells us the total amount of each syrup, 1 kilogram of Vanilla Bean, 1 kilogram of Caramel Drizzle, 2 kilograms of Hazelnut Swirl. Tab 2, Usage Charts tells us what share of each of those totals a given branch used. Neither tab alone gets you a weight in kilograms, you need the total from one tab and the percentage from the other, multiplied together.

Since the question asks for the greatest of five listed values, and every one of those values needs its own multiplication, there's no shortcut that skips checking all five. Guessing based on which slice looks biggest on the chart is risky here, because the three charts represent different sized totals, a big looking slice of the smallest pie can still lose to a modest looking slice of the biggest pie.

Choice A: 0.33 kilograms
The greatest amount of Vanilla Bean syrup used by any one branch.

Vanilla Bean's total is 1 kilogram. Scanning the four Vanilla Bean slices on Tab 2, Downtown's is the largest at 33 percent.

So the biggest single Vanilla Bean value is 0.33 kilograms.

Choice B: 0.48 kilograms
The total amount of Vanilla Bean and Caramel Drizzle syrup used by the Harbor branch.

This one needs two lookups added together, Harbor's Vanilla Bean share and Harbor's Caramel Drizzle share, each against its own 1 kilogram total.

0.18 plus 0.30 comes to 0.48 kilograms.

Choice C: 0.38 kilograms
The greatest amount of Caramel Drizzle syrup used by any one branch.

Caramel Drizzle's total is also 1 kilogram. The largest Caramel Drizzle slice belongs to Uptown, at 38 percent.

That gives 0.38 kilograms, close to choice B but still smaller.

Choice D: 0.64 kilograms, the correct answer
The amount of Hazelnut Swirl syrup used by the Uptown branch.

Here's where the size of the total actually matters. Hazelnut Swirl's total isn't 1 kilogram like the other two flavors, it's 2 kilograms, since Tab 1 tells us twice as much of it was set out. Uptown's slice of that pie is 32 percent.

we_snap_hazelnut_uptown.png

32 percent of a 2 kilogram total is 0.64 kilograms. Because this percentage is being taken of a bigger pot than Vanilla Bean or Caramel Drizzle, a percentage that looks unremarkable on the chart turns into the largest raw weight in the whole list.

Choice E: 0.63 kilograms
The total amount of Vanilla Bean and Caramel Drizzle syrup used by the Uptown branch.

Uptown's Vanilla Bean share is 25 percent of 1 kilogram, and its Caramel Drizzle share is 38 percent of 1 kilogram.

we_snap_vanilla_caramel_uptown.png

0.25 plus 0.38 is 0.63 kilograms. This is the closest competitor to choice D, just one hundredth of a kilogram behind it, which is exactly why eyeballing this question is dangerous. Choice E looks like it should win because it is stacking up two decent sized percentages, but choice D wins because its single percentage is being applied to a much larger total.

Correct answer: D, 0.64 kilograms
Why the others are wrong. A is the largest single Vanilla Bean value, but Vanilla Bean's total is only 1 kilogram, so even its biggest share can't catch up to a strong share of the 2 kilogram Hazelnut Swirl pot. B and C both fall short of D once you actually multiply through, since neither combination beats 0.64. E comes closest of all, at 0.63, but it is still one hundredth of a kilogram short. If you picked E, it's almost certainly because you compared the two percentage figures, 38 plus 25 versus 32, without remembering that Hazelnut Swirl's total is twice the size of the other two totals.
The amount of Hazelnut Swirl syrup used by the Uptown branch was approximately what percent greater than the amount used by the Downtown branch?
A12
B52.4
C37.5
D60
E160

Full Walkthrough

"Percent greater" is a comparison between two specific amounts, not a comparison of the two percentages shown on the pie chart. We need the actual kilogram values for Uptown and Downtown's Hazelnut Swirl usage first, and only then compare them using the percent change idea, where you take the difference between the new and old values and divide by the old value.

It would be tempting to just subtract the chart percentages, 32 minus 20, and call it 12 percent. That skips a step. The chart percentages are shares of the same 2 kilogram total, not percentages of each other, so subtracting them directly doesn't answer what the question is asking.

Finding Uptown's amount

Tab 2, Usage Charts shows Uptown at 32 percent of the Hazelnut Swirl pie, and Tab 1 tells us that pie represents 2 kilograms total.

we_snap_hazelnut_uptown.png

Uptown used 0.64 kilograms.

Finding Downtown's amount

Downtown's slice of the same pie is 20 percent.

we_snap_hazelnut_downtown.png

Downtown used 0.40 kilograms. This is our comparison base, the "old" value in the percent change formula, since the question asks how much greater Uptown is compared to Downtown.

Applying the percent change formula

Percent greater means new minus old, divided by old, times 100. Uptown, 0.64, is the new value. Downtown, 0.40, is the old value, the one we're measuring the increase against.

0.64 minus 0.40 is 0.24. Dividing 0.24 by 0.40 gives 0.6, and multiplying by 100 gives 60 percent.

