WGU C960 – DISCRETE MATHEMATICS II OBJECTIVE
ASSESSMENT REVIEW | FULL QUESTIONS, CORRECT
ANSWERS, AND WORKED SOLUTIONS | 2026 UPDATE | 100%
CORRECT.
WGU C960 — Discrete Mathematics II
Comprehensive Original Practice Examination
Course Code: C960
Course Name: Discrete Mathematics II
Institution: Western Governors University
Academic Year: 2026
Document Type: Original Practice Examination with Answers and Worked
Solutions
Date: August 13, 2026
Author/Creator: OpenAI — Original Study Material
Important: This is an independently created practice examination
Table of Contents
1. Section I — Algorithms and Searching
2. Section II — Sorting Algorithms
3. Section III — Algorithm Analysis and Big-O
4. Section IV — Number Theory and Modular Arithmetic
5. Section V — Cryptography
6. Section VI — Recursion and Mathematical Induction
7. Section VII — Counting and Combinatorics
8. Section VIII — Advanced Counting Techniques
9. Section IX — Discrete Probability
10. Section X — Modeling Computation
11. Section XI — Mixed Comprehensive Review
, 12. Answer Summary
Section I — Algorithms and Searching
Question 1 — Multiple Choice
A sorted array contains 1,024 elements. Which searching algorithm can locate an element in at
most approximately 10 comparisons in the worst case?
A. Linear search
B. Binary search
C. Sequential traversal
D. Bubble search
Correct Answer: B. Binary search
Rationale:
Binary search repeatedly divides the remaining search interval in half. Since (2^{10}=1024), a
set of 1,024 elements can be reduced to one candidate after approximately 10 halvings. Its worst-
case running time is (O(\log n)). Linear search may require all 1,024 comparisons.
Question 2 — Short Answer
What prerequisite must be satisfied for ordinary binary search to work correctly?
Correct Answer: The data must be ordered according to the search key.
Rationale:
Binary search determines whether to continue to the left or right by comparing the target with the
middle element. That decision is meaningful only when the elements are sorted. Without
ordering, eliminating half of the search space is unjustified.
Question 3 — Multiple Choice
Suppose a binary search examines a list of 31 sorted elements. What is the maximum number of
halving operations required to isolate a single candidate?
A. 4
B. 5
C. 15
D. 31
Correct Answer: B. 5
,Rationale:
Because (31=2^5-1), five levels of binary subdivision are sufficient. More generally, binary
search requires logarithmic time, approximately (\log_2 n).
Question 4 — Multiple Choice
Which statement best describes linear search?
A. It requires sorted data.
B. It always examines exactly (\log_2 n) elements.
C. It examines elements sequentially until the target is found or the collection ends.
D. It can only be used with arrays.
Correct Answer: C.
Rationale:
Linear search checks elements one at a time. It does not require sorting and works with many
sequential data structures. Its worst-case time complexity is (O(n)).
Question 5 — Short Answer
What is the worst-case time complexity of linear search through (n) elements?
Correct Answer: (O(n)).
Rationale:
In the worst case, the target is the final element or is absent. Therefore, the algorithm may
inspect all (n) elements.
Question 6 — Multiple Choice
A binary search is performed on a sorted list containing 100,000 elements. Compared with linear
search, its primary advantage is:
A. It uses no comparisons.
B. It reduces the search space exponentially by halving it.
C. It always finds the first element.
D. It requires (O(n)) additional storage.
Correct Answer: B.
, Rationale:
Each binary-search comparison eliminates approximately half the remaining possibilities. This
produces (O(\log n)) search time instead of (O(n)).
Question 7 — Short Answer
If a binary-search algorithm operates on (n) elements, give its worst-case asymptotic running
time.
Correct Answer: (O(\log n)).
Rationale:
Each comparison reduces the problem size from (n) to approximately (n/2), then (n/4), and so on.
The number of reductions required is proportional to (\log_2 n).
Question 8 — Multiple Choice
Which data set is most appropriate for binary search?
A. An unsorted list of employee IDs
B. A sorted list of employee IDs
C. A random stream of network packets
D. A collection whose ordering changes after every comparison
Correct Answer: B.
Rationale:
Binary search depends on an ordering relationship that allows half of the search space to be
eliminated after each comparison.
Question 9 — Short Answer
Why does binary search generally outperform linear search on large sorted collections?
Correct Answer: Binary search eliminates approximately half of the remaining candidates at
each step, giving logarithmic growth in the number of comparisons rather than linear growth.
Rationale:
For large (n), (\log_2 n) grows dramatically more slowly than (n). For example, doubling the
input size increases linear work substantially but adds only about one binary-search level.
