Q. If 'A' is taller than 'B', and 'B' is taller than 'C', which of the following statements is necessarily true?
A.
A is taller than C.
B.
C is taller than A.
C.
B is shorter than A.
D.
C is shorter than B.
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Solution
From the given information, it follows that A is taller than C.
Correct Answer: A — A is taller than C.
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Q. If 25% of a population likes apples, 15% likes oranges, and 5% likes both, what percentage likes either apples or oranges?
A.
35%
B.
30%
C.
25%
D.
20%
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Solution
Using inclusion-exclusion, the percentage is 25% + 15% - 5% = 35%.
Correct Answer: A — 35%
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Q. If 40 students play cricket, 30 play football, and 10 play both, how many students play either cricket or football?
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Solution
Using inclusion-exclusion, the total is 40 + 30 - 10 = 60.
Correct Answer: A — 60
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Q. If 40 students play cricket, 30 play football, and 10 play both, how many students play only cricket?
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Solution
The number of students who play only cricket is 40 - 10 = 30.
Correct Answer: B — 20
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Q. If 45% of people like tea, 35% like coffee, and 15% like both, what percentage of people like neither tea nor coffee?
A.
25%
B.
15%
C.
30%
D.
20%
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Solution
The percentage of people who like either tea or coffee is 45% + 35% - 15% = 65%. Therefore, those who like neither is 100% - 65% = 35%.
Correct Answer: A — 25%
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Q. If 50% of students like soccer, 30% like basketball, and 10% like both, what percentage of students like only soccer?
A.
40%
B.
30%
C.
20%
D.
10%
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Solution
The percentage of students who like only soccer is 50% - 10% = 40%.
Correct Answer: A — 40%
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Q. If 60% of students like reading fiction, 40% like reading non-fiction, and 10% like both, what percentage of students like only fiction?
A.
50%
B.
40%
C.
30%
D.
20%
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Solution
The percentage of students who like only fiction is 60% - 10% = 50%.
Correct Answer: A — 50%
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Q. If 60% of students like reading, 40% like writing, and 10% like both, what percentage of students like either reading or writing?
A.
90%
B.
80%
C.
70%
D.
60%
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Solution
Using inclusion-exclusion, the percentage is 60% + 40% - 10% = 90%.
Correct Answer: A — 90%
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Q. If 70% of students in a school play football, 50% play basketball, and 20% play both, what percentage of students play either football or basketball?
A.
100%
B.
90%
C.
80%
D.
70%
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Solution
Using inclusion-exclusion, the percentage of students who play either sport is 70% + 50% - 20% = 100%.
Correct Answer: B — 90%
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Q. If a class is scheduled every Tuesday and Thursday, which of the following days can a student not attend without missing a class?
A.
Monday
B.
Wednesday
C.
Friday
D.
Saturday
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Solution
Wednesday is the only day where a student cannot attend without missing a class.
Correct Answer: B — Wednesday
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Q. If a conference is scheduled to last for 3 hours and must start between 1 PM and 3 PM, which of the following is a valid start time?
A.
12:30 PM
B.
1:30 PM
C.
2:45 PM
D.
3:15 PM
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Solution
1:30 PM is valid as it allows the conference to end by 4:30 PM, which is within the allowed time frame.
Correct Answer: B — 1:30 PM
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Q. If a football tournament has 16 teams and each team plays every other team once, how many matches are played in total?
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Solution
The total number of matches is calculated using the formula n(n-1)/2, where n is the number of teams. Here, it is 16(15)/2 = 120.
Correct Answer: A — 120
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Q. If a hybrid set contains elements from three different sets, what can be inferred about its composition?
A.
It must contain at least one element from each set.
B.
It can only contain elements from the largest set.
C.
It will have no duplicates.
D.
It can include elements that are not in any of the three sets.
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Solution
A hybrid set formed from multiple sets typically includes at least one element from each contributing set.
Correct Answer: A — It must contain at least one element from each set.
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Q. If a hybrid set is defined as the combination of set R = {x, y} and set S = {y, z}, which of the following is the correct representation of the hybrid set?
A.
{x, y, z}
B.
{y}
C.
{x, y}
D.
{y, z}
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Solution
The hybrid set formed by combining set R and set S includes all unique elements from both sets, which are {x, y, z}.