Correct answer: D, 60 percent
Why A is wrong. 12 comes from subtracting the two chart percentages directly, 32 minus 20. That treats the chart's own percentages as if they were the final answer, but those percentages are shares of the same total, not a comparison of Uptown to Downtown.
Why B is wrong. 52.4 comes from comparing Uptown's amount to the wrong branch, Harbor's Hazelnut Swirl amount instead of Downtown's, which is easy to do if you lose track of which two branches the question named.
Why C is wrong. 37.5 comes from putting the new value in the denominator instead of the old value, dividing the 0.24 difference by 0.64 instead of by 0.40.
Why E is wrong. 160 is what you get from dividing Uptown's amount directly by Downtown's amount and treating that ratio as the answer, without subtracting first. That number tells you Uptown is 1.6 times Downtown's amount, which is a different statement than "60 percent greater."
For each of the following statements, select True if it can be verified to be true based on the information provided. Otherwise, select False.
1 The Downtown and Harbor branches together used most of the Vanilla Bean syrup.
2 Each branch's actual weekly customer traffic was within 1 percent of the average weekly traffic across the four branches.
3 At every stage of the trial, the four branches used the entire amount of syrup provided to them.

Full Walkthrough

All three of these statements can be checked directly against one tab or the other, no combining required. That's worth noticing on its own, since not every MSR question needs the full cross tab treatment, sometimes a single well chosen tab settles the whole thing.

Statement 1: True
The Downtown and Harbor branches together used most of the Vanilla Bean syrup.

"Most" means more than half. So the real question here is whether Downtown's slice plus Harbor's slice of the Vanilla Bean pie clears 50 percent. We don't even need the 1 kilogram total for this one, since we're comparing a share of the whole pie to another share of the same whole pie, the percentages already put everything on the same footing.

we_snap_downtown_harbor_vanilla.png

Downtown's share is 33 percent, and Harbor's share is 18 percent.

33 plus 18 is 51 percent, just over half. So yes, those two branches together used most of the Vanilla Bean syrup.

Correct: True
Why False is wrong here. That would mean either misreading one of the two percentages, or forgetting that 51 percent does clear the 50 percent bar, even though it's a close call.
Statement 2: True
Each branch's actual weekly customer traffic was within 1 percent of the average weekly traffic across the four branches.

This one lives entirely on Tab 1, Trial Details, no chart needed. The tab states the average traffic was 20,000 customers, and each branch's actual traffic was within 200 customers of that average. So the question is just, what percent of 20,000 is 200?

200 divided by 20,000 is exactly 1 percent. The tab's own wording matches the statement precisely.

Correct: True
Why False is wrong here. That would mean not converting 200 out of 20,000 into a percentage, or assuming a made up tolerance instead of using the 200 customer figure the tab actually gives.
Statement 3: True
At every stage of the trial, the four branches used the entire amount of syrup provided to them.

This is a direct factual check against Tab 1, which states plainly that at each stage, the four branches used up the entire amount of syrup provided to them. There's no calculation here at all, just matching the statement's wording to the tab's wording.

Correct: True
Why False is wrong here. That would mean missing the tab's closing sentence, which states this outcome for all three stages without any exception.
Final answer: Statement 1, True. Statement 2, True. Statement 3, True.
Practice Set 1 Medium Table Analysis Graphics Interpretation Problem Solving
Trial Setup · Northgate Transit Authority, night bus ridership survey

Northgate Transit Authority surveyed 1,800 commuters about whether they had used the night bus service in the past year. Of those surveyed, 1,200 said they had never used it.

The 1,200 who had never used the night bus were then asked whether they would consider using it in the next three months. Their responses are shown below.

Would consider Would not consider
400 800

The 400 commuters who said they would consider using the night bus are called Group C, and the 800 who said they would not are called Group D.

Trial Design · six week ridership trial

Group C and Group D were each randomly split into 4 equal subgroups. For the next six weeks, each subgroup received a different treatment:

• Free night fares

• A printed route map mailed to their home

• Both free fares and a mailed route map

• Neither treatment

The trial covered weeknights only. Weekend ridership was excluded from all counts reported after the trial.

Six Week Results · percent of each subgroup by riding outcome

The chart shows, for each subgroup, the percent who rode the night bus weekly, the percent who rode occasionally, and the percent who did not ride at all during the six week trial.

set1_tab3_stackedbar.png
How many people in Group C rode the night bus at least once during the six week trial?
A100
B161
C173
D227
E322

Full Walkthrough

"At least once" covers two of the three outcomes shown on the chart, riding weekly and riding occasionally. Only "did not ride" is excluded. So for each of Group C's four subgroups, we need to add the weekly percentage and the occasional percentage together, then apply that combined percentage to the subgroup's actual size.

Before any of that math happens, we need the subgroup size itself, and that comes from combining two other tabs. Tab 1, Trial Setup tells us Group C has 400 people. Tab 2, Trial Design tells us Group C was split into 4 equal subgroups. Only after dividing 400 by 4 do the chart's percentages on Tab 3 mean anything in terms of actual people.
Finding the subgroup size

Group C has 400 people, straight from the tab 1 table.

snap01_s1_tab1_groupC.png

400 people split into 4 equal subgroups means each subgroup has 100 people.

