24-Hour Crash Course Verbal Section

Hour 13 of 24

CR – Inference & Paradox

Progress 13 / 24 hours complete

54% of the crash course complete — you are past the halfway mark.

What You'll Learn This Hour

Core Concepts

Inference (Must Be True)

The correct answer must follow with 100% certainty from the information given in the stimulus. It cannot merely be possible, probable, or reasonable — it must be absolutely guaranteed.

  • Treat stimulus facts as true premises
  • The answer is a logical consequence, not speculation
  • Watch for absolute language: "all," "never," "must"
  • Eliminate anything that goes beyond the stated info

Bold Face

Two statements in the passage appear in bold. Your task is to identify the logical role each bold statement plays — not whether you agree with it.

  • Is it the main conclusion, an intermediate conclusion, or a premise?
  • Does it support or undermine the argument?
  • Is it a background fact or a counterargument?
  • Ignore content — focus on structural function

Paradox / Explain

The stimulus presents two facts that seem to contradict each other. The correct answer must resolve the apparent contradiction by making both facts simultaneously true and logical.

  • Identify BOTH contradictory facts precisely
  • The answer must address both facts — not just one
  • An answer that explains only one fact is a trap
  • New information is always introduced in the answer

Evaluate

Find the piece of information that would most help assess whether the argument's conclusion is valid. Use the "Variance Test": if YES would strengthen and NO would weaken (or vice versa), it is the right answer.

  • Identify the gap between premises and conclusion
  • Ask: "Would knowing this change my verdict?"
  • Apply the Variance Test on every answer choice
  • Eliminate answers that are irrelevant to the gap

Visual Frameworks

Inference: The "Must Be True" Zone

The correct inference answer must live inside the smaller circle — guaranteed by the facts, not merely possible.

Could Be True (large area) Must Be True Correct answers here

Answers in the outer region only (possible but not certain) are wrong — classic GMAT trap.

Paradox: The Resolution Framework

Two contradictory facts must both remain true. The correct answer provides a bridge that makes both facts logically compatible.

FACT A Sales increased by 20% FACT B Profit fell by 15% ? EXPLANATION Costs rose sharply due to new factory, offsetting revenue Resolves

The explanation must make BOTH facts true simultaneously — partial explanations are wrong.

Worked Examples

INFERENCE Worked Example 1
"All employees at Nexora Corp who work in the engineering department hold advanced degrees. Some employees with advanced degrees earn more than $120,000 annually. No employee who earns less than $80,000 works in the engineering department."

Which of the following must be true based on the statements above?

(A)All engineering employees earn more than $120,000.
(B)Some employees at Nexora earn less than $80,000.
(C)All engineering employees earn at least $80,000.
(D)Some employees with advanced degrees work in engineering.
(E)No employee without an advanced degree earns more than $80,000.

Answer: (C) — Step-by-Step Solution

Fact 1: All engineering employees have advanced degrees.

Fact 3: No employee earning <$80k works in engineering. This means: if you work in engineering, you earn $80k or more (contrapositive).

Logic chain: Engineering employee → earns ≥ $80k. This is 100% guaranteed by Fact 3.

Why others fail: (A) goes too far — some may earn exactly $90k, not over $120k. (B) is not stated. (D) is possible but not certain — "some" is not guaranteed. (E) adds a restriction about non-engineering employees not found in the stimulus.

PARADOX Worked Example 2
"The Midvale Public Library reduced its book inventory by 40% last year, donating or discarding thousands of volumes. Yet the number of books borrowed by library patrons increased by 25% over the same period."

Which of the following, if true, best explains the apparent paradox?

(A)The library hired additional staff to assist patrons.
(B)Several nearby libraries also reduced their collections.
(C)The library replaced its physical inventory with a large digital e-book collection that patrons can borrow remotely.
(D)The library extended its operating hours by two hours per day.
(E)The library's most popular titles were among those discarded.

Answer: (C) — Step-by-Step Solution

Paradox: Fewer physical books yet MORE borrowing.

Why (C) works: If physical books were replaced by e-books, there can be fewer physical volumes but substantially more borrowing (digital loans). This reconciles BOTH facts — inventory fell (physical) and loans rose (digital).

Why others fail: (A) explains possible efficiency but not why borrowing increased when inventory fell. (B) worsens the paradox. (D) only addresses one side — hours alone don't explain borrowing rising when inventory dropped. (E) actively deepens the paradox.

