All roses are flowers, and all flowers need water. Which conclusion must be true?

Correct: A) All roses need water.

Transitivity: rose ⊆ flower ⊆ needs-water, so every rose needs water. B reverses the relation, C contradicts the premise, and D over-restricts. Only A is guaranteed.

What number continues the series?　2, 6, 12, 20, 30, ___

Correct: C) 42

The gaps are 4, 6, 8, 10 — increasing by 2 — so the next gap is 12, giving 42. (Also n×(n+1): 6×7 = 42.)

Which one does not belong with the others?　Square, Triangle, Circle, Cube

Correct: D) Cube

Square, triangle, and circle are two-dimensional; a cube is three-dimensional. So the cube (D) is the odd one out.

Author is to book as composer is to ___?

Correct: B) Song

An author creates a book; a composer creates a song. An orchestra performs it and an audience hears it, but the 'creator → creation' relation points to song (B).

“If it rains, the game is canceled.” The game was not canceled. What must be true?

Correct: B) It did not rain.

Contrapositive: not canceled implies not rain. Had it rained, the game would have been canceled. So it did not rain (B).

If 3 workers build a wall in 12 days, how long do 6 workers take at the same rate?

Correct: B) 6 days

Work is constant: 3×12 = 36 worker-days. With 6 workers, 36 ÷ 6 = 6 days (B). Doubling the workers halves the time.

Which letter continues the series?　A, C, F, J, O, ___

Correct: C) U

The letters sit at positions 1, 3, 6, 10, 15, with steps +2, +3, +4, +5. The next step +6 lands on position 21 = U.

What is the logical negation of “All cats are black”?

Correct: C) At least one cat is not black.

The negation of 'all are' is 'at least one is not' (C). 'No cat is black' is the contrary, not the negation; B and D do not negate the universal claim.

All athletes are healthy. Some students are athletes. Which must be true?

Correct: A) Some students are healthy.

Some students are athletes, and athletes are healthy, so those students are healthy — hence some students are healthy (A). B, C, and D claim more than the premises allow.

An item priced at 1500 yen is sold at 20% off. What is the sale price?

Correct: B) 1200 yen

20% off means 80% of the price: 1500 × 0.8 = 1200 yen (B).

What continues the series?　1, 4, 9, 16, 25, ___

Correct: C) 36

These are the squares 1², 2², 3², 4², 5². Next is 6² = 36 (C).

A hospital is to a doctor as ___ is to a teacher.

Correct: B) a school

A doctor works at a hospital; a teacher works at a school (B). A student is whom they serve, and a textbook or blackboard is a tool — the 'workplace' relation points to school.

A is faster than B. C is faster than A. B is faster than D. Who is the fastest?

Correct: C) C

C > A > B and B > D, so overall C > A > B > D. The fastest is C.

5 apples cost 400 yen. At the same rate, how much for 8 apples?

Correct: C) 640 yen

Each apple is 400 ÷ 5 = 80 yen. Eight apples cost 80 × 8 = 640 yen (C).

What continues the series?　1, 1, 2, 3, 5, 8, ___

Correct: C) 13

Each term is the sum of the previous two (Fibonacci). 5 + 8 = 13 (C).

If “every product in this store is domestic” is true, which must be true?

Correct: A) This store carries no imported goods.

All products being domestic means no imports at all, so A holds. B reverses it, C is unrelated, and D isn't implied by the premise.

“All birds can fly. A penguin is a bird. Therefore a penguin can fly.” Which best describes this argument?

Correct: C) The form is valid, but the premise 'all birds can fly' is factually false.

The argument form (syllogism) is valid — if the premises were true, the conclusion would follow. The flaw is that the premise 'all birds can fly' is factually false (validity and truth of premises are separate). A penguin is a bird, so D is wrong.

Three times a number plus 6 equals five times the number minus 10. What is the number?

Correct: C) 8

Solve 3x + 6 = 5x − 10: 16 = 2x, so x = 8 (C).

What continues the series?　A2, C4, E6, G8, ___

Correct: B) I10

Letters skip one each time (A, C, E, G → I) and numbers rise by 2 (2, 4, 6, 8 → 10). So I10 (B).

“People who exercise are healthy. Healthy people live long.” If both are true, what must follow?

Correct: A) People who exercise live long.

Transitivity: exercise → healthy → long life, so people who exercise live long (A). B and C reverse the direction, and D is not the contrapositive.

