Recognize the distinction
A percentage needs a denominator, an average needs a defined group, and a claim about all members is stronger than a claim about some. Translate each quantity into a small model before comparing groups. A larger percentage of a small group may represent fewer people than a smaller percentage of a large group. A change in an average can arise from changing membership.
Choose a method
Use concrete compatible numbers to test a proposed inference. If a conclusion must follow, one counterexample consistent with the premises defeats that necessity. Some does not identify which members overlap, and most does not mean every member. When two most claims concern the same finite population, some overlap must exist, but universal overlap still does not follow.
Worked contrast
School A can have thirty scholarship students out of one hundred, while B has one hundred out of one thousand. A has the larger percentage and B the larger count. In the clinic example, a shrinking regional total can raise the clinic's share even when its count falls. The arithmetic illustrates a logical distinction rather than predicting actual schools or clinics.
Transfer and check
For transfer, contrast a relative risk reduction with a percentage-point reduction. Moving from two per thousand to one per thousand halves the risk but changes the absolute risk by one per thousand. Include units in the answer. An option that repeats fifty percent without identifying the reference quantity may conceal a scope error.
Average annual pay at a shop rose after a highly paid manager joined. The shop kept the same number of hourly employees. An advocate concludes: The hourly employees must now earn more than before. Which statement is the advocate's main conclusion?
- The advocate offers these observations: Average annual pay at a shop rose after a highly paid manager joined. The shop kept the same number of hourly employees.
- The target claim is introduced as what the advocate concludes: The hourly employees must now earn more than before.
- Identifying a conclusion does not require accepting it; the task concerns its argumentative role.
Compare the other answer choices
This is a stated premise, offered as evidence rather than the target conclusion.
This is background or supporting information, not the claim the advocate infers.
This adds a stronger claim than the advocate actually states.
This is a possible counterfinding, not the claim the advocate aims to establish.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which evidence or rule supports your decision and why the alternatives do not fit.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
Logical Reasoning skills