Mathematics
Algebra
Solve: |x - 9| = 5.
A. x = 14
B. x = 14 or x = 4
C. x = 45
D. x = -4 or x = 14
Correct Answer: B
x-9=±5.
Mathematics
Algebra
Solve: |x - 8| = 4.
A. x = -4 or x = 12
B. x = 12 or x = 4
C. x = 32
D. x = 12
Correct Answer: B
x-8=±4.
Mathematics
Algebra
Solve: |x - 7| = 3.
A. x = 10
B. x = 21
C. x = -4 or x = 10
D. x = 10 or x = 4
Correct Answer: D
x-7=±3.
Mathematics
Algebra
Solve: |x - 6| = 7.
A. x = 42
B. x = 13 or x = -1
C. x = 13
D. x = 1 or x = 13
Correct Answer: B
x-6=±7.
Mathematics
Algebra
Solve: |x - 5| = 6.
A. x = 11
B. x = 1 or x = 11
C. x = 30
D. x = 11 or x = -1
Correct Answer: D
x-5=±6.
Mathematics
Algebra
Solve: |x - 4| = 5.
A. x = 1 or x = 9
B. x = 20
C. x = 9 or x = -1
D. x = 9
Correct Answer: C
x-4=±5.
Mathematics
Algebra
Solve: |x - 3| = 4.
A. x = 1 or x = 7
B. x = 7 or x = -1
C. x = 12
D. x = 7
Correct Answer: B
x-3=±4.
Mathematics
Algebra
Solve: |x - 2| = 3.
A. x = 6
B. x = 1 or x = 5
C. x = 5 or x = -1
D. x = 5
Correct Answer: C
x-2=±3.
Mathematics
Average / Arithmetic Mean
Two equal-sized groups have means 42 and 58. What is their combined mean?
A. 52
B. 48
C. 50
D. 54
Correct Answer: C
Equal-sized groups: (42+58)/2 = 50.
Mathematics
Average / Arithmetic Mean
The mean of 8 observations is 25. A ninth observation is added and the mean becomes 27. What is the ninth value?
A. 45
B. 47
C. 43
D. 41
Correct Answer: C
9×27−8×25 = 43.
Mathematics
Average / Arithmetic Mean
The average of x, x+10, x+20, x+30, x+40 is 60. Find x.
A. 40
B. 44
C. 38
D. 42
Correct Answer: A
Middle term x+20 equals mean 60; x=40.
Mathematics
Average / Arithmetic Mean
A dataset has mean 50. Every value is replaced by 100−x. What is the new mean?
A. 52
B. 48
C. 50
D. 54
Correct Answer: C
New mean = 100−50 = 50.
Mathematics
Average / Arithmetic Mean
A group mean is 25. One value equal to the mean is removed. What happens to the mean of the remaining values?
A. It becomes greater than 25
B. It becomes zero
C. It remains 25
D. It becomes less than 25
Correct Answer: C
Removing a value equal to the current mean does not change the mean.
Mathematics
Average / Arithmetic Mean
The mean of 10 numbers is 30. Removing two numbers 20 and 40 leaves what mean?
A. 32
B. 28
C. 30
D. 34
Correct Answer: C
Removed numbers average 30, so remaining mean stays 30.
Mathematics
Average / Arithmetic Mean
A team's average score is 52 after 25 matches. What score in match 26 will make the average exactly 54?
A. 104
B. 108
C. 102
D. 106
Correct Answer: A
26×54−25×52 = 104.
Mathematics
Average / Arithmetic Mean
A class of 24 students has mean 68. If 6 more students averaging 80 join, what is the new class mean?
A. 72.4
B. 74.4
C. 68.4
D. 70.4
Correct Answer: D
(24×68+6×80)/30 = 70.4.
Mathematics
Average / Arithmetic Mean
The average of 15 values is 32. If each value is tripled, what is the sum of the transformed values?
A. 1444
B. 1438
C. 1442
D. 1440
Correct Answer: D
Original total 480; tripled total 1440.
Mathematics
Average / Arithmetic Mean
The mean of 20 observations is 45. If 5 is added to each observation, by how much does the total increase?
A. 104
B. 98
C. 100
D. 102
Correct Answer: C
20×5 = 100.
Mathematics
Average / Arithmetic Mean
Three values 49, 69, and 89 have weights 1, 3, and 7. What is the weighted mean?
A. 78.91
B. 80.91
C. 81.91
D. 79.91
Correct Answer: D
Weighted mean = (49×1+69×3+89×7)/11 = 79.91.
Mathematics
Average / Arithmetic Mean
Three values 48, 68, and 88 have weights 3, 2, and 6. What is the weighted mean?
A. 75.45
B. 73.45
C. 74.45
D. 72.45
Correct Answer: B
Weighted mean = (48×3+68×2+88×6)/11 = 73.45.