TMUA Mathematical Reasoning & Logical Thinking 2

Question 1

Which of the following is the contrapositive of the statement 'If n is divisible by 6, then n is divisible by 2'?

Accepted Answer

If n is not divisible by 2, then n is not divisible by 6

Answer

The contrapositive of 'If P then Q' is 'If not Q then not P', so 'If n is not divisible by 2, then n is not divisible by 6'.

Question 2

A sequence is defined by a₁ = 3 and aₙ₊₁ = 2aₙ − 1. What is a₄?

Accepted Answer

17

Answer

a₂ = 2(3)−1 = 5, a₃ = 2(5)−1 = 9, a₄ = 2(9)−1 = 17.

Question 3

For integers m and n, which statement is always true if m and n are both odd?

Accepted Answer

m − n is even

Answer

Odd minus odd equals even, since (2j+1)−(2k+1) = 2(j−k), which is always even.

Question 4

How many integers between 1 and 100 inclusive are divisible by 3 but not by 9?

Accepted Answer

22

Answer

Divisible by 3: floor(100/3)=33; divisible by 9: floor(100/9)=11; answer = 33−11 = 22.

Question 5

If p → q and q → r are both true, which conclusion must follow by the chain rule?

Accepted Answer

p → r

Answer

Hypothetical syllogism (chain rule) states: if p→q and q→r, then p→r.

(TMUA) Test of Mathematics for University Admission Practice Test