TMUA Mathematical Reasoning & Logical Thinking — Questions and Answers

Question 1: If all cats are mammals and some mammals are not pets, which of the following is true?

All cats are pets.
Some pets are not cats.
All pets are cats.
Some mammals are not pets (Correct answer)

Correct answer: Some mammals are not pets

The statement 'Some mammals are not pets' is explicitly given as a premise in the question. Therefore, based on the information provided, this statement must be true. The other options cannot be definitively concluded from the given premises without additional information about the relationship between cats and pets.

Question 2: If x + y = 10 and x - y = 2, what is the value of x?

4
5
6 (Correct answer)
8

Correct answer: 6

This is a system of two linear equations. To solve for x, you can add the two equations together: (x + y) + (x - y) = 10 + 2. This simplifies to 2x = 12. Dividing both sides by 2 gives x = 6.

Question 3: What is the contrapositive of 'If it rains, then the ground gets wet'?

If the ground gets wet, then it rains.
If it does not rain, the ground gets wet.
If the ground is not wet, then it does not rain (Correct answer)
If it rains, then the ground is dry.

Correct answer: If the ground is not wet, then it does not rain

The contrapositive of a conditional statement 'If P, then Q' is 'If not Q, then not P.' In this case, P is 'it rains' and Q is 'the ground gets wet.' Therefore, the contrapositive is 'If the ground is not wet (not Q), then it does not rain (not P).' The contrapositive is logically equivalent to the original statement.

Question 4: A number is divisible by both 3 and 4. Which of the following must also divide the number?

6
9
12 (Correct answer)
7

Correct answer: 12

If a number is divisible by two coprime numbers (numbers with a greatest common divisor of 1), it must also be divisible by their product. Since 3 and 4 are coprime, any number divisible by both 3 and 4 must also be divisible by their product, 3 * 4 = 12. This is because 12 is the least common multiple of 3 and 4.

Question 5: What is the next term in the sequence: 2, 4, 8, 16, ...?

18
24
32 (Correct answer)
30

Correct answer: 32

This is a geometric sequence where each term is obtained by multiplying the previous term by a constant ratio. The common ratio here is 2 (2 * 2 = 4, 4 * 2 = 8, 8 * 2 = 16). Therefore, the next term in the sequence is 16 * 2 = 32.

Question 6: Which statement is logically equivalent to 'If A, then B'?

If B, then A.
If not B, then not A (Correct answer)
If A and B.
If not A, then not B.

Correct answer: If not B, then not A

This is the definition of a contrapositive. A conditional statement 'If A, then B' is logically equivalent to its contrapositive 'If not B, then not A.' This means that if one statement is true, the other must also be true, and vice-versa.

Question 7: If a = 3 and b = 4, what is the value of √(a² + b²)?

6
5 (Correct answer)
7
8

Correct answer: 5

To find the value, substitute the given values into the expression: √(3² + 4²). This simplifies to √(9 + 16), which is √25. The square root of 25 is 5. This calculation is also a classic example of the Pythagorean theorem.

Question 8: Which of the following is a counterexample to 'All prime numbers are odd'?

3
5
7
2 (Correct answer)

Correct answer: 2

A counterexample is a specific instance that disproves a general statement. The statement 'All prime numbers are odd' is false because 2 is a prime number (it is only divisible by 1 and itself) but it is an even number. Therefore, 2 serves as a counterexample.

Question 9: If a function f(x) = 2x + 1, what is f(3)?

5
6
7 (Correct answer)
8

Correct answer: 7

To find f(3), substitute x = 3 into the function's equation. So, f(3) = 2*(3) + 1. This calculates to 6 + 1, which equals 7.

TMUA Mathematical Reasoning & Logical Thinking

If all cats are mammals and some mammals are not pets, which of the following is true?