BOLD FACE Worked Example 3
Studies show that cities with congestion-pricing programs have reduced traffic by an average of 22%. Critics argue that such programs unfairly burden low-income commuters who cannot afford to pay the toll. However, revenues from congestion pricing consistently fund expanded public transit, which disproportionately benefits lower-income residents. Therefore, congestion pricing ultimately improves equity.

The two boldfaced statements play which of the following roles in the argument above?

(A)The first is the main conclusion; the second supports a counterargument.
(B)The first is background evidence; the second is a premise that supports the main conclusion against a counterargument.
(C)The first supports the conclusion; the second is the conclusion.
(D)Both are premises that directly support the main conclusion.
(E)The first undermines the conclusion; the second is a concession.

Answer: (B) — Step-by-Step Solution

Main conclusion: "congestion pricing ultimately improves equity" — stated at the end.

First bold statement: Gives traffic data — it is background/contextual evidence, not the main argument for equity.

Second bold statement: Directly rebuts the critic's counterargument (unfair burden) by showing transit benefits flow to low-income residents, thereby supporting the equity conclusion.

Tip: The conclusion is "congestion pricing improves equity" — the second bold statement explicitly refutes the counterargument, making it a premise in the main argument chain.

GMAT Traps to Avoid

Inference Trap: "Could Be True" vs. "Must Be True"

The GMAT frequently offers answers that are reasonable, possible, or even likely — but not 100% certain. If you can imagine a scenario where the answer is false (even a very unlikely scenario), it is wrong. The correct inference must be impossible to disprove given the stated facts.

Paradox Trap: Explaining Only One Fact

A common wrong answer will elegantly explain one of the two contradictory facts and say nothing about the other. Always check: does this answer address BOTH facts? If not, eliminate it immediately, even if it sounds compelling.

Bold Face Trap: Agree/Disagree Instead of Logical Role

Students often pick answers based on whether a bold statement "supports" or "opposes" the conclusion in a content sense. Instead, ask: what structural role does this statement play? A fact that seems to oppose the conclusion might actually be a concession the author uses to strengthen it.

Evaluate Trap: Forgetting the Variance Test

For Evaluate questions, test every choice by asking: "If YES, does it strengthen? If NO, does it weaken (or vice versa)?" An answer that produces the same outcome regardless of YES/NO is irrelevant and wrong. Only an answer with opposite effects on both sides is truly evaluative.

Practice Questions

12 GMAT-style questions — attempt each before revealing the answer.

INFERENCE Question 1

"Every certified organic farm in the Westlake region uses drip irrigation. No farm that uses drip irrigation has reported water usage violations in the past decade. The Hartwell farm has reported three water usage violations in the past five years."

Which of the following can be properly inferred from the statements above?

(A)The Hartwell farm uses drip irrigation.
(B)The Hartwell farm grows non-organic crops.
(C)The Hartwell farm is not a certified organic farm in the Westlake region.
(D)All farms in Westlake with violations are non-organic.
(E)Drip irrigation prevents water usage violations.
Show Answer

Correct Answer: (C)

Logic: Certified organic (Westlake) → drip irrigation → no violations. Hartwell has violations → not drip irrigation → not certified organic in Westlake. This contrapositive chain is airtight.

Why not (B): Not being certified organic doesn't mean the farm doesn't grow organic crops — it just lacks certification. (D) goes beyond stated facts — there may be non-organic farms without violations. (E) is too strong a causal claim.

INFERENCE Question 2

"In Tambria, literacy rates are highest in provinces that receive the most government education funding. However, provinces with the highest literacy rates do not always have the lowest poverty rates. Some provinces with low literacy have recently experienced strong economic growth due to natural resource extraction."

Which of the following must be true?

(A)Education funding is the primary driver of economic growth in Tambria.
(B)Provinces with the highest literacy rates always have the highest poverty rates.
(C)It is not the case that every province with high literacy has low poverty.
(D)Natural resource extraction reduces literacy rates.
(E)Poverty is caused by low education funding.
Show Answer

Correct Answer: (C)

Logic: The stimulus directly states "provinces with the highest literacy rates do not always have the lowest poverty rates." This is logically equivalent to saying: it is not true that every high-literacy province has low poverty. (C) is a direct paraphrase, making it 100% certain.

