Mariano Luiz King
Free logical reasoning reviewer for college entrance exams, with practice questions on syllogisms, if-then statements, ordering, seating arrangements, relationships, and codes. Pick an answer to see the step-by-step explanation. No sign-up needed.
Questions from across the question types, picked from core topics. Pick an answer to see whether you got it right, along with the full explanation.
All squares are rectangles. All rectangles are quadrilaterals. Which must be true?
Topic: Syllogisms.
Explanation: Squares sit inside rectangles, and rectangles sit inside quadrilaterals, so squares sit inside quadrilaterals. "All quadrilaterals are squares" reverses the direction, which doesn't follow.
All doctors are graduates. Some graduates are teachers. Which must be true?
Topic: Syllogisms.
Explanation: The teachers might be graduates who aren't doctors, so "some doctors are teachers" doesn't have to be true. "No doctor is a teacher" doesn't either, since some could overlap. "All teachers are graduates" isn't stated. "Some" doesn't tell you which ones.
If it rains, the game is cancelled. The game was not cancelled. What follows?
Topic: If-then Statements.
Explanation: If rain always cancels the game, and the game went on, then it didn't rain.
If it rains, the game is cancelled. The game was cancelled. What follows?
Topic: If-then Statements.
Explanation: The game could be cancelled for another reason, like a typhoon warning or a power outage. A cancelled game doesn't prove it rained.
Ana is taller than Ben. Carlo is shorter than Ben. Dina is taller than Ana. Who is the shortest?
Topic: Ordering.
Explanation: From tallest to shortest: Dina, Ana, Ben, Carlo.
Five friends, P, Q, R, S, and T, sit in a row. R sits in the middle. P sits at the left end. Q sits next to P. T does not sit next to R. Who sits between R and T?
Topic: Seating Arrangements.
Step 1: Number the seats 1 to 5 from the left. P is in 1, Q in 2, and R in 3.
Step 2: T can't be in 4, since that's next to R, so T is in 5.
Result: S is in 4, between R and T.
Pointing to a man, Liza says, "He is the son of my mother's only brother." How is the man related to Liza?
Topic: Family Relationships.
Explanation: Her mother's brother is her uncle. Her uncle's son is her cousin.
You walk 5 km north, turn right and walk 3 km, then turn right again and walk 5 km. Where are you now from your starting point?
Topic: Directions.
Step 1: Turning right from north faces you east, so you walk 3 km east.
Step 2: Turning right again faces you south, and the 5 km south cancels the 5 km north.
Result: You end 3 km east of the start.
If CAT is written as DBU, how is DOG written?
Topic: Letter Codes.
Explanation: Each letter moves one step forward: C to D, A to B, T to U. So D becomes E, O becomes P, and G becomes H.
If the day before yesterday was Thursday, what day is tomorrow?
Topic: Calendar Reasoning.
Explanation: The day before yesterday was Thursday, so yesterday was Friday and today is Saturday. Tomorrow is Sunday.
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Assuming the reverse of an if-then statement. "If it rains, the game is cancelled" does not mean a cancelled game proves it rained. Another is using real-world knowledge in syllogisms instead of accepting the statements as given.
No. Logical reasoning uses words and statements. Abstract reasoning uses shapes and patterns.
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