Q. If a set of students is defined by the constraint of having a GPA above 3.5, which of the following students would be included?
A.
Alice with a GPA of 3.4
B.
Bob with a GPA of 3.6
C.
Charlie with a GPA of 3.5
D.
Diana with a GPA of 3.2
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Solution
Bob is the only student with a GPA above 3.5, thus he is included in the set.
Correct Answer: B — Bob with a GPA of 3.6
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Q. If a task must be completed by Friday and takes 3 days, starting from Wednesday, which of the following is the latest possible start day?
A.
Monday
B.
Tuesday
C.
Wednesday
D.
Thursday
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Solution
Thursday is the latest start day as the task will then complete by Saturday, which is not allowed.
Correct Answer: D — Thursday
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Q. If all cats are mammals and some mammals are not dogs, which of the following statements must be true?
A.
All cats are dogs.
B.
Some cats are not dogs.
C.
All mammals are cats.
D.
Some dogs are not mammals.
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Solution
Since not all mammals are dogs, it follows that some cats, being mammals, cannot be dogs.
Correct Answer: B — Some cats are not dogs.
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Q. If set A = {a, b, c} and set B = {b, c, d}, what is the hybrid set formed by the intersection of A and B?
A.
{a, b, c, d}
B.
{b, c}
C.
{a, d}
D.
{}
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Solution
The intersection of sets A and B includes only the elements that are present in both sets, which are {b, c}.
Correct Answer: B — {b, c}
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Q. If set A contains 15 elements, set B contains 10 elements, and the intersection of A and B contains 5 elements, how many elements are in the union of sets A and B?
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Solution
The number of elements in the union of sets A and B is given by |A ∪ B| = |A| + |B| - |A ∩ B| = 15 + 10 - 5 = 20.
Correct Answer: A — 20
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Q. If set C is a hybrid set formed by combining set A and set B, which of the following is a possible characteristic of set C?
A.
Set C cannot have any elements from set A.
B.
Set C must have all elements from set B.
C.
Set C may have elements that are exclusive to either set A or set B.
D.
Set C will always be larger than both set A and set B.
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Solution
Hybrid sets can include elements that are exclusive to either of the original sets, making them versatile in composition.
Correct Answer: C — Set C may have elements that are exclusive to either set A or set B.
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Q. If set C is defined as the set of all x such that x is a multiple of 3 and less than 15, which of the following is a member of set C?
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Solution
Both 12 and 9 are multiples of 3 and less than 15, but 12 is the first option listed.
Correct Answer: A — 12
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Q. If set C is defined as {x | x is an integer and x is divisible by 3}, which of the following integers is NOT a member of set C?
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Solution
The integer 10 is not divisible by 3, hence it is not a member of set C.
Correct Answer: C — 10
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Q. If set D is a hybrid set that includes elements from set E and set F, which of the following is a valid conclusion?
A.
All elements of set E are in set D.
B.
Set D cannot have any elements from set F.
C.
Set D may contain elements that are not in either set E or set F.
D.
Set D must be equal to the intersection of set E and set F.
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Solution
Hybrid sets can include additional elements beyond those found in the original sets, allowing for greater flexibility.
Correct Answer: C — Set D may contain elements that are not in either set E or set F.
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Q. If set D is defined by the constraints z ≥ 2 and z ≤ 8, which of the following is the range of values for set D?
A.
2 to 8
B.
1 to 9
C.
0 to 10
D.
2 to 9
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Solution
The range of values for set D is from 2 to 8, inclusive.
Correct Answer: A — 2 to 8
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Q. If set T = {1, 2, 3} and set U = {2, 3, 4}, what is the difference T - U?
A.
{1}
B.
{2, 3}
C.
{4}
D.
{}
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Solution
The difference T - U includes elements that are in set T but not in set U, which is {1}.
Correct Answer: A — {1}
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Q. If set X contains {1, 2, 3} and set Y contains {3, 4, 5}, what is the hybrid set formed by the union of X and Y?
A.
{1, 2, 3, 4, 5}
B.
{3}
C.
{1, 2}
D.
{4, 5}
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Solution
The union of set X and set Y includes all unique elements from both sets, resulting in {1, 2, 3, 4, 5}.
Correct Answer: A — {1, 2, 3, 4, 5}
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Q. If set X contains {1, 2, 3} and set Y contains {3, 4, 5}, what is the hybrid set formed by the union of set X and set Y?
A.
{1, 2, 3, 4, 5}
B.
{1, 2, 3}
C.
{3, 4}
D.
{1, 2, 4, 5}
Show solution
Solution
The hybrid set formed by the union of set X and set Y includes all unique elements from both sets, which are {1, 2, 3, 4, 5}.
Correct Answer: A — {1, 2, 3, 4, 5}
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Q. If task C must be completed before task A, and task A must be completed before task D, which of the following is a correct inference?
