All metals conduct electricity. Copper is a metal. Which conclusion must be true?

Correct: B) Copper conducts electricity.

Copper is a metal, and all metals conduct electricity, so copper must conduct it (B). A restricts the converse, C contradicts the premise, and D over-generalizes. Only B is guaranteed.

What number continues the series?　3, 6, 9, 12, 15, ___

Correct: C) 18

An arithmetic series increasing by 3: 15 + 3 = 18 (C). (As multiples of 3, the 6th term is 3 × 6 = 18.)

Which one does not belong with the others?　Rose, Sunflower, Cedar, Tulip

Correct: A) Cedar

Rose, sunflower, and tulip are flowering plants prized for their blooms; a cedar is a tree (a conifer). So the cedar (A) is the odd one out.

Baker is to bread as potter is to ___?

Correct: D) Pot

A baker produces bread; a potter produces a pot. Clay is the material, and a kiln or wheel is a tool, but the 'maker → finished product' relation points to pot (D).

“If the lock is open, the alarm does not sound.” The alarm sounded. What must be true?

Correct: A) The lock was not open.

Contrapositive: 'open → no sound' gives 'sounded → not open.' Since the alarm sounded, the lock was not open (A). B contradicts the premise and C adds information not given.

A job takes 4 printers 10 minutes. At the same rate, how long do 5 printers take?

Correct: D) 8 minutes

The work is fixed: 4 × 10 = 40 printer-minutes. With 5 printers, 40 ÷ 5 = 8 minutes (D). More machines means inversely less time.

Which letter continues the series?　B, D, G, K, P, ___

Correct: B) V

The letters sit at positions 2, 4, 7, 11, 16, with steps +2, +3, +4, +5. The next step +6 lands on position 22 = V (B).

What is the logical negation of “Some employees work from home”?

Correct: A) No employee works from home.

The negation of 'some are' is 'none are' (A). B is a different claim, C can be true alongside the original so it is not the negation, and D is unrelated. Only A makes 'some work from home' false.

All doctors are university graduates. Some mountaineers are doctors. Which must be true?

Correct: C) Some mountaineers are university graduates.

Some mountaineers are doctors, and doctors are graduates, so some mountaineers are graduates (C). A leaps to 'all', B reverses the relation, and D contradicts the premises.

An item priced at 2400 yen is sold at 25% off. What is the sale price?

Correct: B) 1800 yen

25% off means 75% of the price: 2400 × 0.75 = 1800 yen (B). (Equivalently, subtract the 600-yen discount.)

What continues the series?　2, 5, 10, 17, 26, ___

Correct: D) 37

The gaps are 3, 5, 7, 9 (odd numbers), so the next gap is 11: 26 + 11 = 37 (D). (Also n² + 1: 6² + 1 = 37.)

A ship is to a captain as ___ is to a pilot.

Correct: C) an aircraft

A captain operates a ship; a pilot operates an aircraft (C). An airport or runway is a place, and a passenger is whom they carry — the 'vehicle operated' relation points to aircraft.

P is taller than Q. R is taller than P. Q is taller than S. Who is the tallest?

Correct: B) R

R > P > Q and Q > S, so overall R > P > Q > S. The tallest is R (B).

4 notebooks cost 360 yen. At the same rate, how much for 7 notebooks?

Correct: A) 630 yen

Each notebook is 360 ÷ 4 = 90 yen. Seven notebooks cost 90 × 7 = 630 yen (A).

What continues the series?　1, 3, 9, 27, 81, ___

Correct: D) 243

A geometric series multiplying by 3 each step: 81 × 3 = 243 (D). (As powers of 3, 3⁵ = 243.)

If “everything in this box is unused” is true, which must be true?

Correct: C) This box contains no used items.

All contents being unused means there are no used items at all, so C holds. A is about the box's purpose, B reverses it, and D isn't implied by the premise.

“All fish breathe with gills. Whales live in the sea. Therefore whales are fish.” Which best describes this argument?

Correct: D) Living in the sea does not imply being a fish, so the argument form itself is invalid.

The premise says 'fish → gills', not 'lives in the sea → fish'. 'Whales live in the sea' cannot yield 'whales are fish', so the form itself is invalid (D). Whales are mammals, so the conclusion is also factually false.

Four times a number minus 7 equals two times the number plus 9. What is the number?

Correct: A) 8

Solve 4x − 7 = 2x + 9: 2x = 16, so x = 8 (A).

What continues the series?　Z1, X3, V5, T7, ___

Correct: C) R9

Letters move backward skipping one each time (Z, X, V, T → R) and numbers rise by 2 (1, 3, 5, 7 → 9). So R9 (C).

“People who read books have rich vocabularies. People with rich vocabularies write well.” If both are true, what must follow?

Correct: B) People who read books write well.

Transitivity: reading → rich vocabulary → writing well, so people who read books write well (B). A and C reverse the direction, and D is not the contrapositive.

