Q. In a group of 15 people, the ages are: 20, 21, 21, 22, 22, 22, 23, 24, 25, 25, 25, 26, 27, 28, 29. What is the mode of the ages? (2022)
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Solution
The age 22 appears 3 times, which is more than any other age, so the mode is 22.
Correct Answer: C — 25
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Q. In a group of friends, the number of games played is: 3, 3, 4, 4, 4, 5, 6. What is the mode of the games played?
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Solution
The mode is 4, as it appears most frequently (3 times) in the data set.
Correct Answer: B — 4
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Q. In a lottery, the probability of winning is 0.2. What is the probability of losing?
A.
0.2
B.
0.5
C.
0.8
D.
0.1
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Solution
Probability of losing = 1 - P(winning) = 1 - 0.2 = 0.8.
Correct Answer: C — 0.8
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Q. In a pair of intersecting lines, if one angle measures 35 degrees, what is the measure of the adjacent angle?
A.
145 degrees
B.
35 degrees
C.
180 degrees
D.
90 degrees
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Solution
Adjacent angles on a straight line are supplementary. Therefore, the adjacent angle measures 180 - 35 = 145 degrees.
Correct Answer: A — 145 degrees
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Q. In a pair of vertically opposite angles, if one angle measures 120 degrees, what is the measure of the other angle? (2021)
A.
60 degrees
B.
120 degrees
C.
180 degrees
D.
90 degrees
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Solution
Vertically opposite angles are equal. Therefore, if one angle measures 120 degrees, the other angle also measures 120 degrees.
Correct Answer: B — 120 degrees
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Q. In a parallelogram, if one angle is 70 degrees, what is the measure of the opposite angle? (2019)
A.
70 degrees
B.
110 degrees
C.
90 degrees
D.
80 degrees
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Solution
In a parallelogram, opposite angles are equal. Therefore, if one angle is 70 degrees, the opposite angle is also 70 degrees.
Correct Answer: A — 70 degrees
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Q. In a parallelogram, if the base is 8 cm and the height is 5 cm, what is the area? (2021)
A.
40 cm²
B.
30 cm²
C.
50 cm²
D.
20 cm²
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Solution
Area = base * height = 8 * 5 = 40 cm²
Correct Answer: A — 40 cm²
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Q. In a right triangle, if one angle is 30 degrees and the hypotenuse is 10 cm, what is the length of the side opposite the 30-degree angle? (2020)
A.
5 cm
B.
10 cm
C.
8 cm
D.
7 cm
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Solution
Opposite side = hypotenuse * sin(30°) = 10 * 1/2 = 5 cm.
Correct Answer: A — 5 cm
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Q. In a right triangle, if one angle is 30 degrees, what is the ratio of the lengths of the sides opposite to the 30 degrees and 60 degrees angles? (2019)
A.
1:√3
B.
1:2
C.
√3:1
D.
2:1
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Solution
In a 30-60-90 triangle, the sides opposite the 30 degrees and 60 degrees angles are in the ratio 1:√3.
Correct Answer: A — 1:√3
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Q. In a right triangle, if one angle is 45 degrees, what is the measure of the other non-right angle? (2021)
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
75 degrees
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Solution
In a right triangle, the sum of the angles is 180 degrees. If one angle is 45 degrees and the right angle is 90 degrees, the other angle must be 180 - (90 + 45) = 45 degrees.
Correct Answer: B — 45 degrees
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Q. In a set of data: 5, 6, 7, 7, 8, 8, 8, 9, 10, 10, what is the mode?
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Solution
The mode is 8, as it appears most frequently (3 times) in the data set.
Correct Answer: C — 8
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Q. In a set of numbers: 10, 20, 30, 40, 50, what is the median? (2023)
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Solution
The numbers are in order. The median is the average of the 3rd and 4th numbers: (30 + 40) / 2 = 35.
Correct Answer: B — 30
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Q. In a set of numbers: 5, 6, 7, 5, 8, 5, 9, 6, what is the mode?
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Solution
The mode is 5, as it appears four times in the data set.
Correct Answer: A — 5
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Q. In a survey of favorite fruits, the responses were: Apple, Banana, Banana, Cherry, Cherry, Cherry, Date. What is the mode?
A.
Apple
B.
Banana
C.
Cherry
D.
Date
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Solution
The mode is Cherry, as it appears most frequently (3 times) in the data set.
Correct Answer: C — Cherry
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Q. In a survey of favorite fruits, the results were: Apple, Banana, Banana, Cherry, Cherry, Cherry, Date. What is the mode?