Adding weekly and occasional riders in each subgroup
snap02_s1_groupC_rode.png

Free fares: 32 percent rode weekly and 41 percent rode occasionally, 73 percent combined. Route map: 14 plus 29 is 43 percent. Both treatments: 45 plus 33 is 78 percent. Neither treatment: 9 plus 24 is 33 percent.

Applying each of those combined percentages to the 100 person subgroup gives 73, 43, 78, and 33 people.

Adding those four subgroup counts together gives the total for all of Group C.

Correct answer: D, 227
Why A, 100, is wrong. This comes from adding only the four weekly percentages applied to their subgroups, 32, 14, 45, and 9, and forgetting to include anyone who rode occasionally.
Why B, 161, is wrong. This comes from reading Group D's percentages on the chart instead of Group C's, then applying them to Group C's 100 person subgroups. It's an easy mix up since Group C and Group D sit side by side on the same chart.
Why C, 173, is wrong. This is the mirror image of the correct answer, the number of Group C people who did not ride at all, 27 plus 57 plus 22 plus 67. It's what you'd get if you answered "how many never rode" instead of "how many rode at least once."
Why E, 322, is wrong. This is Group D's total number of people who rode at least once, using Group D's own 200 person subgroups. It answers a real question, just not the one this question asked.
In Group D, the number of people in the "both treatments" subgroup who rode weekly was approximately what percent greater than the number of people in the "free fares" subgroup who rode weekly?
A8
B30.8
C44.4
D61.1
E144.4

Full Walkthrough

This is a percent greater question, which means we need two actual head counts first, not just the two chart percentages. Percent greater is calculated as the difference between the new and old amounts, divided by the old amount, then multiplied by 100. Here, "both treatments" is the amount we're checking, and "free fares" is the baseline we're checking it against.

Just like the last question, the chart percentages by themselves don't answer anything. Group D's subgroup size has to come from Tab 1's 800 people divided by Tab 2's 4 equal subgroups before Tab 3's percentages turn into real numbers.
Finding Group D's subgroup size

800 divided by 4 is 200 people per subgroup.

Both treatments, weekly riders
snap03_s1_D_both_weekly.png

The chart shows 26 percent of the both treatments subgroup rode weekly.

That's 52 people.

Free fares, weekly riders
snap04_s1_D_free_weekly.png

The chart shows 18 percent of the free fares subgroup rode weekly.

That's 36 people, our comparison baseline.

Applying the percent greater formula

52 is the new value, 36 is the old value we're measuring against.

52 minus 36 is 16. Dividing 16 by 36 and multiplying by 100 gives approximately 44.4 percent.

Correct answer: C, approximately 44.4 percent
Why A, 8, is wrong. That's just the raw percentage point gap on the chart, 26 minus 18, mistaken for a percent greater figure. The chart's percentages are shares of two different subgroup totals converted to the same 100 point scale, not directly comparable by subtraction.
Why B, 30.8, is wrong. This comes from putting the new value, 52, in the denominator instead of the old value, dividing 16 by 52 instead of by 36.
Why D, 61.1, is wrong. This comes from picking the wrong pair of subgroups to compare, mixing up which chart segment belongs to which treatment.
Why E, 144.4, is wrong. This is the plain ratio of the two values, 52 divided by 36, expressed as a percentage. That number tells you Group D's both treatments subgroup rode at 1.444 times the rate of the free fares subgroup, which is a different statement than "44.4 percent greater."
For each of the following statements, select True if it can be verified to be true based on the information provided. Otherwise, select False.
1 More people rode weekly in the Group D both treatments subgroup than in the Group C both treatments subgroup.
2 Most of the people in Group D rode at least once during the trial.
3 The results shown in the six week results chart include rides that Group C members took on weekends.

Full Walkthrough

All three of these statements draw on more than one tab, which is worth noticing since it's easy to assume a chart heavy question set only needs the chart.

Statement 1: True
More people rode weekly in the Group D both treatments subgroup than in the Group C both treatments subgroup.

This statement is comparing actual head counts across two groups, not percentages, so the trap here is stopping at the chart and comparing 26 percent against 45 percent, seeing Group C's percentage is higher, and calling the statement false without ever converting to people.

snap05_s1_both_compare.png

Group C's both treatments subgroup has 100 people, and 45 percent of them rode weekly, which is 45 people. Group D's both treatments subgroup has 200 people, twice as many, and 26 percent of them rode weekly.

52 is greater than 45, so more people really did ride weekly in Group D's both treatments subgroup, even though its percentage was lower. The larger subgroup size more than makes up for the smaller percentage.

Correct: True
Why False is wrong here. That's the trap of comparing the two percentages directly, 26 percent against 45 percent, without ever converting either one into an actual number of people using the subgroup sizes from Tab 1 and Tab 2.
Statement 2: False
Most of the people in Group D rode at least once during the trial.

"Most" means more than half of Group D's 800 people, which is more than 400. So we need Group D's full at least once total across all four subgroups, the same weekly plus occasional addition from question 1, but for Group D's percentages instead of Group C's.

snap06_s1_groupD_rode.png

Free fares: 18 plus 27 is 45 percent. Route map: 11 plus 21 is 32 percent. Both: 26 plus 35 is 61 percent. Neither: 7 plus 16 is 23 percent.

Applying those to the 200 person subgroups gives 90, 64, 122, and 46 people.

