Q. In a league of 5 teams, if each team plays every other team twice, how many total matches are played?
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Solution
Each team plays 4 other teams twice, so total matches = 5 * 4 / 2 * 2 = 20.
Correct Answer:
B
— 20
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Q. In a library, 50 books are fiction, 30 are non-fiction, and 10 are both. How many books are only fiction?
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Solution
The number of books that are only fiction is calculated by subtracting the number of books that are both from the total fiction books: 50 - 10 = 40.
Correct Answer:
B
— 40
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Q. In a line of five students, if X is to the left of Y and Z is to the right of Y, which of the following is true?
A.
X is to the left of Z
B.
Y is to the left of Z
C.
Z is to the left of X
D.
Y is to the right of X
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Solution
Since X is to the left of Y and Z is to the right of Y, it follows that X must be to the left of Z.
Correct Answer:
A
— X is to the left of Z
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Q. In a line of four friends, if R is to the left of S and T is to the right of R, which of the following is a possible order?
A.
R, S, T, U
B.
S, R, U, T
C.
T, R, S, U
D.
R, T, S, U
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Solution
The order R, S, T, U satisfies the condition of R being to the left of S and T being to the right of R.
Correct Answer:
A
— R, S, T, U
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Q. In a line of people, if X is at the front and Y is at the back, and Z is in the middle, which of the following is true?
A.
Y is in front of X
B.
Z is behind Y
C.
X is behind Z
D.
Y is in the middle
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Solution
The arrangement is X, Z, Y. Therefore, Z is behind Y.
Correct Answer:
B
— Z is behind Y
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Q. In a line of people, if X is at the front and Y is at the back, which of the following statements is necessarily true?
A.
Y is in front of X
B.
X is behind Y
C.
There are no people between X and Y
D.
X is to the left of Y
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Solution
If X is at the front and Y is at the back, it is necessary that there are no people between them.
Correct Answer:
C
— There are no people between X and Y
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Q. In a linear arrangement of eight people, if person X is at one end and person Y is at the other end, which of the following must be true?
A.
X is to the left of Y
B.
Y is to the right of X
C.
X and Y are adjacent
D.
There are six people between X and Y
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Solution
If X is at one end and Y at the other, there can be six people between them, making this statement true.
Correct Answer:
D
— There are six people between X and Y
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Q. In a linear arrangement of five friends A, B, C, D, and E, A is to the left of B but to the right of C. D is to the left of E. Who is in the middle?
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Solution
The arrangement is C, A, B, D, E. A is in the middle.
Correct Answer:
A
— A
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Q. In a linear arrangement of five friends A, B, C, D, and E, if A is to the left of B and C is to the right of D, which of the following must be true?
A.
A is to the left of C
B.
D is to the right of A
C.
B is to the left of D
D.
E is in the middle
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Solution
Since A is to the left of B and C is to the right of D, we cannot definitively place E without additional information. However, A being to the left of C is a possible arrangement.
Correct Answer:
A
— A is to the left of C
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Q. In a linear arrangement of five people, if D is sitting next to E and F is sitting at one end, which of the following must be true?
A.
D is at one end
B.
E is next to F
C.
F is not next to D
D.
D is not at one end
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Solution
Since F is at one end and D is next to E, D cannot be at one end.
Correct Answer:
D
— D is not at one end
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Q. In a linear arrangement of five people, if E is at one end and A is to the right of E, which of the following must be true?
A.
A is at the end
B.
E is to the left of A
C.
A is to the left of E
D.
E is to the right of A
Show solution
Solution
Since E is at one end and A is to the right of E, it is clear that E is to the left of A.
Correct Answer:
B
— E is to the left of A
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Q. In a linear arrangement of five people, if E is to the left of F and G is to the right of F, which of the following is true?
A.
E is to the right of G
B.
F is in the middle
C.
G is to the left of E
D.
E is at one end
Show solution
Solution
The arrangement E, F, G satisfies the condition, placing F in the middle.
Correct Answer:
B
— F is in the middle
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Q. In a linear arrangement of four friends, if A is to the left of B and C is to the right of A, who is in the middle?
A.
A
B.
B
C.
C
D.
None of the above
Show solution
Solution
The arrangement is A, B, C. A is in the middle.
Correct Answer:
A
— A
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Q. In a linear arrangement of four friends, if P is to the left of Q and R is to the right of P, which of the following must be true?
A.
Q is to the right of R
B.
R is to the left of Q
C.
P is in the middle
D.
Q is to the left of R
Show solution
Solution
Since P is to the left of Q and R is to the right of P, R must be to the left of Q.
Correct Answer:
B
— R is to the left of Q
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Q. In a linear arrangement of four people P, Q, R, and S, if P is sitting next to Q and R is sitting at one of the ends, which of the following is a possible arrangement?
A.
R, P, Q, S
B.
S, R, P, Q
C.
Q, P, R, S
D.
P, S, R, Q
Show solution
Solution
R can be at one end, and since P is next to Q, the arrangement R, P, Q, S satisfies all conditions.
Correct Answer:
A
— R, P, Q, S
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Q. In a linear arrangement of four people P, Q, R, and S, if P is sitting next to Q and R is sitting at one end, which of the following is a possible arrangement?
A.
R, P, Q, S
B.
S, R, P, Q
C.