All metals conduct electricity. Copper is a metal. Which conclusion must be true?

Correct: B) Copper conducts electricity.

Copper is a metal, and all metals conduct electricity, so copper must conduct it (B). A restricts the converse, C contradicts the premise, and D over-generalizes. Only B is guaranteed.

What number continues the series?　3, 6, 9, 12, 15, ___

Correct: C) 18

An arithmetic series increasing by 3: 15 + 3 = 18 (C). (As multiples of 3, the 6th term is 3 × 6 = 18.)

Which one does not belong with the others?　Rose, Sunflower, Cedar, Tulip

Correct: A) Cedar

Rose, sunflower, and tulip are flowering plants prized for their blooms; a cedar is a tree (a conifer). So the cedar (A) is the odd one out.

Baker is to bread as potter is to ___?

Correct: D) Pot

A baker produces bread; a potter produces a pot. Clay is the material, and a kiln or wheel is a tool, but the 'maker → finished product' relation points to pot (D).

“If the lock is open, the alarm does not sound.” The alarm sounded. What must be true?

Correct: A) The lock was not open.

Contrapositive: 'open → no sound' gives 'sounded → not open.' Since the alarm sounded, the lock was not open (A). B contradicts the premise and C adds information not given.

A job takes 4 printers 10 minutes. At the same rate, how long do 5 printers take?

Correct: D) 8 minutes

The work is fixed: 4 × 10 = 40 printer-minutes. With 5 printers, 40 ÷ 5 = 8 minutes (D). More machines means inversely less time.

Which letter continues the series?　B, D, G, K, P, ___

Correct: B) V

The letters sit at positions 2, 4, 7, 11, 16, with steps +2, +3, +4, +5. The next step +6 lands on position 22 = V (B).

What is the logical negation of “Some employees work from home”?

Correct: A) No employee works from home.

The negation of 'some are' is 'none are' (A). B is a different claim, C can be true alongside the original so it is not the negation, and D is unrelated. Only A makes 'some work from home' false.

All doctors are university graduates. Some mountaineers are doctors. Which must be true?

Correct: C) Some mountaineers are university graduates.

Some mountaineers are doctors, and doctors are graduates, so some mountaineers are graduates (C). A leaps to 'all', B reverses the relation, and D contradicts the premises.

An item priced at 2400 yen is sold at 25% off. What is the sale price?

Correct: B) 1800 yen

25% off means 75% of the price: 2400 × 0.75 = 1800 yen (B). (Equivalently, subtract the 600-yen discount.)

What continues the series?　2, 5, 10, 17, 26, ___

Correct: D) 37

The gaps are 3, 5, 7, 9 (odd numbers), so the next gap is 11: 26 + 11 = 37 (D). (Also n² + 1: 6² + 1 = 37.)

A ship is to a captain as ___ is to a pilot.

Correct: C) an aircraft

A captain operates a ship; a pilot operates an aircraft (C). An airport or runway is a place, and a passenger is whom they carry — the 'vehicle operated' relation points to aircraft.

P is taller than Q. R is taller than P. Q is taller than S. Who is the tallest?

Correct: B) R

R > P > Q and Q > S, so overall R > P > Q > S. The tallest is R (B).

4 notebooks cost 360 yen. At the same rate, how much for 7 notebooks?

Correct: A) 630 yen

Each notebook is 360 ÷ 4 = 90 yen. Seven notebooks cost 90 × 7 = 630 yen (A).

What continues the series?　1, 3, 9, 27, 81, ___

Correct: D) 243

A geometric series multiplying by 3 each step: 81 × 3 = 243 (D). (As powers of 3, 3⁵ = 243.)

If “everything in this box is unused” is true, which must be true?

Correct: C) This box contains no used items.

All contents being unused means there are no used items at all, so C holds. A is about the box's purpose, B reverses it, and D isn't implied by the premise.

“All fish breathe with gills. Whales live in the sea. Therefore whales are fish.” Which best describes this argument?

Correct: D) Living in the sea does not imply being a fish, so the argument form itself is invalid.

The premise says 'fish → gills', not 'lives in the sea → fish'. 'Whales live in the sea' cannot yield 'whales are fish', so the form itself is invalid (D). Whales are mammals, so the conclusion is also factually false.

Four times a number minus 7 equals two times the number plus 9. What is the number?

Correct: A) 8

Solve 4x − 7 = 2x + 9: 2x = 16, so x = 8 (A).

What continues the series?　Z1, X3, V5, T7, ___

Correct: C) R9

Letters move backward skipping one each time (Z, X, V, T → R) and numbers rise by 2 (1, 3, 5, 7 → 9). So R9 (C).

“People who read books have rich vocabularies. People with rich vocabularies write well.” If both are true, what must follow?

Correct: B) People who read books write well.

Transitivity: reading → rich vocabulary → writing well, so people who read books write well (B). A and C reverse the direction, and D is not the contrapositive.