322 is less than 400, so it is not most of Group D, it's only about 40 percent.

Correct: False
Why True is wrong here. That would mean either miscounting one of the four subgroups, or stopping after checking just the "both treatments" subgroup, where 61 percent does look like a majority, without checking the other three subgroups where ridership was much lower.
Statement 3: False
The results shown in the six week results chart include rides that Group C members took on weekends.

This one doesn't need any chart reading at all, it's a direct check against a sentence on Tab 2, Trial Design, which states plainly that the trial covered weeknights only, and that weekend ridership was excluded from every count reported after the trial.

Correct: False
Why True is wrong here. That would mean missing Tab 2's exclusion sentence, or assuming a six week trial must include weekends just because most six week spans naturally do.
Final answer: Statement 1, True. Statement 2, False. Statement 3, False.
Practice Set 2 Medium Reading Comprehension Table Analysis Problem Solving
Program Background · Fernwood Middle School, district nutrition office

For years, Fernwood Middle School noticed that a large share of its students skipped breakfast, and staff worried this was hurting focus during first period classes. Last spring, the district's nutrition coordinator surveyed 900 students and found that 540 had not eaten a school provided breakfast at all during the previous term.

District nutrition staff proposed two competing explanations for this pattern. One group of staff argued that students skipped breakfast mainly because they doubted it would actually help their schoolwork, and that a persuasion campaign explaining the benefits would fix the problem. A second group argued that the deeper issue was simply forgetfulness and inconvenient timing, not doubt, and that practical reminders would work better than a persuasion campaign. This second group predicted that reminders alone would outperform persuasion alone if the two were ever tested side by side.

District leadership designed a small study to test both theories before committing to a district wide program. Of the 540 students who had not eaten breakfast, 180 said they would be willing to try some kind of support program, and 360 said they would not.

The 180 willing students are called Group W, and the 360 unwilling students are called Group U.

Even the strongest results from this study came with a caveat. The coordinator noted that the study ran during a single term, and that any effects seen might fade once the novelty of the new outreach wore off.

Study Arms · program design and definitions

Group W and Group U were each randomly split into 3 equal arms. Over the course of Term 1 and Term 2, each arm received a different form of outreach: reminder texts sent to a student's phone before the school day, a peer buddy assigned to walk with the student to the cafeteria, or both reminder texts and a peer buddy together.

Definition. A student is counted as achieving "regular attendance" in a given term only if that student ate a school breakfast on at least 4 of the 5 school days in a typical week during that term. A student who ate breakfast less often than that, even occasionally, does not meet the regular attendance standard.

Term Results · attendance outcomes by group and arm

The table shows, for each arm within Group W and Group U, the percent of students who achieved regular attendance, the percent who attended occasionally but did not meet the regular standard, and the mean number of days per week the arm attended, with the standard deviation shown in parentheses.

set2_tab3_table.png
How many students in Group U's peer buddy arm achieved regular attendance in Term 2?
A18
B24
C36
D42
E108

Full Walkthrough

The Term Results table gives us a percentage, not a headcount, so before that percentage means anything we need the actual size of Group U's peer buddy arm. That size isn't sitting anywhere on Tab 3 itself, it has to be built from the other two tabs.

Tab 1, Program Background gives us Group U's total, 360 students. Tab 2, Study Arms tells us Group U was split into 3 equal arms. Dividing first is the only way the table's percentage turns into a real number of students, jumping straight to the percentage and guessing a base would just be guessing.
Finding the arm size

360 students split into 3 equal arms means each arm has 120 students.

Reading the correct cell
snap07_s2_U_peer_t2.png

Cross referencing Group U's row with the peer buddy arm and the Term 2 column, the regular attendance figure is 30 percent.

Correct answer: C, 36
Why A, 18, is wrong. This comes from applying 30 percent to Group W's arm size, 60, instead of Group U's arm size, 120. Both groups have 3 equal arms, but the two groups aren't the same size, so their arm sizes differ too.
Why B, 24, is wrong. This is 20 percent of 120, which is Term 1's regular attendance figure for this same arm, not Term 2's. The question specifically asks about Term 2.
Why D, 42, is wrong. This is 35 percent of 120, which is the occasional attendance percentage for this cell, not the regular attendance percentage. Occasional attendance does not meet the Tab 2 definition of regular attendance.
Why E, 108, is wrong. This comes from applying 30 percent to the whole of Group U, 360 students, instead of just the one arm within Group U that this question is asking about.
Combining Group W and Group U, which study arm produced the greatest total number of students achieving regular attendance in Term 2?
APeer buddy, Group W alone
BTexts and buddy, Group U alone
CTexts and buddy, combined across both groups
DPeer buddy, combined across both groups
EReminder texts, combined across both groups

Full Walkthrough

This question is about total people, not the highest percentage. Since Group W and Group U are different sizes, sixty students per arm against a hundred twenty students per arm, the arm with the single highest percentage on the table doesn't automatically win once you're counting actual students. The only reliable approach is to convert every arm's percentage into a headcount, for both groups, and add each arm's two headcounts together before comparing.

