Q. In a modular arithmetic system, if a ≡ b (mod m), which of the following statements is true?
A.
a - b is divisible by m
B.
a + b is divisible by m
C.
a * b is divisible by m
D.
a / b is divisible by m
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Solution
The statement a ≡ b (mod m) means that the difference a - b is divisible by m.
Correct Answer: A — a - b is divisible by m
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Q. In a parallelogram, if one angle measures 60 degrees, what is the measure of the opposite angle?
A.
60 degrees
B.
120 degrees
C.
90 degrees
D.
180 degrees
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Solution
In a parallelogram, opposite angles are equal, so the opposite angle also measures 60 degrees.
Correct Answer: A — 60 degrees
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Q. In a parallelogram, if the base is 12 cm and the height is 5 cm, what is the area? (2020)
A.
60 cm²
B.
70 cm²
C.
80 cm²
D.
90 cm²
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Solution
Area of a parallelogram = base * height = 12 * 5 = 60 cm².
Correct Answer: A — 60 cm²
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Q. In a partnership agreement, which clause is essential to prevent disputes?
A.
Profit-sharing ratio
B.
Business location
C.
Partner's personal interests
D.
Market competition
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Solution
A clearly defined profit-sharing ratio is crucial to prevent disputes among partners.
Correct Answer: A — Profit-sharing ratio
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Q. In a partnership, what does the term 'joint venture' refer to?
A.
A partnership formed for a specific project
B.
A permanent partnership with no end date
C.
A partnership that requires equal capital contribution
D.
A partnership that is limited to two partners only
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Solution
A joint venture is a partnership formed for a specific project or purpose, often with a defined time frame.
Correct Answer: A — A partnership formed for a specific project
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Q. In a partnership, which of the following is NOT typically a reason for dissolution?
A.
Mutual agreement of partners
B.
Insolvency of one partner
C.
Change in business strategy
D.
Increase in profit margins
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Solution
Increase in profit margins is generally not a reason for dissolution; rather, it is a positive outcome.
Correct Answer: D — Increase in profit margins
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Q. In a quadratic equation ax^2 + bx + c = 0, what does the term 'b' represent?
A.
The coefficient of x^2
B.
The constant term
C.
The coefficient of x
D.
The product of the roots
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Solution
'b' is the coefficient of the linear term x in the quadratic equation.
Correct Answer: C — The coefficient of x
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Q. In a quadratic equation, if the discriminant is negative, what can be inferred about the roots?
A.
The roots are real and distinct.
B.
The roots are real and equal.
C.
The roots are complex and conjugate.
D.
The roots are imaginary.
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Solution
A negative discriminant indicates that the roots are complex and conjugate.
Correct Answer: C — The roots are complex and conjugate.
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Q. In a quadrilateral ABCD, if angle A is 70 degrees and angle B is 110 degrees, what can be inferred about the sum of angles C and D?
A.
C and D must be 100 degrees
B.
C and D must be 180 degrees
C.
C and D must be 90 degrees
D.
C and D must be 360 degrees
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Solution
The sum of the angles in any quadrilateral is 360 degrees. Given angles A and B, we can find C + D = 360 - (70 + 110) = 180 degrees.
Correct Answer: B — C and D must be 180 degrees
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Q. In a quadrilateral ABCD, if angle A is 90 degrees and angle B is 45 degrees, what can be inferred about the other angles? (2023)
A.
Angle C is 45 degrees and angle D is 90 degrees.
B.
Angle C is 90 degrees and angle D is 45 degrees.
C.
Angle C is 135 degrees and angle D is 135 degrees.
D.
Angle C is 180 degrees and angle D is 0 degrees.
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Solution
In a quadrilateral, the sum of the angles is 360 degrees. Given angle A (90) and angle B (45), angle C + angle D = 360 - (90 + 45) = 225 degrees. The only option that fits is angle C = 135 degrees and angle D = 135 degrees.
Correct Answer: C — Angle C is 135 degrees and angle D is 135 degrees.
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Q. In a quadrilateral, if one angle is 90 degrees and the other three angles are equal, what is the measure of each of the equal angles?
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
75 degrees
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Solution
Let each of the equal angles be x. The sum of angles in a quadrilateral is 360 degrees. Therefore, 90 + 3x = 360. Solving this gives x = 90 degrees, which is not an option. Hence, the correct answer is 45 degrees.
Correct Answer: B — 45 degrees
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Q. In a quadrilateral, if three angles are 70 degrees, 80 degrees, and 90 degrees, what is the measure of the fourth angle?
A.
120 degrees
B.
100 degrees
C.
110 degrees
D.
130 degrees
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Solution
The sum of the angles in a quadrilateral is 360 degrees. Thus, the fourth angle is 360 - (70 + 80 + 90) = 120 degrees.
Correct Answer: B — 100 degrees
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Q. In a race, the average speed of a runner is 10 km/h. If he runs for 2 hours, how far does he run? (2023)
A.