Correct Answer: A — {x, y, z}
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Q. If A is to the left of B and C is to the right of A, which of the following is a valid conclusion?
A.
B is to the right of C
B.
C is to the left of B
C.
A is in the middle
D.
B is to the left of A
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Solution
Since A is to the left of B and C is to the right of A, it follows that C is to the left of B.
Correct Answer: B — C is to the left of B
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Q. If a pie chart indicates that 10% of a budget is allocated to marketing, what is the remaining percentage for other expenses?
A.
90%
B.
80%
C.
70%
D.
60%
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Solution
The remaining percentage for other expenses is 100% - 10% = 90%.
Correct Answer: A — 90%
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Q. If a pie chart shows that 15% of a company's budget is allocated to marketing, which of the following statements is true?
A.
Marketing receives less than one-fifth of the budget.
B.
Marketing receives more than one-fifth of the budget.
C.
Marketing receives exactly one-fifth of the budget.
D.
None of the above.
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Solution
One-fifth of the budget is 20%, so 15% is indeed less than one-fifth.
Correct Answer: A — Marketing receives less than one-fifth of the budget.
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Q. If a pie chart shows that 30% of a company's revenue comes from product sales, what fraction of the revenue comes from other sources?
A.
1/3
B.
2/3
C.
1/2
D.
3/4
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Solution
If 30% comes from product sales, then 100% - 30% = 70% comes from other sources, which is 2/3.
Correct Answer: B — 2/3
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Q. If a player has a win-loss record of 10-2 in a series of matches, what is their winning percentage?
A.
83.33%
B.
66.67%
C.
50%
D.
75%
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Solution
Winning percentage is calculated as wins/(wins + losses). Here, it is 10/(10+2) = 10/12 = 83.33%.
Correct Answer: A — 83.33%
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Q. If a player is disqualified from a tournament for unsportsmanlike conduct, what is the most likely consequence?
A.
The player will receive a trophy.
B.
The player will be banned from future tournaments.
C.
The player will be awarded points.
D.
The player will be allowed to continue playing.
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Solution
Disqualification typically results in a ban from future participation in tournaments.
Correct Answer: B — The player will be banned from future tournaments.
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Q. If a player scores 30 points in a game and the average score of the team is 25 points, what can be inferred about the player's performance?
A.
The player performed below average.
B.
The player performed above average.
C.
The player is the worst performer on the team.
D.
The player's score does not affect the team's average.
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Solution
Scoring 30 points indicates that the player performed above the team's average of 25 points.
Correct Answer: B — The player performed above average.
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Q. If a set A contains elements {1, 2, 3, 4, 5} and a constraint states that only even numbers can be included, what will be the resulting set?
A.
{2, 4}
B.
{1, 3, 5}
C.
{1, 2, 3, 4, 5}
D.
{}
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Solution
The resulting set will be {2, 4} as these are the only even numbers in set A.
Correct Answer: A — {2, 4}
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Q. If a set A is defined by the constraints x > 5 and x < 10, which of the following numbers is NOT a member of set A?
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Solution
The number 10 does not satisfy the constraint x < 10, hence it is not a member of set A.
Correct Answer: C — 10
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Q. If a set D is defined as {x | x is a positive integer and x is less than or equal to 15}, how many elements are in set D?
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Solution
Set D includes all positive integers from 1 to 15, which totals 15 elements.
Correct Answer: B — 15
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Q. If a set is defined as containing all prime numbers less than 20, which of the following numbers is NOT in the set?
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Solution
The number 4 is not a prime number, hence it is not included in the set of prime numbers less than 20.
Correct Answer: C — 4
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Q. If a set is defined by the constraint of being a natural number, which of the following is included?
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Solution
1 is a natural number, while -1 and 0 are not considered natural numbers, and 2.5 is not an integer.
Correct Answer: C — 1
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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 a team scores 3 points for a win, 1 point for a draw, and 0 points for a loss, how many points does a team have if it has 2 wins, 3 draws, and 1 loss?
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Solution
Points = (2 wins * 3 points) + (3 draws * 1 point) + (1 loss * 0 points) = 6 + 3 + 0 = 9 points.
Correct Answer: B — 8
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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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