Reasoning clue phrases: what each one actually means

Row and linear seating

A row has two ends, so a clue naming an end pins an exact seat. Everything else is relative, and the difference between “left of” and “immediate left of” is the difference between a range and a single seat.

immediate left of A

The seat directly adjacent to A on A's left, with nobody in between. It names exactly one seat.

Trap: Reading it as “somewhere to the left”, which leaves the seat unfixed and lets a wrong arrangement survive.

to the left of A

Anywhere on A's left side, at any distance. It constrains the side only, never the gap.

Trap: Treating it as adjacent. Without the word “immediate”, no distance is stated at all.

third to the left of A

Exactly three positions along, moving left from A, so exactly two people sit between them.

Trap: Counting A as the first, which shifts the whole arrangement one seat and breaks every later clue.

third from the left end

Counted from the end of the row, not from a person. The named person occupies seat three of the row.

Trap: Confusing it with “third to the left of A”. One is absolute, one is relative — mixing them is the commonest row error.

exactly two persons sit between A and B

Two people occupy the seats strictly between them — no more and no fewer, and A and B are never counted.

Trap: Including A or B in the count of two.

at least two persons sit between A and B

Two or more people sit between them. The gap has a floor but no ceiling, so several arrangements stay open.

Trap: Fixing the gap at two and closing off valid cases too early.

A sits at an extreme end

A occupies either the leftmost or the rightmost seat. Which end is not stated, so both cases are live until another clue decides.

Trap: Assuming the left end because the diagram was drawn left to right.

as many persons sit between A and B as between B and C

The two gaps are equal in size. The value is not given, so the clue is a relation, not a number.

Trap: Assuming the gaps must be non-zero. If no clue forbids it, an equal gap of zero can be valid.

A and B are immediate neighbours

A and B are adjacent, in either order. The clue fixes the pair, not which of them is on the left.

Trap: Locking the order in and never revisiting it when a later clue contradicts the arrangement.

Circular seating and facing direction

A circle has no ends, so no clue is absolute — you supply the reference point yourself. The facing direction decides which way “left” runs, and getting it backwards invalidates the whole set.

all facing the centre

Every person's left is the clockwise direction and their right is anticlockwise.

Trap: Applying the reader's own left and right to the diagram instead of the seated person's.

facing outward (facing away from the centre)

That person's left and right are reversed relative to everyone facing in: their left is anticlockwise.

Trap: Finding the outward-facing person late, after several neighbour clues have already been applied the wrong way round.

sits directly opposite B

B occupies the seat exactly half a circle away. This is only possible when the number of seats is even.

Trap: Applying it in an odd-sized circle, where no seat faces another and the clue cannot exist.

second to the left of A

Two seats along in A's left direction, which depends on whether A faces in or out.

Trap: Counting seats clockwise by habit without first checking A's facing.

third to the right of the one who likes blue

An indirect reference: identify the person the description picks out first, then count from them.

Trap: Counting from the person who was mentioned in the previous clue rather than the one the description names.

the middle neighbour between A and B

With an odd number of people strictly between A and B, the one at the halfway point of that arc. Count along the shorter arc unless the clue says otherwise.

Trap: Counting A or B themselves, which shifts the midpoint by one seat.

Floor and building puzzles

Bank papers number floors from the bottom: the ground floor is floor one and the topmost floor carries the highest number. Fix that convention on the diagram before the first clue.

lives immediately above B

Exactly one floor higher than B, with no floor in between.

Trap: Reading it as “higher than B”, which leaves the floor unfixed.

lives above B

Any floor higher than B's. The clue orders the two people and says nothing about the gap.

Trap: Treating it as adjacent when the word “immediately” is absent.

the topmost floor

The highest-numbered floor in the stated building — floor seven in a seven-floor building.

Trap: Numbering from the top down, which inverts every above-and-below clue on the page.

exactly three floors between A and B

Three floors lie strictly between them, so their floor numbers differ by four.

Trap: Reading the difference as three instead of four.

an odd-numbered floor

Floor one, three, five and so on, counting from the ground floor as one.

Trap: Starting the count at the ground floor as zero, which flips odd and even throughout.

Blood relations

Relation clues are read one hop at a time, and the sentence structure matters more than the vocabulary. Draw the family tree rather than reasoning in words.

A is the maternal uncle of B

A is the brother of B's mother.

Trap: Assuming a gender for B, which the clue never states.

A is the paternal aunt of B

A is the sister of B's father.

Trap: Confusing it with the father's brother's wife, who is an aunt by marriage, not a paternal aunt.

A is the only daughter of B

B has exactly one daughter, and she is A. It says nothing at all about how many sons B has.

