WGU C960 Discrete Mathematics II:
The Ultimate 2026 OA Practice Bank –
Questions, Verified Answers, and
Step-by-Step Rationales
Algorithms & Pseudocode
Question
Consider the following pseudocode:
text
x := 2
If (x > 0)
abs := x
Else
abs := -x
End-if
What is the final value of abs?
Answer: C. 2
Rationale: The condition (x > 0) evaluates to true because x = 2. The line abs := x is
executed, assigning the value 2 to abs. The Else branch is skipped entirely.
,Question
What is the final value of product after the following pseudocode is run?
text
x := -2
product := 1
count := 5
While (count > 0)
product := product * count
count := count - 2
End-while
Answer: C. 15
Rationale: First iteration: count = 5, product = 1 × 5 = 5, count becomes 3. Second
iteration: count = 3, product = 5 × 3 = 15, count becomes 1. The loop executes a third
iteration: count = 1, product = 15 × 1 = 15, count becomes -1. The loop stops
because count > 0 is false.
Question
How many iterations will the loop in the previous question execute?
Answer: C. 3
Rationale: The count values during the loop are 5, 3, and 1. Each time count > 0, the
loop executes. When count becomes -1, the condition is false. Therefore, the loop
executes exactly 3 iterations.
,Question
Function Sampler(Sequence Data) sets N to the length of Data and processes while N ≥ 1.
If Data = [1, 3, 5, 7, 9], how many times does the loop iterate?
Answer: C. 5
Rationale: The loop continues as long as N ≥ 1. Starting with N = 5, it will iterate for N =
5, 4, 3, 2, 1 — a total of 5 iterations — before N becomes 0 and the condition fails.
Question
What is the worst-case time complexity of the Merge0 function that merges two sorted
lists of length n?
Answer: B. O(n)
Rationale: The Merge0 function processes each element from both lists exactly once.
Each removal and addition operation is O(1). With two lists of total length 2n, the
algorithm performs exactly 2n operations, giving linear time complexity O(n).
Question
Assume Sort(list L) operates in O(n log n) time for n = length of list. Given Sort3(L1,
L2, L3) where each list has length n, which function dominates the run time?
Answer: C. O(n³ log n)
Rationale: The algorithm includes Sort operations (O(n log n) each) nested within loops
that iterate through lists. Analysis shows the nested structure yields O(n³ log n) as the
dominant time complexity.
, Question
Which function is Θ(x³)?
Answer: B. 4x³ + √x − 1
Rationale: A function is Θ(x³) if its highest-degree term is exactly x³ (constant
coefficients do not affect asymptotic growth). Option B has the leading term 4x³, making
it Θ(x³). All other options have different leading terms (x², x⁴, or x).
Question
The primary resources to optimize when analyzing an algorithm are:
Answer: time complexity (the time the algorithm requires to run) and space complexity
(the amount of memory used).
Rationale: Algorithm analysis focuses on two main resources: time (how long the
algorithm takes to execute) and space (how much memory it uses). These are the
fundamental measures of algorithm efficiency.
Question
The time an algorithm takes to run depends on:
Answer: the speed of the processing unit, the number of calculations that need to be
performed, and the number of conditions that need to be evaluated.
The Ultimate 2026 OA Practice Bank –
Questions, Verified Answers, and
Step-by-Step Rationales
Algorithms & Pseudocode
Question
Consider the following pseudocode:
text
x := 2
If (x > 0)
abs := x
Else
abs := -x
End-if
What is the final value of abs?
Answer: C. 2
Rationale: The condition (x > 0) evaluates to true because x = 2. The line abs := x is
executed, assigning the value 2 to abs. The Else branch is skipped entirely.
,Question
What is the final value of product after the following pseudocode is run?
text
x := -2
product := 1
count := 5
While (count > 0)
product := product * count
count := count - 2
End-while
Answer: C. 15
Rationale: First iteration: count = 5, product = 1 × 5 = 5, count becomes 3. Second
iteration: count = 3, product = 5 × 3 = 15, count becomes 1. The loop executes a third
iteration: count = 1, product = 15 × 1 = 15, count becomes -1. The loop stops
because count > 0 is false.
Question
How many iterations will the loop in the previous question execute?
Answer: C. 3
Rationale: The count values during the loop are 5, 3, and 1. Each time count > 0, the
loop executes. When count becomes -1, the condition is false. Therefore, the loop
executes exactly 3 iterations.
,Question
Function Sampler(Sequence Data) sets N to the length of Data and processes while N ≥ 1.
If Data = [1, 3, 5, 7, 9], how many times does the loop iterate?
Answer: C. 5
Rationale: The loop continues as long as N ≥ 1. Starting with N = 5, it will iterate for N =
5, 4, 3, 2, 1 — a total of 5 iterations — before N becomes 0 and the condition fails.
Question
What is the worst-case time complexity of the Merge0 function that merges two sorted
lists of length n?
Answer: B. O(n)
Rationale: The Merge0 function processes each element from both lists exactly once.
Each removal and addition operation is O(1). With two lists of total length 2n, the
algorithm performs exactly 2n operations, giving linear time complexity O(n).
Question
Assume Sort(list L) operates in O(n log n) time for n = length of list. Given Sort3(L1,
L2, L3) where each list has length n, which function dominates the run time?
Answer: C. O(n³ log n)
Rationale: The algorithm includes Sort operations (O(n log n) each) nested within loops
that iterate through lists. Analysis shows the nested structure yields O(n³ log n) as the
dominant time complexity.
, Question
Which function is Θ(x³)?
Answer: B. 4x³ + √x − 1
Rationale: A function is Θ(x³) if its highest-degree term is exactly x³ (constant
coefficients do not affect asymptotic growth). Option B has the leading term 4x³, making
it Θ(x³). All other options have different leading terms (x², x⁴, or x).
Question
The primary resources to optimize when analyzing an algorithm are:
Answer: time complexity (the time the algorithm requires to run) and space complexity
(the amount of memory used).
Rationale: Algorithm analysis focuses on two main resources: time (how long the
algorithm takes to execute) and space (how much memory it uses). These are the
fundamental measures of algorithm efficiency.
Question
The time an algorithm takes to run depends on:
Answer: the speed of the processing unit, the number of calculations that need to be
performed, and the number of conditions that need to be evaluated.