All roses are flowers, and all flowers need water. Which conclusion must be true?

Correct: A) All roses need water.

Transitivity: rose ⊆ flower ⊆ needs-water, so every rose needs water. B reverses the relation, C contradicts the premise, and D over-restricts. Only A is guaranteed.

What number continues the series?　2, 6, 12, 20, 30, ___

Correct: C) 42

The gaps are 4, 6, 8, 10 — increasing by 2 — so the next gap is 12, giving 42. (Also n×(n+1): 6×7 = 42.)

Which one does not belong with the others?　Square, Triangle, Circle, Cube

Correct: D) Cube

Square, triangle, and circle are two-dimensional; a cube is three-dimensional. So the cube (D) is the odd one out.

Author is to book as composer is to ___?

Correct: B) Song

An author creates a book; a composer creates a song. An orchestra performs it and an audience hears it, but the 'creator → creation' relation points to song (B).

“If it rains, the game is canceled.” The game was not canceled. What must be true?

Correct: B) It did not rain.

Contrapositive: not canceled implies not rain. Had it rained, the game would have been canceled. So it did not rain (B).

If 3 workers build a wall in 12 days, how long do 6 workers take at the same rate?

Correct: B) 6 days

Work is constant: 3×12 = 36 worker-days. With 6 workers, 36 ÷ 6 = 6 days (B). Doubling the workers halves the time.

Which letter continues the series?　A, C, F, J, O, ___

Correct: C) U

The letters sit at positions 1, 3, 6, 10, 15, with steps +2, +3, +4, +5. The next step +6 lands on position 21 = U.

What is the logical negation of “All cats are black”?

Correct: C) At least one cat is not black.

The negation of 'all are' is 'at least one is not' (C). 'No cat is black' is the contrary, not the negation; B and D do not negate the universal claim.

All athletes are healthy. Some students are athletes. Which must be true?

Correct: A) Some students are healthy.

Some students are athletes, and athletes are healthy, so those students are healthy — hence some students are healthy (A). B, C, and D claim more than the premises allow.

An item priced at 1500 yen is sold at 20% off. What is the sale price?

Correct: B) 1200 yen

20% off means 80% of the price: 1500 × 0.8 = 1200 yen (B).

What continues the series?　1, 4, 9, 16, 25, ___

Correct: C) 36

These are the squares 1², 2², 3², 4², 5². Next is 6² = 36 (C).

A hospital is to a doctor as ___ is to a teacher.

Correct: B) a school

A doctor works at a hospital; a teacher works at a school (B). A student is whom they serve, and a textbook or blackboard is a tool — the 'workplace' relation points to school.

A is faster than B. C is faster than A. B is faster than D. Who is the fastest?

Correct: C) C

C > A > B and B > D, so overall C > A > B > D. The fastest is C.

5 apples cost 400 yen. At the same rate, how much for 8 apples?

Correct: C) 640 yen

Each apple is 400 ÷ 5 = 80 yen. Eight apples cost 80 × 8 = 640 yen (C).

What continues the series?　1, 1, 2, 3, 5, 8, ___

Correct: C) 13

Each term is the sum of the previous two (Fibonacci). 5 + 8 = 13 (C).

If “every product in this store is domestic” is true, which must be true?

Correct: A) This store carries no imported goods.

All products being domestic means no imports at all, so A holds. B reverses it, C is unrelated, and D isn't implied by the premise.

“All birds can fly. A penguin is a bird. Therefore a penguin can fly.” Which best describes this argument?

Correct: C) The form is valid, but the premise 'all birds can fly' is factually false.

The argument form (syllogism) is valid — if the premises were true, the conclusion would follow. The flaw is that the premise 'all birds can fly' is factually false (validity and truth of premises are separate). A penguin is a bird, so D is wrong.

Three times a number plus 6 equals five times the number minus 10. What is the number?

Correct: C) 8

Solve 3x + 6 = 5x − 10: 16 = 2x, so x = 8 (C).

What continues the series?　A2, C4, E6, G8, ___

Correct: B) I10

Letters skip one each time (A, C, E, G → I) and numbers rise by 2 (2, 4, 6, 8 → 10). So I10 (B).

“People who exercise are healthy. Healthy people live long.” If both are true, what must follow?

Correct: A) People who exercise live long.

Transitivity: exercise → healthy → long life, so people who exercise live long (A). B and C reverse the direction, and D is not the contrapositive.

