What You'll Learn This Hour
- 1 Master the Inference (Must Be True) question type — understand that inference answers must follow 100% from the stated facts, not just be possible or likely.
- 2 Crack Paradox/Explain questions by finding the single answer that reconciles both seemingly contradictory facts simultaneously.
- 3 Decode Bold Face questions by identifying the logical role each highlighted statement plays in the argument structure.
- 4 Tackle Evaluate questions by pinpointing what additional information would most affect whether the conclusion is valid.
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.
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.
The explanation must make BOTH facts true simultaneously — partial explanations are wrong.
Worked Examples
Which of the following must be true based on the statements above?
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.
Which of the following, if true, best explains the apparent paradox?
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.
The two boldfaced statements play which of the following roles in the argument above?
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.
"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?
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.
"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?
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.
"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?
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.
"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?
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.
"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?
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.
"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?
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.
"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?
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.
"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?
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.
What roles do the two boldfaced statements play?
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.
The two boldfaced portions relate to the overall argument as follows:
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.
"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?
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.
"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?
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