IPMAT Logical Reasoning Syllabus

What is the 'Odd One Out' (classification) question type, and what is the solving strategy?

You are given several items and must pick the one that does not share the common property of the rest. Strategy: find the rule/category that the majority of items satisfy, then the single item that fails that rule is the odd one out.

Find the odd one out and state the rule: 3, 5, 7, 9, 11, 13.

9 is the odd one out. All the others are prime numbers, while 9 = 3×3 is composite.

Find the odd one out and state the rule: 8, 27, 64, 100, 125.

100 is the odd one out. The others (8, 27, 64, 125) are perfect cubes (2³, 3³, 4³, 5³), whereas 100 is a perfect square, not a cube.

In a word-based 'odd one out', name three category bases commonly used to group words.

Common bases: by class/type (e.g. all fruits except one), by function/use, and by characteristic property (e.g. all can fly, all are metals). Less common bases include letter patterns or number of vowels.

What is a syllogism in logical reasoning?

A syllogism is a form of deductive argument with two given premises and a conclusion; you must determine whether the conclusion(s) logically and necessarily follow from the premises, regardless of real-world truth.

What are the four standard categorical statement types (A, E, I, O) used in syllogisms?

A = Universal affirmative ('All S are P'); E = Universal negative ('No S is P'); I = Particular affirmative ('Some S are P'); O = Particular negative ('Some S are not P').

What valid immediate conversions can be drawn from 'All A are B', 'No A is B', and 'Some A are B'?

'All A are B' converts to 'Some B are A'. 'No A is B' converts to 'No B is A'. 'Some A are B' converts to 'Some B are A'. ('Some A are not B' has no valid conversion.)

In syllogisms, what conclusion can be drawn from 'All A are B' and 'All B are C'?

'All A are C' (and therefore 'Some C are A' and 'Some A are C'). This is the classic transitive chain through the middle term B.

In syllogisms, what can be concluded from 'All A are B' and 'No B is C'?

'No A is C' (and its conversion 'No C is A', plus 'Some A are not C'). A definite negative conclusion follows.

What is the rule about two particular premises or two negative premises in syllogisms?

No definite conclusion can be drawn from two particular premises (both 'Some...') nor from two negative premises (both 'No.../Some... not'). At least one premise must be universal and at least one must be affirmative for a valid conclusion.

What is the 'complementary pair' (either-or) rule in advanced syllogisms?

When two conclusions individually do not follow but together exhaust the possibilities (e.g. 'Some A are B' and 'Some A are not B', or 'All A are B' and 'Some A are not B'), they form a complementary pair and the answer is 'Either I or II follows'. They must have the same subject and predicate and be a contradictory (I–O or A–O) pairing.

In syllogisms, what is the 'possibility' type conclusion and when is it true?

A possibility conclusion uses 'can be'/'possibly'. It is true whenever the premises do not forbid that arrangement. For example, from 'All A are B', the conclusion 'Some B can be A' or 'All B can be A is a possibility' holds because nothing rules it out.

How does a Venn diagram help solve advanced syllogisms, and what must you check?

Draw circles representing the premises, trying every legitimate arrangement of overlaps. A conclusion 'follows' only if it is true in EVERY possible diagram consistent with the premises; if any valid diagram makes it false, it does not follow.

In syllogisms, does 'Some A are B' guarantee 'Some A are not B'?

No. 'Some A are B' means at least one A is B and is compatible with 'All A are B'. Therefore 'Some A are not B' does not necessarily follow; together they form an either-or complementary pair, not a definite conclusion.

What is a linear arrangement puzzle and what two facing conventions must you fix first?

A linear arrangement places people/objects in a single row. First fix: (1) the direction everyone faces — typically all facing north (then for an observer, left/right is the reverse of the person's own left/right unless stated) and (2) whether positions are counted from a defined left or right end.

In a single row of people all facing north, if a person says 'to my left', which direction is that for an observer facing them?