Q, P, R, S
D.
P, S, R, Q
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Solution
R can be at one end, and P must be next to Q, making R, P, Q, S a valid arrangement.
Correct Answer:
A
— R, P, Q, S
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Q. In a linear arrangement of seven students, if A is to the left of B, and C is to the right of D, which of the following cannot be true?
A.
A is to the left of C
B.
B is to the right of D
C.
D is to the left of A
D.
C is to the right of B
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Solution
If A is to the left of B, D cannot be to the left of A without contradicting the arrangement.
Correct Answer:
C
— D is to the left of A
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Q. In a linear arrangement of six friends A, B, C, D, E, and F, A is to the left of B but to the right of C. D is to the right of E but to the left of F. Who is in the middle of the arrangement?
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Solution
The arrangement from left to right is C, A, B, E, D, F. A is in the middle.
Correct Answer:
A
— A
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Q. In a linear arrangement, if A is at one end and E is at the other end, which of the following cannot be true?
A.
B is between A and C
B.
D is to the left of B
C.
C is to the right of D
D.
E is to the left of A
Show solution
Solution
If A is at one end and E is at the other, E cannot be to the left of A as that would contradict their positions.
Correct Answer:
D
— E is to the left of A
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Q. In a linear arrangement, if E is sitting between A and B, and C is sitting to the left of A, which of the following is true?
A.
C is to the left of E
B.
B is to the right of C
C.
A is to the right of C
D.
E is to the left of A
Show solution
Solution
Since C is to the left of A and E is between A and B, it follows that C must also be to the left of E.
Correct Answer:
A
— C is to the left of E
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Q. In a linear arrangement, if G is to the right of H and I is to the left of H, which of the following is true?
A.
G is to the left of I
B.
H is in the middle
C.
I is to the left of G
D.
H is to the right of I
Show solution
Solution
Since G is to the right of H and I is to the left of H, it follows that I is to the left of G.
Correct Answer:
C
— I is to the left of G
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Q. In a linear arrangement, if X is at one end and Y is at the other end, and Z is between X and Y, which of the following is true?
A.
Z is at one end
B.
X is to the left of Z
C.
Y is to the right of Z
D.
Both B and C are true
Show solution
Solution
Since Z is between X and Y, X is to the left of Z and Y is to the right of Z.
Correct Answer:
D
— Both B and C are true
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Q. In a linear equation, if the slope is 3 and the y-intercept is -2, what is the equation of the line?
A.
y = 3x + 2
B.
y = 3x - 2
C.
y = -3x + 2
D.
y = -3x - 2
Show solution
Solution
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Here, m = 3 and b = -2, so the equation is y = 3x - 2.
Correct Answer:
B
— y = 3x - 2
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Q. In a linear equation, what does the term 'slope' indicate?
A.
The steepness of the line.
B.
The length of the line segment.
C.
The position of the line on the graph.
D.
The direction of the line.
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Solution
The slope indicates the steepness of the line, representing the ratio of the rise over the run.
Correct Answer:
A
— The steepness of the line.
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Q. In a logical argument, if 'P implies Q' is true, which of the following is a valid conclusion?
A.
If Q is true, then P must be true.
B.
If P is false, then Q must be false.
C.
If P is true, then Q must be true.
D.
If Q is false, then P must be false.
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Solution
In logic, if 'P implies Q' is true, it means that whenever P is true, Q must also be true.
Correct Answer:
C
— If P is true, then Q must be true.
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Q. In a logical argument, what does the term 'premise' refer to?
A.
The conclusion drawn from the argument
B.
The evidence supporting the conclusion
C.
The contradiction in the argument
D.
The assumption made without proof
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Solution
A premise is a statement or proposition that provides the basis for a conclusion in a logical argument.
Correct Answer:
B
— The evidence supporting the conclusion
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Q. In a logical deduction puzzle, if A is taller than B, and B is taller than C, which of the following must be true? (2023)
A.
A is shorter than C.
B.
C is taller than A.
C.
B is taller than A.
D.
A is taller than C.
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Solution
If A is taller than B and B is taller than C, then A must be taller than C.
Correct Answer:
D
— A is taller than C.
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Q. In a logical sequence, if A is taller than B, and B is taller than C, which of the following statements is true? (2023)
A.
A is shorter than C.
B.
C is taller than A.
C.
B is shorter than A.
D.
C is shorter than B.
Show solution
Solution
If A is taller than B, then B must be shorter than A, making statement 3 true.
Correct Answer:
C
— B is shorter than A.
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Q. In a lottery, the probability of winning is 0.05. If a person buys 10 tickets, what is the probability of winning at least once?
A.
0.5
B.
0.4
C.
0.6
D.
0.3
Show solution
Solution
P(winning at least once) = 1 - P(not winning) = 1 - (0.95^10) ≈ 0.4013.
Correct Answer:
A
— 0.5
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Q. In a lottery, the probability of winning is 0.05. If a person plays the lottery 10 times, what is the probability of winning exactly once?
A.
0.5
B.
0.4
C.
0.3
D.
0.2
Show solution
Solution
Using the binomial probability formula, P(X=1) = C(10,1) * (0.05)^1 * (0.95)^9 = 10 * 0.05 * 0.630 = 0.315, approximately 0.2.
Correct Answer:
D
— 0.2
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