Why others fail: (A), (D), (E) introduce causal claims not stated. (B) reverses the direction — the stimulus says they don't always have the LOWEST poverty, not that they have the HIGHEST.

INFERENCE Question 3

"Verimont Airlines operates only on routes with more than 500 weekly passengers. The airline's safety record is reviewed quarterly only for routes it operates. Route 7 between Kelford and Dunmore has not had a safety review in over two years."

The statements above, if true, most strongly support which of the following?

(A)Route 7 is unsafe for passengers.
(B)Route 7 has fewer than 500 weekly passengers.
(C)Verimont Airlines does not fly Route 7.
(D)Route 7 will never receive a safety review.
(E)Safety reviews are not necessary for lightly traveled routes.
Show Answer

Correct Answer: (C)

Logic: Verimont reviews routes quarterly only if it operates them. Route 7 has had no review in over 2 years (8+ quarters). Therefore Verimont does not operate Route 7. This follows directly by modus tollens.

Why not (B): We can infer Verimont doesn't fly it, but we cannot be certain WHY — low passengers is plausible but not the only reason. (C) is directly provable; (B) requires an additional assumption. (A), (D), (E) go well beyond the facts.

INFERENCE Question 4

"Globex Corp gives performance bonuses only to employees who meet both their individual target and their team target. This quarter, the sales team missed its target. No employee on the sales team met their individual target."

Which of the following is properly inferred?

(A)Some sales employees will receive partial bonuses.
(B)The sales team will be dissolved next quarter.
(C)No sales team employee will receive a performance bonus this quarter.
(D)Employees in other departments also missed targets.
(E)Globex Corp will reduce its bonus pool next quarter.
Show Answer

Correct Answer: (C)

Logic: Bonus requires BOTH conditions (individual target + team target). The sales team missed its team target AND no individual met their individual target. Neither condition is met for any sales employee — therefore no sales employee receives a bonus. This is 100% certain.

Note: Even if only one condition failed (e.g., just the team target), no bonus would be given since both are required. Here both failed, making (C) even more certain. (A) is unsupported — no "partial bonus" is mentioned.

PARADOX Question 5

"Despite installing 200 new traffic lights across Millhaven last year, the city's average commute time increased by 8 minutes."

Which of the following, if true, best resolves this apparent paradox?

(A)Millhaven's traffic lights are synchronized during peak hours.
(B)The new lights were installed at previously uncontrolled intersections, which caused drivers to slow down significantly for the first time.
(C)Several neighboring cities also experienced increased commute times last year.
(D)Traffic engineers recommended the installations based on accident data.
(E)The number of registered vehicles in Millhaven has remained constant for three years.
Show Answer

Correct Answer: (B)

Paradox: More traffic control infrastructure → longer commutes (expected: shorter commutes).

Why (B) works: Installing lights at previously uncontrolled intersections introduces mandatory stopping where none existed before. This directly explains why commutes lengthened — the new infrastructure added delay rather than reducing it. Both facts are reconciled.

Why others fail: (A) suggests optimization, which would shorten commutes — doesn't resolve the paradox. (C) is irrelevant. (D) explains the decision rationale, not the longer commutes. (E) rules out a cause but explains nothing.

PARADOX Question 6

"A pharmaceutical company spent three times more on marketing its new pain medication than it did developing it, yet the drug's market share fell compared to its predecessor despite receiving better clinical trial results."

Which of the following best explains the paradox?

(A)The predecessor drug had a longer history of use and stronger physician trust.
(B)The new drug's clinical trials were conducted over a shorter period.
(C)Marketing spending is not an accurate predictor of drug quality.
(D)The company also launched two other products during the same period.
(E)The new drug was priced significantly higher than the predecessor, causing insurers to exclude it from formularies.
Show Answer

Correct Answer: (E)

Paradox: Better clinical results + more marketing → lower market share.

Why (E) works: If the new drug costs more and insurers won't cover it, patients and doctors can't easily prescribe it regardless of efficacy or advertising. This explains why better clinical results and heavy marketing still produced lower market share — coverage exclusion blocked access.

Why not (A): Physician trust is relevant but doesn't directly address why MORE marketing failed to overcome it. (E) provides a structural barrier (formulary exclusion) that marketing cannot overcome.

