TMUA Mathematical Reasoning & Logical Thinking

Question 1

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

Accepted Answer

Some mammals are not pets

Answer

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?

Accepted Answer

6

Answer

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'?

Accepted Answer

If the ground is not wet, then it does not rain

Answer

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?

Accepted Answer

12

Answer

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, ...?

Accepted Answer

32

Answer

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.

(TMUA) Test of Mathematics for University Admission Practice Test

(TMUA) Test of Mathematics for University Admission Practice Test

TMUA Mathematical Reasoning & Logical Thinking