TMUA Mathematical Reasoning & Logical Thinking 4

Question 1

Which of the following is an example of a proof by contradiction?

Accepted Answer

Assuming ¬P and showing this leads to a logical impossibility

Answer

Proof by contradiction assumes the negation of the claim and derives a contradiction, establishing the original claim.

Question 2

Given that log₂(x) + log₂(x−2) = 3, what is x?

Accepted Answer

4

Answer

log₂(x(x−2))=3 gives x(x−2)=8, so x²−2x−8=0, factoring to (x−4)(x+2)=0; x=4 (rejecting x=−2 as x>2).

Question 3

How many subsets does a set with 4 elements have?

Accepted Answer

16

Answer

A set with n elements has 2ⁿ subsets; for n=4, that is 2⁴=16.

Question 4

Two events A and B are mutually exclusive. If P(A)=0.3 and P(B)=0.4, what is P(A or B)?

Accepted Answer

0.70

Answer

For mutually exclusive events, P(A∪B)=P(A)+P(B)=0.3+0.4=0.7.

Question 5

What is the smallest positive integer n such that n! is divisible by 10⁶?

Accepted Answer

25

Answer

10⁶=2⁶×5⁶; the number of factors of 5 in n! determines the constraint. 25! contributes floor(25/5)+floor(25/25)=5+1=6 factors of 5, so n=25.

(TMUA) Test of Mathematics for University Admission Practice Test