It's tempting to scan the Term 2 column for the biggest percentage and stop there. That number, 85 percent, belongs to Group W's peer buddy arm. But Group W's arms only have 60 students each, while Group U's arms have 120. A high percentage of a small arm can easily lose to a more modest percentage of a larger one, so the percentage alone can't settle this.
Reminder texts, combined

Group W's reminder texts arm, 60 percent of 60 students. Group U's reminder texts arm, 35 percent of 120 students.

36 plus 42 is 78 students combined.

Peer buddy, combined
snap09_s2_pct_vs_count.png

Group W's peer buddy arm shows the highest single percentage on the whole table, 85 percent of 60 students. Group U's peer buddy arm is 30 percent of 120 students.

51 plus 36 is 87 students combined, a strong number, but notice it's driven mostly by Group W's small arm hitting a very high percentage.

Texts and buddy, combined
snap08_s2_t2_regular_col.png

Group W's texts and buddy arm is 70 percent of 60 students. Group U's texts and buddy arm is 55 percent of 120 students.

42 plus 66 is 108 students combined, the largest of the three totals, even though neither individual percentage in this row was the highest on the table.

Correct answer: C, Texts and buddy, combined across both groups
Why A is wrong. Group W's peer buddy arm alone, 51 students, is only Group W's contribution. It leaves out Group U's peer buddy students entirely, and 51 is smaller than the texts and buddy combined total anyway.
Why B is wrong. Group U's texts and buddy arm alone, 66 students, is only half the picture. Adding Group W's 42 students from that same arm is what actually gets you to the correct total of 108.
Why D is wrong. Peer buddy's combined total, 87, is respectable, and it's the arm with the single highest percentage on the table, which is exactly why it's a tempting choice. But 87 is still less than texts and buddy's 108 once both groups are actually added together.
Why E is wrong. Reminder texts, at 78 combined, is the lowest of the three arm totals, not the highest.
For each of the following statements, select True if it can be verified to be true based on the information provided. Otherwise, select False.
1 In Term 2, most Group U students in the reminder texts arm ate breakfast on at least four of five school days.
2 In Term 2, the arm with the highest mean days per week also had the least variation in days attended.
3 The staff who favored the reminder based explanation predicted that reminders alone would outperform persuasion alone.

Full Walkthrough

These three statements pull from three different places, a table cell, two table columns, and the argument laid out in the background passage.

Statement 1: False
In Term 2, most Group U students in the reminder texts arm ate breakfast on at least four of five school days.

"At least four of five school days" is the exact wording Tab 2, Study Arms uses to define regular attendance. So this statement is really just asking, does the regular attendance percentage for this cell clear 50 percent?

snap10_s2_definition_row.png

The Term 2 regular attendance figure for Group U, reminder texts, is 35 percent. The occasional attendance figure sitting right beside it is 30 percent. Adding those two together gives 65 percent, which might look like "most students attended somewhat regularly," but occasional attendance does not satisfy the four of five days standard that Tab 2 defines. Only the 35 percent regular figure counts toward this statement.

35 percent is well under half.

Correct: False
Why True is wrong here. That's the trap of adding regular and occasional together, 35 plus 30, and treating 65 percent as if it satisfied "at least four of five days." Occasional attendance is a different, looser category that Tab 2 explicitly does not count as regular.
Statement 2: False
In Term 2, the arm with the highest mean days per week also had the least variation in days attended.

This statement is comparing two different columns, the mean days column and the standard deviation column, and asking whether the same single cell tops one list and bottoms the other.

snap11_s2_t2_mean_sd.png

Scanning the Term 2 mean days column, the highest figure is 4.6 days, belonging to Group W's peer buddy arm. Scanning the Term 2 standard deviation column, the lowest figure is 0.5, belonging to Group W's texts and buddy arm. Those are two different cells.

Correct: False
Why True is wrong here. That would mean only checking the highest mean cell's own standard deviation, 0.9, and assuming it must also be the lowest in the column without actually scanning the rest of the column to find that 0.5 is lower still.
Statement 3: True
The staff who favored the reminder based explanation predicted that reminders alone would outperform persuasion alone.

This statement doesn't need any arithmetic at all, it's a direct paraphrase check against Tab 1, Program Background's description of the second staff group's position.

Tab 1 states that the second group argued forgetfulness and timing, not doubt, were the real problem, and that practical reminders would work better than a persuasion campaign, and specifically that this group predicted reminders alone would outperform persuasion alone if the two were ever tested side by side. That's exactly what the statement says, just restated.

Correct: True
Why False is wrong here. That would mean missing the specific sentence in Tab 1 describing what the reminder focused staff group predicted, or confusing that group's position with the first group's persuasion based argument.
Final answer: Statement 1, False. Statement 2, False. Statement 3, True.
Practice Set 3 Hard Table Analysis Graphics Interpretation Problem Solving
First Contact Log · Larkspur Community Clinic, dated 3 March

Larkspur Community Clinic contacted 2,400 residents to check seasonal vaccination status. Of those contacted, 1,440 had not received the seasonal vaccine.

Those 1,440 unvaccinated residents were asked whether they would consider receiving the vaccine if the clinic followed up. Their responses are shown below.

Would consider Would not consider
480 960

The 480 residents who said they would consider it are called Group R, and the 960 who said they would not are called Group S.

