Critical Thinking and Problem Solving Flashcards

Which of the following is the strongest counter-argument to the claim: 'Students who attend selective schools always outperform those who don't'?

Answer: Some non-selective school students outperform selective school graduates.

A single counter-example that contradicts an 'always' claim is sufficient to disprove it.

Four students each solve a puzzle in 12, 15, 9, and 18 minutes respectively. What is the average time taken?

Answer: 13.5 minutes

(12 + 15 + 9 + 18) ÷ 4 = 54 ÷ 4 = 13.5 minutes.

Which type of reasoning moves from specific observations to a general conclusion?

Answer: Inductive reasoning

Inductive reasoning generalizes from specific cases to form a broader conclusion.

A rectangle has a perimeter of 36 cm and a length of 10 cm. What is its width?

Answer: 8 cm

Perimeter = 2(l + w), so 36 = 2(10 + w), giving w = 18 − 10 = 8 cm.

Which of the following represents the most logical sequence of steps when solving a word problem?

Answer: Re-read, identify key information, set up equation, calculate, verify

A systematic approach — understand the problem, extract key data, model it, compute, and verify — is the most effective problem-solving sequence.

If no cats are dogs, and all dogs are animals, which statement must be true?

Answer: No dogs are cats

If no cats are dogs, then logically no dogs are cats — the relationship of exclusion is symmetric.

A school ranks students by combined score. Maya scores 85 in math and 90 in English. Jake scores 92 in math and 82 in English. Who has the higher combined score?

Answer: Maya, with 175

Maya: 85 + 90 = 175; Jake: 92 + 82 = 174. Maya's combined score is higher.