Logic puzzles ask you to combine clues into an order or decide what follows from statements. Use only the information given, and choose an answer that must hold in every valid arrangement.
Read the clues, then answer the question.
Which statement must be true?
Answer: C
Why. The clues fix one order from first to last to arrive: Cara, Ana, Fay. "Fay arrived later than Cara" is true in that order, and every other option is false in it.
Read the clues, then answer the question.
Who finished first?
Answer: D
Why. The clues fix one order from first to last to finish: Jun, Dev, Gus, Ana. In that order Jun finished first, so Jun is the answer.
Read the clues, then answer the question.
Which statement must be true?
Answer: E
Why. The clues fix one order from first to last to finish: Ana, Eli, Gus, Jun. "Jun finished behind Eli" is true in that order, and every other option is false in it.
Read the clues, then answer the question.
Which statement must be true?
Answer: A
Why. The clues allow 10 orders from first to last to arrive, for example (Hana, Dev, Fay, Cara, Eli) and (Hana, Dev, Cara, Eli, Fay). "Fay arrived later than Hana" is true in every one of them, while each other option is false in at least one.
Assume the statements are true, then answer the question.
Which statement must be true?
Answer: B
Why. All blickets are zems, and no zems are tovs, so no blickets can be tovs.
Assume the statements are true, then answer the question.
Which statement must be true?
Answer: C
Why. Draw each group as a circle and try every way the circles can overlap while the premises stay true. In every such picture "Some florps are not pells" is true, and this holds whether or not a group might be empty. Each other option is false in at least one picture that fits the premises.
Assume the statements are true, then answer the question.
Which statement must be true?
Answer: D
Why. Draw each group as a circle and try every way the circles can overlap while the premises stay true. In every such picture "Some wugs are not blickets" is true, and this holds whether or not a group might be empty. Each other option is false in at least one picture that fits the premises.
Assume the statements are true, then answer the question.
Which statement must be true?
Answer: E
Why. Draw each group as a circle and try every way the circles can overlap while the premises stay true. In every such picture "Some florps are not zems" is true, and this holds whether or not a group might be empty. Each other option is false in at least one picture that fits the premises.
Ordering puzzles combine clues about who is ahead of whom into one order. Draw a line for the places, then place each person where the clues allow. A clue that someone is not ahead limits their position, but it may not give an exact place.
Connect clues that share a person to find what follows from them together. If Mira is ahead of Lee and Lee is ahead of Sam, Mira is ahead of Sam. When asked who holds a place, check each possible order against every clue before you choose.
A syllogism answer must follow in every possible case allowed by the statements. “All A are B” puts every A in B, but does not put every B in A. “No A are B” rules out overlap. “Some A are B” says that at least one A is also B, while “some A are not B” says that at least one A is outside B.
Invented words keep everyday knowledge out of the reasoning. Treat each word as a label and picture groups that fit the statements. If an answer works in one arrangement but fails in another valid arrangement, it could be true, but it is not required.
Watch for added assumptions, reversed clues, and answers that could be true but do not have to be true. In an ordering puzzle, “not ahead” does not mean “behind by one place.” In a syllogism, a statement about some members does not describe every member.
There are 8 puzzles below, with answers and explanations. Try each puzzle first, then use the explanation to see which clue rules out other answers. For more practice, see all practice sets; the free test also includes reasoning questions.
Write down the people and places, then turn each clue into a relation or a limit on place. Connect clues that share a person. Check every candidate order against all the clues before answering.
It means the answer holds in every arrangement that fits the clues. If you can create even one valid arrangement where it does not hold, the answer may be possible, but it is not required.
Try to arrange the groups so that all the statements are true and the conclusion is false. If such an arrangement exists, the conclusion does not follow. Ignore what you know about the everyday meanings of the words.