From: Outreach Coordination
To: Clinic Staff
Date: 9 March
Subject: Outreach Plan for Group R and Group S

Group R and Group S will each be split into 3 equal arms. Each arm will receive one of three outreach methods: a home visit, a phone campaign, or a mailed voucher.

Note that the mailed voucher arm's results should be read as a proportion of residents who were actually reachable in that arm, since a portion of that arm could not be reached by mail at their listed address.

From: Outreach Coordination
To: Clinic Staff
Date: 22 March
Subject: Revised Outreach Plan and Final Results

Due to the mailed voucher method's poor reach, that arm was discontinued after week two for both groups. Members of Group R's mailed voucher arm were all reassigned to the home visit method. Members of Group S's mailed voucher arm were split evenly between the home visit and phone campaign methods.

Final outcomes for the two remaining methods, home visit and phone campaign, are shown below. Each pie shows the share of that arm's final membership who were vaccinated, scheduled for a future appointment, declined the vaccine, or could not be reached at all.

set3_tab3_pies.png
How many residents in Group R's final home visit arm were vaccinated?
A68
B136
C224
D204
E44

Full Walkthrough

The word "final" in this question is doing real work, and it's the reason this question needs all three tabs read in order, not just the two that seem to have numbers on them.

It would be easy to take Tab 2, Outreach Plan's 3 equal arms at face value and stop there. But Tab 3, Revised Plan and Results, dated two weeks after Tab 2, tells us the arms changed partway through. Since Tab 3 is the more recent memo and it specifically revises the arm sizes, its numbers are what "final" refers to, not Tab 2's original 3 way split.
Starting point from Tab 1 and Tab 2

Group R has 480 residents, straight from the tab 1 table.

snap12_s3_tab1_groupR.png

Tab 2 splits that into 3 equal arms.

So originally, home visit, phone campaign, and mailed voucher each had 160 residents.

Applying the revision from Tab 3

Tab 3 states that Group R's entire mailed voucher arm, all 160 residents, was reassigned to home visit, and that phone campaign was left alone.

Group R's final home visit arm has 320 residents, twice its original size.

Reading the pie chart
snap13_s3_R_home_vacc.png

The home visit, Group R pie shows 42.5 percent vaccinated.

Correct answer: B, 136
Why A, 68, is wrong. This applies the correct 42.5 percent to the original Tab 2 arm size of 160, stopping before the Tab 3 revision is applied. This is the single tab sufficiency trap in reverse, looking like a complete answer while actually skipping the most recent information.
Why C, 224, is wrong. This adds the vaccinated and scheduled slices of the pie together, 42.5 plus 32.5 percent, applied to the correct 320 arm size. Scheduled residents have not yet been vaccinated, so they don't belong in this count.
Why D, 204, is wrong. This applies 42.5 percent to the whole of Group R, 480, rather than just the home visit arm within Group R.
Why E, 44, is wrong. This reads the phone campaign pie's vaccinated slice, 27.5 percent, instead of the home visit pie's, and applies it to the phone campaign arm's final size of 160.
The number of Group R residents vaccinated through the home visit method was approximately what percent greater than the number of Group S residents vaccinated through the home visit method?
A21.4
B38.2
C61.9
D161.9
E25.0

Full Walkthrough

Just like question 1, this needs the final, revised arm sizes for both groups, and the revision affected Group R and Group S differently, which is exactly what makes this version of the question harder than it first looks.

Tab 3 states Group R's mailed voucher arm went entirely into home visit, but Group S's mailed voucher arm split evenly between home visit and phone campaign. Because the two groups' arms grew by different amounts, a comparison using Tab 2's original equal arms would give a completely different, and wrong, percentage than a comparison using Tab 3's final arms.
Group R's final home visit arm

As found in question 1, Group R's home visit arm absorbed its entire 160 person voucher arm, landing at 320 residents, and 42.5 percent of that arm was vaccinated.

snap13_s3_R_home_vacc.png

136 residents.

Group S's final home visit arm

Group S starts with 960 residents, 3 equal arms of 320 each. Its voucher arm split evenly between home visit and phone campaign, meaning half of 320, or 160, joined home visit.

Group S's final home visit arm has 480 residents. The home visit, Group S pie shows 17.5 percent vaccinated.

snap15_s3_S_home_vacc.png

84 residents, our comparison baseline.

Applying the percent greater formula

136 is the new value, 84 is the old value.

136 minus 84 is 52. Dividing 52 by 84 and multiplying by 100 gives approximately 61.9 percent.

Correct answer: C, approximately 61.9 percent
Why A, 21.4, is wrong. This uses Tab 2's original, unrevised arm sizes for both groups, 160 for Group R and 160 for Group S, before either group's voucher arm was reassigned. Since the trap in this question is exactly that the two groups' arms didn't grow by the same amount, this decoy quietly erases that difference and lands on the wrong percentage.
Why B, 38.2, is wrong. This divides the 52 person difference by the new value, 136, instead of the old value, 84.
Why D, 161.9, is wrong. This is the plain ratio of 136 to 84 expressed as a percentage, which tells you Group R vaccinated about 1.619 times as many people as Group S through this method, not "61.9 percent greater."
Why E, 25.0, is wrong. This is the raw percentage point gap between the two pie charts, 42.5 minus 17.5, mistaken for a percent greater figure, without ever converting either percentage into an actual headcount.
For each of the following statements, select True if it can be verified to be true based on the information provided. Otherwise, select False.
1 More Group R residents received a home visit than received a phone campaign contact.
2 Most residents in the Group S home visit arm were either vaccinated or scheduled for a future appointment.
3 Exactly 32 residents in Group R's final home visit arm were recorded as unreachable.

