PI - Cognitive Assessment Logical Deduction Problems 2 — Questions and Answers

Question 1: All managers attend the conference. Sarah is a manager. Which conclusion must be true?

Sarah does not attend the conference
Sarah might attend the conference
Sarah attends the conference (Correct answer)
Only managers attend the conference

Correct answer: Sarah attends the conference

Since all managers attend the conference and Sarah is a manager, Sarah must attend the conference. This is a direct syllogism.

This is a classic categorical syllogism. The major premise states ALL managers attend the conference (universal affirmative). The minor premise states Sarah IS a manager (specific case). Therefore, the conclusion must be that Sarah attends the conference. Option D is a common trap — the premise says all managers attend, but doesn't say ONLY managers attend; others might attend too.

Question 2: If it rains, the game is cancelled. The game was not cancelled. What can you conclude?

It rained
It did not rain (Correct answer)
The game was postponed
Nothing can be concluded

Correct answer: It did not rain

This is modus tollens: If P then Q. Not Q. Therefore, not P. Since the game wasn't cancelled, it didn't rain.

This uses modus tollens (denying the consequent), one of the fundamental rules of logical deduction. The conditional states: rain → cancellation. We know the cancellation didn't occur (not Q). Therefore, rain didn't occur (not P). Note: if the game WAS cancelled, we couldn't conclude it rained — other reasons could cancel it. But the reverse (no cancellation → no rain) is logically valid.

Question 3: Tom is taller than Jerry. Jerry is taller than Sam. Mike is shorter than Sam. Who is the tallest?

Sam
Jerry
Tom (Correct answer)
Mike

Correct answer: Tom

Ordering from tallest to shortest: Tom > Jerry > Sam > Mike. Tom is the tallest.

Build the complete ordering step by step. Tom > Jerry (given). Jerry > Sam (given). Sam > Mike (given, since Mike is shorter than Sam). Combining: Tom > Jerry > Sam > Mike. Tom is at the top of the ordering, making him the tallest. This is a transitive ordering problem — a common type on the PI Cognitive Assessment.

Question 4: In a group of 30 people, 18 speak English, 15 speak French, and 5 speak neither. How many speak both languages?

3
8 (Correct answer)
10
5

Correct answer: 8

People who speak at least one language: 30 - 5 = 25. Using inclusion-exclusion: 18 + 15 - both = 25, so both = 8.

Using the inclusion-exclusion principle: Total = English only + French only + Both + Neither. People speaking at least one language = 30 - 5 = 25. English + French = 18 + 15 = 33, but this double-counts those who speak both. So: 33 - both = 25, meaning both = 8. Eight people speak both English and French.

Question 5: No reptiles are mammals. All snakes are reptiles. Which conclusion is valid?

Some snakes are mammals
No snakes are mammals (Correct answer)
All reptiles are snakes
Some mammals are reptiles

Correct answer: No snakes are mammals

Since no reptiles are mammals and all snakes are reptiles, no snakes can be mammals.

This is a syllogism with a universal negative major premise. No reptiles are mammals (universal negative). All snakes are reptiles (universal affirmative). Since snakes are a subset of reptiles, and no reptile is a mammal, it follows that no snake is a mammal. Option C reverses the subset relationship (not all reptiles are snakes). Options A and D contradict the first premise.

Question 6: A code uses: circle = 1, triangle = 2, square = 3. The code for a sequence is: triangle, square, circle, square. What is the sum?

7
8
9 (Correct answer)
10

Correct answer: 9

Triangle(2) + Square(3) + Circle(1) + Square(3) = 9.

Substituting the code values: triangle = 2, square = 3, circle = 1, square = 3. Sum = 2 + 3 + 1 + 3 = 9. This tests your ability to apply a coding system and perform arithmetic — a common PI Cognitive Assessment task that combines symbol decoding with numerical computation.

PI - Cognitive Assessment Logical Deduction Problems 2

All managers attend the conference.
Sarah is a manager.
Which conclusion must be true?