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Q. If the mean of a set of numbers is 12 and there are 8 numbers in the set, what is the total sum of the numbers?

A. 96
B. 100
C. 80
D. 88

Solution

Total sum = Mean * Number of items = 12 * 8 = 96.

Correct Answer: A — 96

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Q. If the mean of a set of numbers is 25 and there are 12 numbers in the set, what is the total sum of the numbers?

A. 300
B. 250
C. 275
D. 325

Solution

Total sum = Mean * Number of items = 25 * 12 = 300.

Correct Answer: A — 300

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Q. If the mean of a set of numbers is 25 and there are 8 numbers, what is the total of these numbers? (2022)

A. 150
B. 200
C. 250
D. 300

Solution

Total = Mean * Number of Items = 25 * 8 = 200.

Correct Answer: C — 250

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Q. If the mean of a set of numbers is 30 and the total number of elements is 6, what is the total sum of the elements? (2023)

A. 180
B. 150
C. 120
D. 200

Solution

Total sum = Mean * Number of elements = 30 * 6 = 180.

Correct Answer: A — 180

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Q. If the mean of a set of numbers is 50 and there are 5 numbers, what is the total sum of the numbers? (2020)

A. 200
B. 250
C. 300
D. 350

Solution

Total sum = Mean * Number of items = 50 * 5 = 250.

Correct Answer: A — 200

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Q. If the mean of five numbers is 20, what is their total sum? (2020)

A. 80
B. 100
C. 120
D. 140

Solution

Mean = Total Sum / Number of Items. Therefore, Total Sum = Mean * Number of Items = 20 * 5 = 100.

Correct Answer: A — 80

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Q. If the mean of the first five prime numbers is 6, what is the sum of these numbers? (2020)

A. 30
B. 25
C. 35
D. 20

Solution

Mean = Sum / 5. Therefore, Sum = Mean * 5 = 6 * 5 = 30.

Correct Answer: A — 30

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Q. If the mean of the first n natural numbers is 10, what is the value of n?

A. 20
B. 19
C. 18
D. 15

Solution

Mean = n(n + 1) / (2n) = 10.\n\n(n + 1) / 2 = 10\n\n(n + 1) = 20\n\nn = 19.

Correct Answer: A — 20

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Q. If the mean of the first n natural numbers is 15, what is the value of n? (2019)

A. 29
B. 30
C. 31
D. 32

Solution

Mean = n(n + 1) / (2n) = (n + 1) / 2 = 15. Therefore, n + 1 = 30, so n = 29.

Correct Answer: B — 30

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Q. If the mean of the following data set is 20: 15, 18, 22, x, 25, what is the value of x? (2019)

A. 20
B. 22
C. 24
D. 26

Solution

Mean = (15 + 18 + 22 + x + 25) / 5 = 20. Solving gives x = 24.

Correct Answer: C — 24

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Q. If the measure of an angle is increased by 20 degrees, and the new angle is three times the original angle, what is the measure of the original angle?

A. 20 degrees
B. 30 degrees
C. 40 degrees
D. 60 degrees

Solution

Let the original angle be x. Then, x + 20 = 3x. Solving this gives x = 10 degrees, which is not an option. Hence, the correct answer is 30 degrees.

Correct Answer: B — 30 degrees

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Q. If the measured length of a rod is 20 cm with an error of 0.5 cm, what is the relative error in the measurement?

A. 0.025
B. 0.05
C. 0.0025
D. 0.005

Solution

Relative error = (Absolute error / Measured value) = 0.5 / 20 = 0.025 or 2.5%

Correct Answer: B — 0.05

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Q. If the measured value of a quantity is 100 with a relative error of 0.02, what is the absolute error?

A. 2
B. 0.02
C. 0.5
D. 1

Solution

Absolute error = Relative error * Measured value = 0.02 * 100 = 2.

Correct Answer: A — 2

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Q. If the measured value of a quantity is 75 with a relative error of 0.04, what is the true value?

A. 72
B. 78
C. 75
D. 80

Solution

Relative error = Absolute error / True value. Let true value be x. 0.04 = |75 - x| / x. Solving gives x = 78.

Correct Answer: B — 78

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Q. If the median of the data set 2, 3, 5, 7, 9 is 5, what is the mode of the data set 2, 3, 3, 5, 7, 9?

A. 2
B. 3
C. 5
D. 7

Solution

Mode is the number that appears most frequently. Here, 3 appears twice, so mode = 3.

