Q. A number is increased by 20% and then decreased by 20%. What is the net change in the number?
A.0%
B.4%
C.5%
D.10%
Solution
Let the original number be 100. After a 20% increase, it becomes 120. After a 20% decrease, it becomes 120 - 24 = 96. The net change is (96 - 100)/100 * 100% = -4%.
Correct Answer: B — 4%
Q. A number is increased by 20% and then decreased by 20%. What is the net change?
A.0%
B.4%
C.5%
D.10%
Solution
Let the number be 100. After a 20% increase, it becomes 120. After a 20% decrease, it becomes 120 - 24 = 96. The net change is (96 - 100)/100 * 100% = -4%.
Correct Answer: A — 0%
Q. If 3x + 5 = 20, what is the value of x?
A.3
B.5
C.7
D.10
Solution
To solve for x, subtract 5 from both sides: 3x = 15. Then divide by 3: x = 5.
Correct Answer: A — 3
Q. If 5x + 3 = 23, what is the value of x?
A.2
B.3
C.4
D.5
Solution
To solve for x, subtract 3 from both sides: 5x = 20. Then divide by 5: x = 4.
Correct Answer: B — 3
Q. If a number is divided by 6, the remainder is 4. What is the number?
A.10
B.16
C.22
D.28
Solution
A number that gives a remainder of 4 when divided by 6 can be expressed as 6k + 4. For k = 2, the number is 6*2 + 4 = 16.
Correct Answer: B — 16
Q. If a number is multiplied by 3 and then decreased by 9, the result is 0. What is the number?
A.1
B.2
C.3
D.4
Solution
Let the number be x. The equation is 3x - 9 = 0. Solving gives x = 3.
Correct Answer: C — 3
Q. If a number is multiplied by 9 and then decreased by 9, the result is 72. What is the number?
A.8
B.9
C.10
D.11
Solution
Let the number be x. The equation is 9x - 9 = 72. Adding 9 to both sides gives 9x = 81, so x = 81/9 = 9.
Correct Answer: A — 8
Q. If the ratio of boys to girls in a class is 3:2 and there are 30 students, how many girls are there?
A.10
B.12
C.18
D.20
Solution
Let the number of boys be 3x and girls be 2x. Then, 3x + 2x = 30, which gives 5x = 30, so x = 6. Therefore, the number of girls is 2x = 12.
Correct Answer: B — 12
Q. If the ratio of boys to girls in a class is 3:4 and there are 28 girls, how many boys are there?
A.21
B.24
C.25
D.30
Solution
Let the number of boys be 3x and girls be 4x. Given 4x = 28, we find x = 7. Thus, boys = 3x = 3*7 = 21.
Correct Answer: A — 21
Q. What is 15% of 200?
A.25
B.30
C.35
D.40
Solution
15% of 200 is calculated as (15/100) * 200 = 30.
Correct Answer: B — 30
Q. What is 25% of 200?
A.25
B.50
C.75
D.100
Solution
25% of 200 is calculated as (25/100) * 200 = 50.
Correct Answer: B — 50
Q. What is the greatest common divisor (GCD) of 24 and 36?
A.6
B.8
C.12
D.18
Solution
The GCD of 24 and 36 can be found by listing the factors: 24 = 2^3 * 3, 36 = 2^2 * 3^2. The GCD is 2^2 * 3 = 12.
Correct Answer: C — 12
Q. What is the least common multiple (LCM) of 12 and 15?
A.30
B.60
C.90
D.120
Solution
The LCM of two numbers is found by taking the highest power of each prime factor. The prime factorization of 12 is 2^2 * 3 and for 15 is 3 * 5. Thus, LCM = 2^2 * 3 * 5 = 60.
Correct Answer: B — 60
Q. What is the product of the first 4 prime numbers?
A.30
B.60
C.70
D.120
Solution
The first 4 prime numbers are 2, 3, 5, and 7. Their product is 2 * 3 * 5 * 7 = 210.
Correct Answer: A — 30
Q. What is the product of the first 5 prime numbers?
A.30
B.210
C.2310
D.30030
Solution
The first 5 prime numbers are 2, 3, 5, 7, and 11. Their product is 2 * 3 * 5 * 7 * 11 = 2310.
Correct Answer: C — 2310
Q. What is the product of the first three prime numbers?
A.30
B.60
C.42
D.70
Solution
The first three prime numbers are 2, 3, and 5. Their product is 2 * 3 * 5 = 30.
Correct Answer: A — 30
Q. What is the square root of 144?
A.10
B.11
C.12
D.13
Solution
The square root of 144 is 12, since 12 * 12 = 144.
Correct Answer: C — 12
Q. What is the sum of the first 10 natural numbers?
A.45
B.50
C.55
D.60
Solution
The sum of the first n natural numbers is given by the formula n(n + 1)/2. For n = 10, the sum is 10(10 + 1)/2 = 10 * 11 / 2 = 55.