A.
C can start after A
B.
D can start before A
C.
A can start before C
D.
D can start only after C
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Solution
D can only start after both A and C are completed, making the inference correct.
Correct Answer: D — D can start only after C
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Q. If task E cannot start until both tasks A and C are completed, which of the following statements is true?
A.
E can start before A
B.
E can start before C
C.
E can start after A and C
D.
E can start only after A or C
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Solution
E can only start after both A and C are completed, making the statement true.
Correct Answer: C — E can start after A and C
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Q. If task F must be completed before task G, and task G must be completed before task H, which of the following is a valid sequence?
A.
H, G, F
B.
F, H, G
C.
F, G, H
D.
G, F, H
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Solution
The sequence F, G, H respects the order that F is before G and G is before H.
Correct Answer: C — F, G, H
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Q. If task M must be completed before task N, and task N must be completed before task O, which of the following is a valid inference?
A.
M can start after N
B.
O can start before M
C.
N can start before M
D.
M must be completed before O
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Solution
Since M must be completed before N, and N before O, M must indeed be completed before O.
Correct Answer: D — M must be completed before O
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Q. If task X is dependent on tasks Y and Z being completed first, which of the following statements is true?
A.
X can start before Y and Z
B.
Y and Z can start after X
C.
X can only start after Y and Z
D.
Y and Z are independent of X
Show solution
Solution
Task X can only start after both tasks Y and Z are completed, making this statement true.
Correct Answer: C — X can only start after Y and Z
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Q. If tasks A, B, and C must be completed in that order, which of the following sequences is invalid?
A.
A, B, C
B.
B, A, C
C.
A, C, B
D.
C, A, B
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Solution
The sequence B, A, C is invalid as it does not respect the order of A before B.
Correct Answer: B — B, A, C
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Q. If tasks A, B, and C must be completed in that order, which of the following sequences is valid?
A.
C, B, A
B.
A, C, B
C.
B, A, C
D.
A, B, C
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Solution
The sequence A, B, C follows the required order.
Correct Answer: D — A, B, C
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Q. If tasks L, M, and N are to be completed with L before M and N, which of the following sequences is correct?
A.
M, L, N
B.
L, N, M
C.
N, M, L
D.
L, M, N
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Solution
The sequence L, M, N is correct as it respects the order of L before both M and N.
Correct Answer: D — L, M, N
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Q. If the meetings of a project team are scheduled on Monday, Wednesday, and Friday, and no two meetings can occur on consecutive days, which day can be added for an additional meeting without violating the schedule?
A.
Tuesday
B.
Thursday
C.
Saturday
D.
Sunday
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Solution
Thursday can be added as it does not fall on a consecutive day with the existing meetings.
Correct Answer: B — Thursday
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Q. In a class of 40 students, 25 study Mathematics, 20 study Science, and 10 study both subjects. How many students study only Mathematics?
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Solution
The number of students who study only Mathematics is |Mathematics| - |Both| = 25 - 10 = 15.
Correct Answer: A — 15
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Q. In a class of 50 students, 20 study Mathematics, 25 study Science, and 10 study both. How many students study only Mathematics?
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Solution
The number of students who study only Mathematics is 20 - 10 = 10.
Correct Answer: A — 10
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Q. In a class of 50 students, 20 study Mathematics, 25 study Science, and 10 study both. How many students study at least one of the subjects?
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Solution
Using inclusion-exclusion, the total is 20 + 25 - 10 = 35.
Correct Answer: B — 40
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Q. In a constraint-based set of colors, if red and blue are included, which of the following colors could be excluded based on the constraint of primary colors?
A.
Green
B.
Yellow
C.
Purple
D.
Orange
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Solution
Purple is a secondary color formed by mixing red and blue, thus it could be excluded if only primary colors are considered.
Correct Answer: C — Purple
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Q. In a constraint-based set of fruits, if the constraint is that all fruits must be tropical, which of the following would be excluded?
A.
Mango
B.
Banana
C.
Apple
D.
Pineapple
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Solution
Apple is not a tropical fruit, thus it would be excluded from the set.
Correct Answer: C — Apple
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Q. In a constraint-based set, if the constraints are x < 0 and x > -5, which of the following values is valid?
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Solution
The value -3 satisfies both constraints, making it a valid member of the set.
Correct Answer: A — -3
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Q. In a group of 200 people, 120 like dogs, 80 like cats, and 50 like both. How many people like only dogs?
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Solution
The number of people who like only dogs is 120 - 50 = 70.
Correct Answer: A — 70
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Q. In a group of 50 people, 30 like dogs, 25 like cats, and 10 like both. How many people do not like either dogs or cats?
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Solution
The number of people who like either dogs or cats is 30 + 25 - 10 = 45. Therefore, those who do not like either is 50 - 45 = 5.
Correct Answer: B — 10
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