Logical Reasoning: The Inference Family
Drawing well-supported conclusions: must be true, most strongly supported, cannot be true, completing a passage, and the answer drawn one step too far.
7 topics · 30 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Must Be True
- How it worksHow do the stated facts act as solid boxes with the credited answer drawn strictly inside them?
- How it worksWalk me through killing a choice by building one case where every fact holds and that choice fails.
- Worked exampleFind what must be true from 'Every chemist in the lab published, and Ravi works in that lab'.
- Common mistakeWhy isn't the most plausible-sounding choice the one that has to be true?
- Going furtherWhat changes when a stem asks what must be true instead of what the author would agree with?
Your turneasy1 of 3
Every chemist in the Farrow laboratory published at least 5 papers last year. Ravi works in the Farrow laboratory, which employs 39 people in all, of whom 13 are chemists.
If the statements above are true, which one of the following must also be true?Most Strongly Supported
- How it worksHow does the standard slide from airtight proof down to likelihood when a stem changes two words?
- Worked exampleWalk me through supporting 'the cafe is busiest on rainy days' from sales figures and rainfall totals.
- Common mistakeWhy isn't 'most strongly supported' an invitation to pick whatever sounds reasonable?
- Going furtherWhat happens when two choices are both supported and you have to rank how much?
Your turneasy1 of 3
The Marlow Cafe sells 61 percent more hot drinks on days when rain falls than on dry days, and its total receipts on rainy days run 20 percent above those on dry days. Rain fell on 39 of the past 68 days.
Which one of the following is most strongly supported by the information above?Cannot Be True
- How it worksHow does a contradiction show up as an answer box that will not fit anywhere in the picture?
- Worked exampleFind what cannot be true given 'All finalists submitted essays' and 'Dana submitted nothing'.
- Common mistakeWhy doesn't an answer that simply goes unmentioned count as one that cannot be true?
Your turneasy1 of 3
All 20 finalists submitted an essay, and the panel read every essay that was submitted to it. The panel did not read Dana's essay.
If the statements above are true, which one of the following CANNOT be true?Complete the Passage
- How it worksHow does the word sitting right before a blank tell you whether to supply evidence or a conclusion?
- Worked exampleWalk me through finishing 'The bridge closed for repairs, so commuters' with the ending the facts support.
- Common mistakeWhy isn't the most dramatic ending the one a short passage actually supports?
- Ties togetherHow does a blank sitting after 'therefore' collapse into exactly the same work as Must Be True?
Your turneasy1 of 3
The bridge on the coast road closed for repairs lasting 12 weeks, and the only other route into town adds 21 kilometers to the trip. Deliveries to the town's 57 shops are made by vans whose operators charge by the kilometer. Therefore, while the repairs last, ___
Which one of the following most logically completes the passage?Combining Two Statements into a Valid Inference
- How it worksHow do you hunt down the shared term that lets two separate statements be joined at all?
- Worked exampleFind what follows from 'No reptile is warm-blooded' plus 'Every gecko is a reptile'.
- Worked exampleWalk me through joining 'Most of the crew were divers' to 'All divers carried tanks'.
- Common mistakeWhy doesn't pairing two facts that share no common term produce anything whatsoever?
- Going furtherWhat happens when three facts must be joined and the one in the middle is a quantifier?
Your turneasy1 of 3
No reptile is warm-blooded. Every one of the 31 gecko species catalogued in the region is a reptile.
Which one of the following follows logically from the statements above?The Answer One Step Too Far
- How it worksHow does a dotted box one step out stay legal while the very next step falls off the edge?
- Worked exampleWalk me through why 'the drug is safe' overreaches from 'no side effects appeared in eight weeks'.
- Common mistakeWhy isn't an answer that quietly adds the word 'only' supported by facts that never said 'only'?
- Going furtherWhat changes about overreach when a stimulus already hedges with 'probably' or 'in most cases'?
Your turneasy1 of 3
In a trial lasting 12 weeks, none of the 88 volunteers who took the compound reported any side effect.
Which one of the following is most strongly supported by the statement above?Reading an Inference Off a Conditional Chain
- How it worksHow does linking every rule into a single path let you read the credited answer off its two ends?
- Worked exampleWalk me through chaining 'if hired then trained' with 'if trained then badged' and stating the inference.
- Worked exampleFind the valid inference from 'No badge means no access' plus 'All new hires get badges'.
- Common mistakeWhy doesn't an answer that quietly reverses one link of a chain still count as valid?
- Ties togetherHow does the contrapositive of an entire chain hand you a second set of inferences for free?
Your turneasy1 of 3
Anyone the firm hires is trained within 45 days. Anyone the firm trains is issued a badge. No one without a badge may enter the 9 secure rooms.
If the statements above are true, which one of the following must be true?AP®, SAT® and PSAT/NMSQT® are trademarks registered by the College Board (PSAT/NMSQT® jointly with the National Merit Scholarship Corporation). ACT® is a registered trademark of ACT Education Corp. GRE® is a registered trademark of ETS. LSAT® is a registered trademark of the Law School Admission Council. MCAT® is a registered trademark of the Association of American Medical Colleges. ISEE® and SSAT® are registered trademarks of their owners. None of these organizations is affiliated with, or endorses, Jentoo.