GMA Logical Reasoning 2

Question 1

If all A are B, and all B are C, which statement must be true?
(A) All C are A
(B) All A are C
(C) Some B are not A
(D) No A are C

Accepted Answer

All A are C

Answer

By transitivity: if A⊆B and B⊆C, then A⊆C. Therefore 'All A are C' must be true.

Question 2

A shopkeeper says: 'If it rains, I close early.' It is raining. What can you conclude?
(A) It will stop raining soon.
(B) The shopkeeper closes early.
(C) The shopkeeper never closes early when it's sunny.
(D) The shopkeeper is closed.

Accepted Answer

The shopkeeper closes early.

Answer

Given 'If rain then close early' and the fact that it is raining, we can apply modus ponens: the shopkeeper closes early.

Question 3

Five people sit in a row: Alice, Bob, Carol, David, Eve. Alice sits to the left of Bob. Carol sits between Alice and David. Eve sits to the right of Bob. Where is Carol relative to Bob?

Accepted Answer

To the left of Bob

Answer

Order: Alice, Carol, David, Bob, Eve (or similar). Carol sits between Alice and David, who are both to the left of Bob, so Carol is to the left of Bob.

Question 4

In a logic puzzle, exactly one of the following statements is true:
(A) All cats have wings.
(B) Some cats have wings.
(C) No cats have wings.
Which statement is true?

Accepted Answer

Statement C

Answer

Statement A (all cats have wings) is false. Statement B (some cats have wings) is also false — cats do not have wings. Statement C (no cats have wings) is true and is the only true statement.

Question 5

A code states: 'Only employees with Level 3 clearance may enter Room X.' A person enters Room X. What can you conclude?
(A) They definitely have Level 3 clearance.
(B) They might not have Level 3 clearance.
(C) All Level 3 employees are in Room X.
(D) Room X is secure.

Accepted Answer

They definitely have Level 3 clearance.

Answer

If only Level 3 employees may enter, and someone has entered, they must have Level 3 clearance. This is modus tollens in reverse (contrapositive applied positively).

(GMA) General Mental Ability Practice Test

(GMA) General Mental Ability Practice Test

GMA Logical Reasoning 2