A.
Apple
B.
Banana
C.
Cherry
D.
Date
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Solution
The mode is Cherry, as it appears most frequently (3 times) in the survey results.
Correct Answer: C — Cherry
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Q. In a survey, 60% of people prefer tea over coffee. If 200 people were surveyed, how many prefer tea? (2019)
A.
120
B.
100
C.
80
D.
60
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Solution
Number of people preferring tea = 60% of 200 = 0.6 * 200 = 120.
Correct Answer: A — 120
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Q. In a survey, 70% of people prefer tea over coffee. If 200 people were surveyed, how many prefer tea? (2019)
A.
140
B.
150
C.
160
D.
170
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Solution
Number of people preferring tea = 70% of 200 = 0.7 * 200 = 140.
Correct Answer: A — 140
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Q. In a survey, the ages of 15 participants are: 22, 22, 23, 24, 24, 24, 25, 26, 27, 27, 28, 29, 30, 30, 30. What is the mode?
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Solution
The mode is 30, as it appears 3 times, which is more than any other age.
Correct Answer: D — 30
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Q. In a survey, the ages of 15 participants are: 22, 23, 23, 24, 25, 25, 25, 26, 27, 28, 28, 29, 30, 30, 30. What is the mode of the ages?
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Solution
The mode is 30, as it appears most frequently (3 times) in the data set.
Correct Answer: D — 30
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Q. In a survey, the number of languages spoken by individuals is recorded as follows: 1, 2, 2, 3, 3, 3, 4. What is the mode?
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Solution
The mode is 3, as it appears three times in the data set.
Correct Answer: C — 3
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Q. In a survey, the number of languages spoken by participants is recorded as follows: 1, 2, 2, 3, 3, 3, 4, 5. What is the mode?
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Solution
The mode is 3, as it appears 3 times, more than any other number.
Correct Answer: C — 3
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Q. In a survey, the number of siblings reported by participants is: 0, 1, 2, 1, 2, 2, 3. What is the mode?
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Solution
The mode is 2, which appears 3 times in the data set.
Correct Answer: C — 2
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Q. In a triangle, if one angle is 45 degrees and the other is 45 degrees, what is the measure of the third angle? (2020)
A.
90 degrees
B.
45 degrees
C.
60 degrees
D.
30 degrees
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Solution
The sum of the angles in a triangle is always 180 degrees. Therefore, if two angles are 45 degrees each, the third angle = 180 - (45 + 45) = 90 degrees.
Correct Answer: A — 90 degrees
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Q. In a triangle, if one angle is 50 degrees and another is 60 degrees, what is the measure of the third angle?
A.
70 degrees
B.
80 degrees
C.
90 degrees
D.
100 degrees
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Solution
The sum of angles in a triangle is 180 degrees. Therefore, the third angle = 180 - (50 + 60) = 70 degrees.
Correct Answer: A — 70 degrees
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Q. In a triangle, if one angle measures 60 degrees and another measures 80 degrees, what is the measure of the third angle? (2019)
A.
40 degrees
B.
60 degrees
C.
80 degrees
D.
100 degrees
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Solution
The sum of angles in a triangle is 180 degrees. Therefore, the third angle = 180 - 60 - 80 = 40 degrees.
Correct Answer: A — 40 degrees
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Q. In a triangle, if two sides are 7 cm and 10 cm, what is the maximum possible length of the third side? (2019)
A.
16 cm
B.
17 cm
C.
18 cm
D.
19 cm
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Solution
The maximum length of the third side = sum of the other two sides - 1 = 7 + 10 - 1 = 16 cm.
Correct Answer: B — 17 cm
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Q. In the data set 1, 2, 2, 3, 4, 4, 4, 5, 5, what is the mode?
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Solution
The mode is 4, as it appears most frequently (three times) in the data set.
Correct Answer: C — 4
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Q. In the data set 9, 10, 10, 11, 12, 12, 12, 13, what is the mode?
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Solution
The mode is 12, as it appears 3 times, which is more than any other number.
Correct Answer: D — 12
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Q. In the data set: 2, 3, 3, 4, 4, 5, 5, 5, what is the mode?
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Solution
The mode is 5, as it appears most frequently (three times) in the data set.
Correct Answer: D — 5
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Q. In the equation x^2 - 4x + 4 = 0, what is the nature of the roots? (2021)
A.
Real and distinct
B.
Real and equal
C.
Complex
D.
None of the above
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Solution
The discriminant is 0, which indicates that the roots are real and equal.
Correct Answer: B — Real and equal
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