Full Walkthrough

Every statement in this grid depends on catching the 22 March revision. This is deliberate, since the whole teaching point of this set is that a later, dated memo can override an earlier one, and answer keys need to name exactly which memo each step is using.

Statement 1: True
More Group R residents received a home visit than received a phone campaign contact.

Under Tab 2, dated 9 March alone, home visit and phone campaign were equal, 160 residents each, since all three original arms were the same size. A student who stops at Tab 2 would answer this statement false.

But Tab 3, dated 22 March, is the more recent memo, and it states Group R's entire voucher arm moved into home visit, while phone campaign was left untouched.

320 is greater than 160, so the statement holds once the most recent information is used.

Correct: True
Why False is wrong here. That's the trap of stopping at Tab 2's original equal split and never checking whether a later memo changed anything.
Statement 2: False
Most residents in the Group S home visit arm were either vaccinated or scheduled for a future appointment.

"Most" means more than half, and since vaccinated and scheduled are both shares of the same pie, we can check this directly against the percentages without needing the arm's actual size at all.

snap16_s3_S_vacc_sched.png

The home visit, Group S pie shows 17.5 percent vaccinated and 22.5 percent scheduled.

40 percent is under half.

Correct: False
Why True is wrong here. That would mean misreading one of the two slices, or perhaps including the declined slice by mistake, since declined plus vaccinated does happen to clear 50 percent even though the statement never asked about declined residents.
Statement 3: True
Exactly 32 residents in Group R's final home visit arm were recorded as unreachable.

This one needs the same final arm size from question 1, 320 residents, combined with the unreachable slice of the home visit, Group R pie.

snap17_s3_R_unreachable.png

That slice is 10 percent.

10 percent of 320 is exactly 32, matching the statement precisely.

Correct: True
Why False is wrong here. That would mean applying the 10 percent figure to the original Tab 2 arm size of 160 instead of the revised 320, which gives 16, not 32, and would make this statement look false when it is actually true.
Final answer: Statement 1, True. Statement 2, False. Statement 3, True.
Practice Set 4 Hard Graphics Interpretation Table Analysis Problem Solving
Trial Population · Halvorsen Aquaculture, feed response study

Halvorsen Aquaculture tracked 5,600 fish across two ponds. At the start of the trial, 3,360 of those fish were below their target weight for their age.

Those 3,360 fish were split into two groups based on how they had responded to earlier feed adjustments.

Responsive (Group L) Non responsive (Group M)
1,120 2,240

Group L had responded to prior feed changes, and Group M had not.

Feed Protocols · cohort design and daily dosing

Group L and Group M were each split into 4 equal cohorts. Each cohort received a different daily feed dose, measured in grams per fish per day:

• Cohort 1: 2.0 grams per fish per day

• Cohort 2: 3.0 grams per fish per day

• Cohort 3: 4.0 grams per fish per day

• Cohort 4: 5.0 grams per fish per day

The trial ran for eight weeks, with fish weighed weekly.

Eight Week Outcomes · target weight results and growth over time

The scatterplot shows, for each cohort, the daily feed dose against the percent of that cohort that reached target weight by the end of the trial.

set4_tab3_scatter.png

The line chart shows mean fish weight across the eight week trial, tracked separately by pond and by group.

set4_tab3_lines.png
How many fish in Group M's Cohort 3 reached target weight by the end of the trial?
A126
B252
C392
D1,008
E280

Full Walkthrough

The scatterplot gives us a percentage for each cohort, plotted against that cohort's feed dose. To turn that percentage into an actual fish count, we need the cohort's size, which comes from combining the other two tabs.

Tab 1, Trial Population gives Group M's total, 2,240 fish. Tab 2, Feed Protocols tells us Group M was split into 4 equal cohorts. Only after dividing does the scatterplot's percentage turn into a real number of fish.
Finding the cohort size

Group M has 2,240 fish, straight from the tab 1 table.

snap18_s4_tab1_groupM.png

2,240 fish split into 4 equal cohorts means each cohort has 560 fish.

Reading the scatterplot
snap19_s4_scatter_M3.png

Group M's Cohort 3 point sits at a dose of 4 grams per fish per day, and its height on the vertical axis shows 45 percent reached target weight.