PARADOX Question 7

"In Crestwood County, a new recycling center that accepts all categories of waste opened last year. Since its opening, the total weight of waste sent to landfills from the county has increased by 12%."

Which of the following, if true, most helps explain the apparent discrepancy?

(A)The recycling center employs 40 full-time workers from the county.
(B)The recycling center diverts 30% of incoming material from landfill.
(C)Residents, now aware of proper disposal options, discarded large quantities of previously hoarded household waste.
(D)The county's population grew by 2% during the same year.
(E)The recycling center charges a fee that some residents find inconvenient.
Show Answer

Correct Answer: (C)

Paradox: Recycling center opens → more waste goes to landfill.

Why (C) works: If residents previously hoarded large amounts of waste (unsure what to do with it) and the recycling center's opening prompted them to finally dispose of it — some items go to recycling but others still go to landfill — total landfill volume increases even though recycling is happening. The recycling center triggered a burst of total disposal activity.

Why not (D): 2% population growth cannot explain a 12% increase in landfill waste. (B) confirms the center diverts waste, which deepens the paradox rather than resolving it.

PARADOX Question 8

"A software company introduced a generous unlimited paid time-off (PTO) policy last year. Employee surveys show that satisfaction scores increased by 15%. Nevertheless, voluntary employee turnover also increased significantly after the policy was introduced."

Which of the following best explains both facts?

(A)Unlimited PTO is considered a standard benefit at competitor firms.
(B)The company simultaneously froze salaries, causing financially motivated employees to leave for better-paying firms while others remained satisfied with new flexibility.
(C)Employee surveys are known to be unreliable measures of true satisfaction.
(D)The software industry as a whole experienced higher turnover last year.
(E)The company expanded its workforce by 30%, bringing in employees who later found the culture a poor fit.
Show Answer

Correct Answer: (B)

Paradox: Higher satisfaction scores + higher voluntary turnover — these seem contradictory.

Why (B) works: The salary freeze explains both: employees who value flexibility are satisfied and stay (satisfaction rises), while salary-focused employees are dissatisfied with the freeze and leave (turnover rises). Two distinct groups, two different outcomes — both facts are explained.

Why not (C): Undermining the surveys dissolves one fact but doesn't explain the other. We need both facts to remain true. (D) is a partial external explanation that doesn't address why satisfaction also rose.

BOLD FACE Question 9
Proponents of mandatory corporate carbon reporting argue that transparency drives emissions reductions. Several large companies voluntarily publishing emissions data have indeed reduced their carbon footprints over the past decade. Opponents counter that mandatory reporting imposes excessive compliance costs on small businesses. However, the cost of regulatory compliance is consistently lower than the long-term financial benefits of energy efficiency achieved through reporting-driven accountability. Thus, mandatory carbon reporting should be adopted as policy.

What roles do the two boldfaced statements play?

(A)The first is the main conclusion; the second provides supporting evidence.
(B)The first supports the counterargument; the second is the main conclusion.
(C)The first is evidence supporting the argument's position; the second rebuts the stated counterargument.
(D)Both are premises supporting the counterargument against mandatory reporting.
(E)The first is a concession; the second is an intermediate conclusion that supports the main conclusion.
Show Answer

Correct Answer: (C)

Main conclusion: "mandatory carbon reporting should be adopted as policy."

First bold: Evidence that voluntary reporting already works — supports the proponents' position (and thus the main argument).

Second bold: Directly counters the opponent's claim about compliance costs — a rebuttal of the stated counterargument, which in turn supports the main conclusion.

Why not (E): The first statement is not a concession (a concession acknowledges a point that goes against the argument). The first bold statement supports the argument's view.

BOLD FACE Question 10
A 10-year longitudinal study found that students who participated in extracurricular music programs scored an average of 12% higher on standardized math tests than peers who did not. Therefore, schools should increase music program funding. Critics note that schools with stronger music programs also tend to have higher overall budgets and more experienced teachers. This alternative explanation suggests the observed test score difference may be attributable to overall school resources rather than music training itself.

The two boldfaced portions relate to the overall argument as follows:

(A)The first is the main conclusion; the second provides supporting data for it.
(B)The first is a premise supporting the recommendation; the second undermines the causal basis of that recommendation.
(C)The first is background information; the second is the main conclusion.
(D)Both are premises that together support increasing music funding.
(E)The first is a counterargument; the second resolves it.
Show Answer

Correct Answer: (B)

Structure: First bold = study evidence → leads to recommendation (increase music funding). Second bold = alternative explanation that challenges the causal link between music and math scores.