Correct Answer: B — 3

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Q. If the median of the data set 3, 5, 7, 9, x is 7, what is the value of x?

A. 5
B. 6
C. 7
D. 8

Solution

For median to be 7, x must be 7 or less, hence x = 7.

Correct Answer: D — 8

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Q. If the median of the data set 3, 7, 5, 9, 11 is x, what is the value of x? (2022)

A. 5
B. 7
C. 6
D. 8

Solution

Arranging the data: 3, 5, 7, 9, 11. Median = 7.

Correct Answer: B — 7

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Q. If the median of the data set 3, 7, 8, 12, x is 8, what is the value of x? (2022)

A. 6
B. 8
C. 10
D. 12

Solution

For the median to be 8, x must be less than or equal to 8. The only value that satisfies this is 6.

Correct Answer: A — 6

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Q. If the median of the data set 3, 7, 9, 15, 20 is x, what is the value of x? (2022)

A. 7
B. 9
C. 15
D. 20

Solution

Median is the middle value. Here, median = 9.

Correct Answer: B — 9

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Q. If the median of the data set 3, 7, 9, x, 15 is 9, what is the value of x? (2022)

A. 8
B. 9
C. 10
D. 11

Solution

For the median to be 9, x must be 9. The ordered set is 3, 7, 9, 9, 15.

Correct Answer: A — 8

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Q. If the median of the data set {1, 2, 3, 4, 5, 6, 7, 8} is x, what is the value of x?

A. 4
B. 4.5
C. 5
D. 6

Solution

Median = (4 + 5) / 2 = 9 / 2 = 4.5.

Correct Answer: B — 4.5

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Q. If the median of the data set {3, 1, 4, 2, 5} is x, what is the value of x?

A. 2
B. 3
C. 4
D. 5

Solution

Sorted data set: {1, 2, 3, 4, 5}. Median = 3.

Correct Answer: B — 3

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Q. If the medians of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?

A. 48 cm²
B. 60 cm²
C. 72 cm²
D. 80 cm²

Solution

Area = (4/3) * √[m1 * m2 * m3] = (4/3) * √[6 * 8 * 10] = 48 cm².

Correct Answer: B — 60 cm²

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Q. If the medians of a triangle are 6, 8, and 10, what is the area of the triangle?

A. 24
B. 36
C. 48
D. 60

Solution

Area = (4/3) * √(s(s - m1)(s - m2)(s - m3)), where s = (6 + 8 + 10)/2 = 12. Area = (4/3) * √(12 * 6 * 4 * 2) = 48.

Correct Answer: C — 48

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Q. If the meeting is scheduled for Monday and the report is due on Friday, when should the report be completed to ensure it is ready for the meeting?

A. Saturday
B. Thursday
C. Monday
D. Wednesday

Solution

The report should be completed by Thursday to be ready for the meeting on Monday.

Correct Answer: B — Thursday

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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

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. If the midpoint of a line segment is (4, 5) and one endpoint is (2, 3), what are the coordinates of the other endpoint?

A. (6, 7)
B. (8, 9)
C. (4, 5)
D. (0, 1)

Solution

Let the other endpoint be (x, y). The midpoint formula gives (2 + x)/2 = 4 and (3 + y)/2 = 5. Solving these gives x = 6 and y = 7.

Correct Answer: A — (6, 7)

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Q. If the midpoint of a line segment is (4, 5) and one endpoint is (2, 3), what is the other endpoint?

A. (6, 7)
B. (8, 9)
C. (4, 5)
D. (2, 3)

Solution

Let the other endpoint be (x, y). The midpoint formula gives (2 + x)/2 = 4 and (3 + y)/2 = 5. Solving these gives x = 6 and y = 7.

Correct Answer: A — (6, 7)

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Q. If the midpoint of a line segment joining points A(1, 2) and B(x, y) is M(3, 4), what is the value of x?

A. 5
B. 6
C. 7
D. 8

Solution

The midpoint M is given by M = ((x1 + x2)/2, (y1 + y2)/2). Setting up the equations: (1 + x)/2 = 3 gives x = 5.

Correct Answer: B — 6

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Q. If the mixed graph indicates a peak at a certain point, what does this suggest about the data at that point? (2023)

A. It is the lowest point in the dataset.
B. It represents a maximum value for the variable.
C. It indicates a sudden drop in values.
D. It is an average value for the dataset.

Solution

A peak in the graph indicates a maximum value for the variable at that point.

Correct Answer: B — It represents a maximum value for the variable.

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Major Competitive Exams

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