A store marks up a product by 40% over cost and then offers a 15% discount. If the original cost is $80, what is the sale price?
Solution:
Answer: 80 \times 1.25 = 100$).
Approved Denied Total Under 30 45 15 60 30 and over 80 60 140 Total 125 75 200 What fraction of approved applicants were under 30?
Solution: This asks: "Given approved, what fraction is under 30?" — a conditional probability.
Common trap: answers a different question — "What fraction of under-30 applicants were approved?"
A scatterplot shows the relationship between hours of study (-axis) and exam score (-axis). The line of best fit is . What is the best interpretation of ?
Solution: The slope represents the predicted increase in exam score for each additional hour of study. It does NOT mean every student who studies one more hour scores exactly 5.2 points higher — it's the average predicted change.
A poll of 400 randomly selected voters finds 52% support Candidate A, with a margin of error of ±3 percentage points. Which statement is supported?
Solution: The true support is likely between 49% and 55%. Since this range includes 50%, we cannot conclude Candidate A has majority support — the race is too close to call within the margin of error.
SAT trap: A distractor will say "Candidate A will win the election." The poll only estimates the population proportion — it doesn't guarantee an outcome.
A university researcher posts a survey on social media asking graduates about job satisfaction. Of 1,200 respondents, 78% report being satisfied. Can the researcher conclude that 78% of all graduates are satisfied?
Solution: No. This is a voluntary response sample — only people who saw the post and chose to respond are included. People with strong opinions (positive or negative) are more likely to respond. The sample is not representative of all graduates. A valid conclusion would require a random sample.