15 km
B.
20 km
C.
25 km
D.
30 km
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Solution
Distance = Speed × Time = 10 km/h × 2 h = 20 km.
Correct Answer: D — 30 km
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Q. In a race, the average speed of a runner is 12 km/h. If the runner wants to complete the race in 2 hours, how far is the race? (2023)
A.
20 km
B.
24 km
C.
30 km
D.
36 km
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Solution
Distance = Speed × Time = 12 km/h × 2 h = 24 km.
Correct Answer: B — 24 km
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Q. In a rectangle, which of the following is true about the diagonals? (2023)
A.
They are perpendicular.
B.
They are equal and bisect each other.
C.
They are unequal.
D.
They do not bisect each other.
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Solution
In a rectangle, the diagonals are equal in length and bisect each other.
Correct Answer: B — They are equal and bisect each other.
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Q. In a regular dodecagon, what is the measure of each exterior angle?
A.
30 degrees
B.
36 degrees
C.
24 degrees
D.
18 degrees
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Solution
The measure of each exterior angle of a regular polygon is 360/n. For a dodecagon (n=12), it is 360/12 = 30 degrees.
Correct Answer: B — 36 degrees
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Q. In a regular pentagon, what is the measure of each interior angle?
A.
108 degrees
B.
120 degrees
C.
90 degrees
D.
72 degrees
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Solution
The measure of each interior angle in a regular pentagon can be calculated using the formula (n-2) * 180 / n, which results in (5-2) * 180 / 5 = 108 degrees.
Correct Answer: A — 108 degrees
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Q. In a right triangle, if one of the angles is 30 degrees, what is the measure of the other non-right angle?
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
90 degrees
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Solution
In a right triangle, the sum of the angles is 180 degrees. If one angle is 30 degrees and the right angle is 90 degrees, the other angle must be 60 degrees.
Correct Answer: C — 60 degrees
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Q. In a sequence defined by a_n = 3n + 2, what is the value of a_7? (2023)
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Solution
Substituting n = 7 into the formula gives a_7 = 3(7) + 2 = 21 + 2 = 23.
Correct Answer: A — 23
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Q. In a sequence of numbers where each number is a multiple of 3, which of the following cannot be a member of this sequence?
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Solution
22 is not a multiple of 3, while 9, 15, and 27 are.
Correct Answer: C — 22
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Q. In a sequence where each term is double the previous term, starting from 1, what is the 6th term? (2023)
A.
32
B.
64
C.
128
D.
256
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Solution
The sequence is 1, 2, 4, 8, 16, 32, 64. The 6th term is 64.
Correct Answer: C — 128
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Q. In a sequence where each term is the sum of the previous two terms, if the first two terms are 2 and 3, what is the 5th term? (2023)
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Solution
The sequence is 2, 3, 5, 8, 13. The 5th term is 13.
Correct Answer: B — 13
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Q. In a sequence where each term is the sum of the previous two terms, if the first two terms are 2 and 3, what is the fifth term? (2023)
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Solution
The sequence is 2, 3, 5, 8, 13. The fifth term is 13.
Correct Answer: B — 13
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Q. In a series where each term is the square of its position, what is the sum of the first 4 terms? (2023)
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Solution
The first four terms are 1^2, 2^2, 3^2, 4^2 which are 1, 4, 9, 16. Their sum is 1 + 4 + 9 + 16 = 30.
Correct Answer: B — 50
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Q. In a survey of 100 people, 60 like chocolate, 50 like vanilla, and 20 like both. How many like only chocolate?
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Solution
To find the number of people who like only chocolate, we subtract those who like both from those who like chocolate: 60 - 20 = 40.
Correct Answer: A — 30
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Q. In a survey of 120 people, 50 like tea, 40 like coffee, and 20 like both. How many people like only coffee?
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Solution
The number of people who like only coffee is 40 - 20 = 20.
Correct Answer: B — 30
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Q. In a survey of 150 people, 90 like dogs, 60 like cats, and 30 like both. How many people like neither dogs nor cats?
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Solution
Using inclusion-exclusion, the number of people who like either is 90 + 60 - 30 = 120. Therefore, those who like neither is 150 - 120 = 30.
Correct Answer: A — 30
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Q. In a survey, 40 people like tea, 30 like coffee, and 10 like both. How many people like only tea?
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Solution
To find the number of people who like only tea, we subtract those who like both from those who like tea: 40 - 10 = 30.
Correct Answer: B — 20
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Q. In a survey, 40 people like tea, 30 like coffee, and 10 like both. How many people like either tea or coffee?
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Solution
Using the principle of inclusion-exclusion, the number of people who like either tea or coffee is: (Tea + Coffee - Both) = 40 + 30 - 10 = 60.
Correct Answer: A — 60
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Q. In a survey, 45 people like action movies, 35 like drama, and 15 like both. How many people like only action movies?
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Solution
The number of people who like only action movies is 45 - 15 = 30.
Correct Answer: A — 30
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