All roses are flowers, and all flowers need water. Which conclusion must be true?

Correct: A) All roses need water.

Transitivity: rose ⊆ flower ⊆ needs-water, so every rose needs water. B reverses the relation, C contradicts the premise, and D over-restricts. Only A is guaranteed.

What number continues the series?　2, 6, 12, 20, 30, ___

Correct: C) 42

The gaps are 4, 6, 8, 10 — increasing by 2 — so the next gap is 12, giving 42. (Also n×(n+1): 6×7 = 42.)

Which one does not belong with the others?　Square, Triangle, Circle, Cube

Correct: D) Cube

Square, triangle, and circle are two-dimensional; a cube is three-dimensional. So the cube (D) is the odd one out.

Author is to book as composer is to ___?

Correct: B) Song

An author creates a book; a composer creates a song. An orchestra performs it and an audience hears it, but the 'creator → creation' relation points to song (B).

“If it rains, the game is canceled.” The game was not canceled. What must be true?

Correct: B) It did not rain.

Contrapositive: not canceled implies not rain. Had it rained, the game would have been canceled. So it did not rain (B).

If 3 workers build a wall in 12 days, how long do 6 workers take at the same rate?

Correct: B) 6 days

Work is constant: 3×12 = 36 worker-days. With 6 workers, 36 ÷ 6 = 6 days (B). Doubling the workers halves the time.

Which letter continues the series?　A, C, F, J, O, ___

Correct: C) U

The letters sit at positions 1, 3, 6, 10, 15, with steps +2, +3, +4, +5. The next step +6 lands on position 21 = U.

What is the logical negation of “All cats are black”?

Correct: C) At least one cat is not black.

The negation of 'all are' is 'at least one is not' (C). 'No cat is black' is the contrary, not the negation; B and D do not negate the universal claim.

All athletes are healthy. Some students are athletes. Which must be true?

Correct: A) Some students are healthy.

Some students are athletes, and athletes are healthy, so those students are healthy — hence some students are healthy (A). B, C, and D claim more than the premises allow.

An item priced at 1500 yen is sold at 20% off. What is the sale price?

Correct: B) 1200 yen

20% off means 80% of the price: 1500 × 0.8 = 1200 yen (B).

What continues the series?　1, 4, 9, 16, 25, ___

Correct: C) 36

These are the squares 1², 2², 3², 4², 5². Next is 6² = 36 (C).

A hospital is to a doctor as ___ is to a teacher.

Correct: B) a school

A doctor works at a hospital; a teacher works at a school (B). A student is whom they serve, and a textbook or blackboard is a tool — the 'workplace' relation points to school.

A is faster than B. C is faster than A. B is faster than D. Who is the fastest?

Correct: C) C

C > A > B and B > D, so overall C > A > B > D. The fastest is C.

5 apples cost 400 yen. At the same rate, how much for 8 apples?

Correct: C) 640 yen

Each apple is 400 ÷ 5 = 80 yen. Eight apples cost 80 × 8 = 640 yen (C).

What continues the series?　1, 1, 2, 3, 5, 8, ___

Correct: C) 13

Each term is the sum of the previous two (Fibonacci). 5 + 8 = 13 (C).

If “every product in this store is domestic” is true, which must be true?

Correct: A) This store carries no imported goods.

All products being domestic means no imports at all, so A holds. B reverses it, C is unrelated, and D isn't implied by the premise.

“All birds can fly. A penguin is a bird. Therefore a penguin can fly.” Which best describes this argument?

Correct: C) The form is valid, but the premise 'all birds can fly' is factually false.

The argument form (syllogism) is valid — if the premises were true, the conclusion would follow. The flaw is that the premise 'all birds can fly' is factually false (validity and truth of premises are separate). A penguin is a bird, so D is wrong.

Three times a number plus 6 equals five times the number minus 10. What is the number?

Correct: C) 8

Solve 3x + 6 = 5x − 10: 16 = 2x, so x = 8 (C).

What continues the series?　A2, C4, E6, G8, ___

Correct: B) I10

Letters skip one each time (A, C, E, G → I) and numbers rise by 2 (2, 4, 6, 8 → 10). So I10 (B).

“People who exercise are healthy. Healthy people live long.” If both are true, what must follow?

Correct: A) People who exercise live long.

Transitivity: exercise → healthy → long life, so people who exercise live long (A). B and C reverse the direction, and D is not the contrapositive.