For a person facing north, their left is the west side. An observer facing south (looking at the row) sees that as their own right. So 'the person's left' corresponds to the observer's right; always convert relative to the stated facing direction.

In linear arrangements, what is the difference between two people sitting 'adjacent' versus 'with exactly one person between them'?

'Adjacent'/'next to' means they occupy consecutive seats with no one between (gap of 0). 'Exactly one person between them' means one seat separates them (gap of 1). Misreading the gap size is the most common error.

For a linear arrangement of n people in a row, how many total seating orders are possible with no constraints?

n! (n factorial) arrangements, since each of the n positions can be filled distinctly. Constraints (fixed positions, adjacency, blocks) reduce this count.

In two-row (parallel) linear arrangements where rows face each other, how is 'immediate left' affected?

The two rows face opposite directions, so their left/right are mirrored. A person in the north-facing row has left/right opposite to a person in the south-facing row directly across. Also, the person sitting opposite is the one facing them across the rows, which must be aligned by counting positions from corresponding ends.

What defines a circular arrangement puzzle, and what is the key difference from a linear one?

People are seated around a circle. Unlike a row, there are no fixed 'ends'; positions are relative (each person has a left and right neighbour, and the arrangement wraps around). Facing center vs. facing outward must be determined to interpret left/right.

In a circular arrangement, how do left and right change when a person faces the center versus faces away from the center?

When facing the center, a person's right hand points clockwise and left points anticlockwise. When facing outward (away from center), this reverses: right points anticlockwise and left points clockwise. You must apply the correct convention per person based on their facing.

For n distinct people seated around a circular table, how many distinct arrangements are there?

(n−1)! arrangements, because rotations of the same order are considered identical (one person's position is fixed as a reference). If clockwise and anticlockwise are also considered the same (e.g. a necklace), it becomes (n−1)!/2.

In a circular table with people facing the center, where does a person sit who is 'third to the right' of someone?

Move three seats in the clockwise direction (since right = clockwise when facing center), counting the seats one by one from the reference person to land on the third seat clockwise.

In circular arrangements, if all members face the center, are two people 'exactly opposite' each other only when the number of people is even?

Yes. A person sitting exactly opposite exists only when the total number of people is even; with an even number n, the opposite person is n/2 seats away. With an odd number, no seat is exactly diametrically opposite.

What is a 'seating arrangement' puzzle in the general sense, and what are the main sub-types?

It is a constraint-satisfaction puzzle where people/items are placed according to given conditions. Main sub-types: linear (single/double row), circular (round table), rectangular/square table, and grid or matrix-based (combining seating with attributes like jobs, colors, ages).

What is the recommended general strategy for solving any seating arrangement puzzle?

1) Note the shape and facing direction. 2) List all clues, separating definite clues from conditional ones. 3) Start placing using the most definite clues first. 4) Make a diagram, use placeholders for floating clues, and consider all possible cases. 5) Eliminate cases that violate constraints until one consistent arrangement remains.

In a square or rectangular table seating with people on all four sides, how are corner versus middle seats and facings typically defined?

Commonly people at the four corners face outward (away from center) and people in the middle of each side face the center (or vice versa, as stated). You must read the puzzle's facing rule, because it flips each person's left/right relative to the table.

In seating puzzles, what is the difference between a 'definite' clue and a 'conditional/floating' clue, and which should you use first?

A definite clue fixes an exact position or an unambiguous relationship; a floating clue (e.g. 'P is somewhere to the left of Q') allows multiple placements. Use definite clues first to anchor the diagram, then apply floating clues to narrow down cases.

In a rectangular table with 8 people, 3 on each longer side and 1 at each shorter end, how do you interpret 'sitting opposite'?

Only the people on the two longer sides sit opposite one another, aligned position-by-position across the table; the two people at the short ends sit opposite each other. Aligning the correct pairs by counting from corresponding corners is essential before placing 'opposite' clues.