ASSESSMENT REVIEW | FULL QUESTIONS, CORRECT
ANSWERS, AND WORKED SOLUTIONS | 2026 UPDATE | 100%
CORRECT.
WGU C960 — Discrete Mathematics II
Comprehensive Original Practice Examination
Course Code: C960
Course Name: Discrete Mathematics II
Institution: Western Governors University
Academic Year: 2026
Document Type: Original Practice Examination with Answers and Worked
Solutions
Date: August 13, 2026
Author/Creator: OpenAI — Original Study Material
Important: This is an independently created practice examination
Table of Contents
1. Section I — Algorithms and Searching
2. Section II — Sorting Algorithms
3. Section III — Algorithm Analysis and Big-O
4. Section IV — Number Theory and Modular Arithmetic
5. Section V — Cryptography
6. Section VI — Recursion and Mathematical Induction
7. Section VII — Counting and Combinatorics
8. Section VIII — Advanced Counting Techniques
9. Section IX — Discrete Probability
10. Section X — Modeling Computation
11. Section XI — Mixed Comprehensive Review
, 12. Answer Summary
Section I — Algorithms and Searching
Question 1 — Multiple Choice
A sorted array contains 1,024 elements. Which searching algorithm can locate an element in at
most approximately 10 comparisons in the worst case?
A. Linear search
B. Binary search
C. Sequential traversal
D. Bubble search
Correct Answer: B. Binary search
Rationale:
Binary search repeatedly divides the remaining search interval in half. Since (2^{10}=1024), a
set of 1,024 elements can be reduced to one candidate after approximately 10 halvings. Its worst-
case running time is (O(\log n)). Linear search may require all 1,024 comparisons.
Question 2 — Short Answer
What prerequisite must be satisfied for ordinary binary search to work correctly?
Correct Answer: The data must be ordered according to the search key.
Rationale:
Binary search determines whether to continue to the left or right by comparing the target with the
middle element. That decision is meaningful only when the elements are sorted. Without
ordering, eliminating half of the search space is unjustified.
Question 3 — Multiple Choice
Suppose a binary search examines a list of 31 sorted elements. What is the maximum number of
halving operations required to isolate a single candidate?
A. 4
B. 5
C. 15
D. 31
Correct Answer: B. 5
,Rationale:
Because (31=2^5-1), five levels of binary subdivision are sufficient. More generally, binary
search requires logarithmic time, approximately (\log_2 n).
Question 4 — Multiple Choice
Which statement best describes linear search?
A. It requires sorted data.
B. It always examines exactly (\log_2 n) elements.
C. It examines elements sequentially until the target is found or the collection ends.
D. It can only be used with arrays.
Correct Answer: C.
Rationale:
Linear search checks elements one at a time. It does not require sorting and works with many
sequential data structures. Its worst-case time complexity is (O(n)).
Question 5 — Short Answer
What is the worst-case time complexity of linear search through (n) elements?
Correct Answer: (O(n)).
Rationale:
In the worst case, the target is the final element or is absent. Therefore, the algorithm may
inspect all (n) elements.
Question 6 — Multiple Choice
A binary search is performed on a sorted list containing 100,000 elements. Compared with linear
search, its primary advantage is:
A. It uses no comparisons.
B. It reduces the search space exponentially by halving it.
C. It always finds the first element.
D. It requires (O(n)) additional storage.
Correct Answer: B.
, Rationale:
Each binary-search comparison eliminates approximately half the remaining possibilities. This
produces (O(\log n)) search time instead of (O(n)).
Question 7 — Short Answer
If a binary-search algorithm operates on (n) elements, give its worst-case asymptotic running
time.
Correct Answer: (O(\log n)).
Rationale:
Each comparison reduces the problem size from (n) to approximately (n/2), then (n/4), and so on.
The number of reductions required is proportional to (\log_2 n).
Question 8 — Multiple Choice
Which data set is most appropriate for binary search?
A. An unsorted list of employee IDs
B. A sorted list of employee IDs
C. A random stream of network packets
D. A collection whose ordering changes after every comparison
Correct Answer: B.
Rationale:
Binary search depends on an ordering relationship that allows half of the search space to be
eliminated after each comparison.
Question 9 — Short Answer
Why does binary search generally outperform linear search on large sorted collections?
Correct Answer: Binary search eliminates approximately half of the remaining candidates at
each step, giving logarithmic growth in the number of comparisons rather than linear growth.
Rationale:
For large (n), (\log_2 n) grows dramatically more slowly than (n). For example, doubling the
input size increases linear work substantially but adds only about one binary-search level.