All metals conduct electricity. Copper is a metal. Which conclusion must be true?

Correct: B) Copper conducts electricity.

Copper is a metal, and all metals conduct electricity, so copper must conduct it (B). A restricts the converse, C contradicts the premise, and D over-generalizes. Only B is guaranteed.

What number continues the series?　3, 6, 9, 12, 15, ___

Correct: C) 18

An arithmetic series increasing by 3: 15 + 3 = 18 (C). (As multiples of 3, the 6th term is 3 × 6 = 18.)

Which one does not belong with the others?　Rose, Sunflower, Cedar, Tulip

Correct: A) Cedar

Rose, sunflower, and tulip are flowering plants prized for their blooms; a cedar is a tree (a conifer). So the cedar (A) is the odd one out.

Baker is to bread as potter is to ___?

Correct: D) Pot

A baker produces bread; a potter produces a pot. Clay is the material, and a kiln or wheel is a tool, but the 'maker → finished product' relation points to pot (D).

“If the lock is open, the alarm does not sound.” The alarm sounded. What must be true?

Correct: A) The lock was not open.

Contrapositive: 'open → no sound' gives 'sounded → not open.' Since the alarm sounded, the lock was not open (A). B contradicts the premise and C adds information not given.

A job takes 4 printers 10 minutes. At the same rate, how long do 5 printers take?

Correct: D) 8 minutes

The work is fixed: 4 × 10 = 40 printer-minutes. With 5 printers, 40 ÷ 5 = 8 minutes (D). More machines means inversely less time.

Which letter continues the series?　B, D, G, K, P, ___

Correct: B) V

The letters sit at positions 2, 4, 7, 11, 16, with steps +2, +3, +4, +5. The next step +6 lands on position 22 = V (B).

What is the logical negation of “Some employees work from home”?

Correct: A) No employee works from home.

The negation of 'some are' is 'none are' (A). B is a different claim, C can be true alongside the original so it is not the negation, and D is unrelated. Only A makes 'some work from home' false.

All doctors are university graduates. Some mountaineers are doctors. Which must be true?

Correct: C) Some mountaineers are university graduates.

Some mountaineers are doctors, and doctors are graduates, so some mountaineers are graduates (C). A leaps to 'all', B reverses the relation, and D contradicts the premises.

An item priced at 2400 yen is sold at 25% off. What is the sale price?

Correct: B) 1800 yen

25% off means 75% of the price: 2400 × 0.75 = 1800 yen (B). (Equivalently, subtract the 600-yen discount.)

What continues the series?　2, 5, 10, 17, 26, ___

Correct: D) 37

The gaps are 3, 5, 7, 9 (odd numbers), so the next gap is 11: 26 + 11 = 37 (D). (Also n² + 1: 6² + 1 = 37.)

A ship is to a captain as ___ is to a pilot.

Correct: C) an aircraft

A captain operates a ship; a pilot operates an aircraft (C). An airport or runway is a place, and a passenger is whom they carry — the 'vehicle operated' relation points to aircraft.

P is taller than Q. R is taller than P. Q is taller than S. Who is the tallest?

Correct: B) R

R > P > Q and Q > S, so overall R > P > Q > S. The tallest is R (B).

4 notebooks cost 360 yen. At the same rate, how much for 7 notebooks?

Correct: A) 630 yen

Each notebook is 360 ÷ 4 = 90 yen. Seven notebooks cost 90 × 7 = 630 yen (A).

What continues the series?　1, 3, 9, 27, 81, ___

Correct: D) 243

A geometric series multiplying by 3 each step: 81 × 3 = 243 (D). (As powers of 3, 3⁵ = 243.)

If “everything in this box is unused” is true, which must be true?

Correct: C) This box contains no used items.

All contents being unused means there are no used items at all, so C holds. A is about the box's purpose, B reverses it, and D isn't implied by the premise.

“All fish breathe with gills. Whales live in the sea. Therefore whales are fish.” Which best describes this argument?

Correct: D) Living in the sea does not imply being a fish, so the argument form itself is invalid.

The premise says 'fish → gills', not 'lives in the sea → fish'. 'Whales live in the sea' cannot yield 'whales are fish', so the form itself is invalid (D). Whales are mammals, so the conclusion is also factually false.

Four times a number minus 7 equals two times the number plus 9. What is the number?

Correct: A) 8

Solve 4x − 7 = 2x + 9: 2x = 16, so x = 8 (A).

What continues the series?　Z1, X3, V5, T7, ___

Correct: C) R9

Letters move backward skipping one each time (Z, X, V, T → R) and numbers rise by 2 (1, 3, 5, 7 → 9). So R9 (C).

“People who read books have rich vocabularies. People with rich vocabularies write well.” If both are true, what must follow?

Correct: B) People who read books write well.

Transitivity: reading → rich vocabulary → writing well, so people who read books write well (B). A and C reverse the direction, and D is not the contrapositive.