Trap: Reading it as “only child”, which the clue does not say.

A is the brother-in-law of B

Either B's sister's husband or B's spouse's brother. The phrase is genuinely ambiguous and both branches stay open until another clue closes one.

Trap: Picking one reading and building the tree on it without carrying the other case.

the only son of A's father

A himself, provided A is male. If A is female, it refers to her brother.

Trap: Answering without first establishing A's gender, which the question often supplies elsewhere.

how is A related to B

The answer is stated from A's side: A is B's something. The order in the question sets the direction.

Trap: Answering in the reverse direction — giving B's relation to A — which is a different word entirely.

Syllogism

A syllogism conclusion follows only if it holds in every diagram the statements permit. One counter-diagram is enough to reject it.

All A are B

Every member of A is inside B. It permits, but does not require, that some B are outside A.

Trap: Reversing it into “all B are A”, which never follows.

Some A are B

At least one A is also a B. It is compatible with all A being B.

Trap: Reading “some” as “some but not all”, which the standard convention does not mean.

No A is B

The two sets are disjoint. It follows immediately that no B is A.

Trap: Hesitating over the reverse form, which is always valid for a negative universal.

Only a few A are B

In the newer pattern this asserts two things at once: some A are B, and some A are not B. Both are definite.

Trap: Treating it as plain “some”, which loses the second half and the conclusion that depends on it.

Some A are not B

At least one A lies outside B. It says nothing about whether any A is inside B.

Trap: Inferring “some A are B” from it, which does not follow.

a possibility conclusion

It follows if any diagram consistent with the statements makes it true. You are testing whether it can be, not whether it must be.

Trap: Applying the must-be test and rejecting a possibility that a valid diagram allows.

either I or II follows

Neither conclusion follows on its own, the two are complementary, and together they cover every case. Both conditions must hold before this option is correct.

Trap: Choosing it for any two conclusions that merely look opposite, without checking that they exhaust the possibilities.

Inequality and coded inequality

A conclusion is definite only when an unbroken chain of the same direction connects the two terms. A single break, or one reversal, makes it indefinite.

A ≥ B

A is greater than or equal to B. Equality is permitted, so A > B is not guaranteed.

Trap: Concluding a strict inequality from a chain that contains one ≥ link.

A > B = C

A is strictly greater than B, and B equals C, so A > C follows definitely.

Trap: Stopping at B and not carrying the relation through the equality.

the coded inequality key

A table defining each symbol — @ meaning ≥, for example. Substitute every symbol before you reason at all.

Trap: Reasoning on the symbols directly and mixing up two similar-looking codes.

either I or II follows (inequality)

The two conclusions use the same pair of terms, neither is definite alone, and between them they cover every case — typically A ≥ B paired with A < B.

Trap: Selecting it when the two conclusions involve different pairs of terms, where it can never apply.

Direction sense and distance

Every turn is relative to the walker's current facing; every named compass point is absolute. Mixing the two is the whole difficulty of the topic.

turns to his left

A ninety-degree turn relative to the direction he is currently facing, not relative to the page.

Trap: Turning towards the left edge of the diagram regardless of which way he was walking.

turns towards the north-east

An absolute bearing. He now faces north-east whatever direction he was facing before.

Trap: Applying it as a relative turn and compounding the error at every later step.

the shortest distance from the starting point

The straight line between start and finish, found with Pythagoras — not the distance actually walked.

Trap: Adding the leg lengths together, which answers a question that was not asked.

takes a right turn, then an about-turn

Ninety degrees clockwise from the current facing, then a full one-hundred-and-eighty-degree reversal.

Trap: Reading an about-turn as another ninety-degree turn.

Scheduling and data sufficiency

Scheduling clues behave exactly like row clues with days in place of seats. Data sufficiency asks a different question from every other topic: whether you could answer, not what the answer is.

a week from Monday to Sunday

Seven ordered slots with two ends, so it is a row, not a circle. Monday and Sunday are the extreme positions.

Trap: Treating the week as cyclic and letting Sunday sit next to Monday.

immediately before B

The slot directly preceding B's, with no slot in between.

Trap: Reading it as “at some point before”, which fixes nothing.

the meeting is not on Wednesday

A negative constraint. It removes one slot and never places anyone.

Trap: Spending time trying to derive a position from a clue that only eliminates.

statement I alone is sufficient

Statement I determines a unique answer by itself, and statement II is not needed.

Trap: Solving the question fully instead of deciding sufficiency, which costs time you do not get back.

both statements together are sufficient, but neither alone

Each statement leaves more than one answer open, and only their combination narrows it to one.

Trap: Reading the two statements together from the start, which makes it impossible to judge either one alone.