The first bold directly supports the recommendation (premise). The second bold is a critic's alternative explanation that undermines the argument's causal assumption — i.e., it weakens the reasoning behind the recommendation.

Key insight: "Undermines the causal basis" is precise here — it doesn't refute the correlation but questions whether music caused the improvement.

EVALUATE Question 11

"Arkendale's new mayor argues that reducing the city's corporate tax rate by 5% will attract new businesses, grow the tax base, and ultimately increase total tax revenue despite the lower rate. Therefore, the rate cut will benefit the city's budget."

Which of the following would be most useful to know in evaluating the mayor's argument?

(A)Whether the mayor was elected by a majority or a plurality of voters.
(B)Whether other cities that cut corporate tax rates similarly experienced net revenue growth or decline.
(C)Whether the corporate tax rate was previously higher than neighboring cities.
(D)Whether the city's existing businesses support the rate reduction.
(E)How the mayor plans to communicate the rate cut to potential investors.
Show Answer

Correct Answer: (B)

Conclusion: The tax cut will increase net revenue.

Key gap: Will the influx of new businesses actually generate enough revenue to offset the rate reduction? Empirical data from comparable cities directly tests this assumption.

Variance Test: If YES (other cities gained net revenue) → strengthens the argument. If NO (they lost revenue) → weakens it. This is a true evaluative question.

Why not (C): Whether the rate was higher before is relevant context but doesn't directly tell us if the cut will produce more or less total revenue.

EVALUATE Question 12

"A hospital administrator claims that switching to electronic health records (EHR) will reduce medication errors. She bases this on the fact that the prior paper-based system led to illegible prescriptions, which caused dispensing mistakes. Therefore, EHR adoption will improve patient safety."

The answer to which of the following questions would most help evaluate the administrator's argument?

(A)How long will it take to train staff on the new EHR system?
(B)Do medication errors at the hospital arise primarily from illegible prescriptions, or from other sources such as dosage calculation errors and drug interaction oversights?
(C)How much will the EHR system cost to implement?
(D)Did the administrator consult physicians before making this decision?
(E)Are paper records legally required to be maintained for a certain period?
Show Answer

Correct Answer: (B)

Core gap: The argument assumes that illegible prescriptions are the primary (or sole) cause of medication errors. EHR solves legibility — but if most errors come from other sources, EHR won't significantly improve safety.

Variance Test: If YES (illegibility is the main cause) → EHR will greatly reduce errors → argument is strengthened. If NO (most errors are from dosage/drug interactions) → EHR won't help much → argument is weakened.

(A) addresses implementation difficulty, not the validity of the conclusion. (C) is about cost, not safety. Both are out of scope for this particular conclusion.

Quick Reference Card

// CR QUESTION TYPE CHEAT SHEET — Hour 13

// INFERENCE (Must Be True)

Rule 1: Answer must be 100% guaranteed — cannot merely "could be" true

Rule 2: Use only info stated in the stimulus — no outside knowledge

Rule 3: Apply contrapositive chains (If A→B, then Not B→Not A)

Trap: "Probably true" or "likely" answers are WRONG

// PARADOX (Resolve/Explain)

Step 1: Identify BOTH contradictory facts precisely

Step 2: Correct answer must address BOTH facts simultaneously

Step 3: Correct answer always introduces new information

Trap: Answer that explains only one fact = wrong choice

// BOLD FACE

Step 1: Find the MAIN CONCLUSION of the argument first

Step 2: For each bold statement ask: Premise? Counter? Conclusion?

Step 3: Does it support or undermine the main conclusion?

Trap: Never focus on content agreement — focus on LOGICAL ROLE

// EVALUATE

Step 1: Identify the gap between premises and conclusion

Step 2: Apply VARIANCE TEST to every answer choice:

YES → strengthens? NO → weakens? = Evaluative answer

Same effect either way? = Irrelevant, eliminate

Trap: Answers that are interesting but don't affect the conclusion

// TIME TARGETS

Inference: ~1:45 per question | Bold Face: ~2:15 per question

Paradox: ~1:50 per question | Evaluate: ~2:00 per question