Correct answer: B, 252
Why A, 126, is wrong. This applies the correct 45 percent to Group L's cohort size, 280, instead of Group M's, 560. Group L and Group M have the same number of cohorts, but the cohorts themselves aren't the same size, since the two groups started at different sizes.
Why C, 392, is wrong. This reads Group L's Cohort 3 point, 70 percent, instead of Group M's, and applies it to Group M's correct cohort size, 560.
Why D, 1,008, is wrong. This applies 45 percent to the entire Group M population, 2,240, rather than just the one cohort within Group M that the question asks about.
Why E, 280, is wrong. This reads Group M's Cohort 4 point, 50 percent, instead of Cohort 3's 45 percent, an easy mix up on a scatterplot where the cohorts aren't laid out as separate labeled bars the way they would be on a bar chart.
How many kilograms of feed did Group M's Cohort 3 consume in one week?
A2.24
B7.84
C11.76
D15.68
E19.6

Full Walkthrough

Notice something important about this question before doing any arithmetic. It never touches the scatterplot or the line chart at all. Tab 2, Feed Protocols gives the daily dose, and the same 560 fish cohort size from question 1 gets us the rest of the way. Tab 3 is simply not needed here, and part of building good MSR instincts is noticing when a tab you'd expect to use turns out to be irrelevant to the specific question in front of you.

The real difficulty here is a unit mismatch, not a missing tab. Tab 2 states the dose in grams per fish per day. This question asks for kilograms per week. Both a unit conversion, grams to kilograms, and a time conversion, one day to seven days, have to happen, and it's easy to do one and forget the other.
Cohort size and daily dose

Group M's Cohort 3 has 560 fish, and Tab 2 sets its dose at 4.0 grams per fish per day.

2,240 grams per day for the whole cohort.

Scaling to a full week

One week is seven days, so we multiply the daily total by 7.

15,680 grams per week.

Converting grams to kilograms

There are 1,000 grams in a kilogram, so we divide by 1,000.

Correct answer: D, 15.68 kilograms
Why A, 2.24, is wrong. This stops after finding the daily total in grams, 2,240, and converts straight to kilograms, 2.24, without ever multiplying by 7 for the week. It answers "how many kilograms per day," not per week.
Why B, 7.84, is wrong. This uses Group L's cohort size, 280, instead of Group M's, 560, while still applying Cohort 3's correct 4.0 gram dose and the correct weekly and kilogram conversions.
Why C, 11.76, is wrong. This uses Cohort 2's dose, 3.0 grams, instead of Cohort 3's, again with the rest of the calculation done correctly.
Why E, 19.6, is wrong. This uses Cohort 4's dose, 5.0 grams, instead of Cohort 3's 4.0 grams. Both C and E show how easy it is to grab the wrong row from Tab 2's dose list once you're juggling a unit conversion at the same time.
For each of the following statements, select True if it can be verified to be true based on the information provided. Otherwise, select False.
1 Most of the Group L fish that began below target weight reached target weight by the end of the trial.
2 Group L's Cohort 1 consumed more than 4 kilograms of feed per week.
3 Pond B Group L began the trial with a lower mean weight than Pond A Group M, but ended the trial with a higher mean weight than Pond A Group M.

Full Walkthrough

These three statements draw on the scatterplot, the feed dose list, and the line chart in turn, and the second one hides the same unit mismatch that question 2 already warned us about.

Statement 1: True
Most of the Group L fish that began below target weight reached target weight by the end of the trial.

"Most" means more than half of Group L's 1,120 fish, so more than 560. Since Tab 2 tells us all four of Group L's cohorts are the same size, there's a shortcut available here, we can average the four scatterplot percentages directly instead of converting each one to a fish count and adding.

snap20_s4_scatter_L_all.png

Group L's four cohort percentages are 35, 55, 70, and 75.

58.75 percent is above half, so more than half of Group L reached target weight. Converting to actual fish confirms it, 98 plus 154 plus 196 plus 210 comes to 658 fish out of 1,120, comfortably over half.

Correct: True
Why False is wrong here. That would mean either misreading one of the four scatterplot points, most likely swapping a Group L point for its lower Group M counterpart at the same dose, or stopping after checking just Cohort 1's 35 percent and assuming the rest of the group looked similar.
Statement 2: False
Group L's Cohort 1 consumed more than 4 kilograms of feed per week.

This is the same gram to kilogram, day to week conversion from question 2, applied to a different cohort. Cohort 1's dose is 2.0 grams per fish per day, and Group L's Cohort 1 has 280 fish.

3.92 kilograms per week, which is under 4, not over it.

Correct: False
Why True is wrong here. That's the trap of multiplying 2.0 grams by 280 fish and seeing 560, a number bigger than 4, and stopping there without ever converting from grams to kilograms or from one day to a full week. 560 grams per day is not the same thing as more than 4 kilograms per week.
Statement 3: True
Pond B Group L began the trial with a lower mean weight than Pond A Group M, but ended the trial with a higher mean weight than Pond A Group M.

This statement is about a crossing point between two of the four lines on the growth chart, so it needs two specific weeks checked, not the whole eight week span.

snap21_s4_line_crossing.png

At week 0, Pond B Group L starts at 172 grams, while Pond A Group M starts at 175 grams, so Pond B Group L begins lower.

At week 8, Pond B Group L ends at 302 grams, while Pond A Group M ends at 258 grams, so Pond B Group L finishes higher.

Correct: True
Why False is wrong here. That would mean checking only one end of the chart, either week 0 or week 8 alone, and assuming whichever relationship held at that single point held for the whole trial, when the two lines actually cross partway through.
Final answer: Statement 1, True. Statement 2, False. Statement 3, True.
Calculator
0
Mouse only, enable Teaching Mode for keyboard