Number problems

(11) The product of three consecutive even numbers is 3840. What are the numbers?

• (a) 14, 16, 18
• (b) 10, 12, 14
• (c) 16, 18, 20
• (d) 12, 14, 16

Answer

Correct Answer: (c) 16, 18, 20

Let the three consecutive even numbers be \(x\), \(x+2\), and \(x+4\).

Then, \(x \cdot (x+2) \cdot (x+4) = 3840\).

Solving this equation, you’ll find \(x = 16\), so the numbers are 16, 18, and 20.

(12) If the sum of two numbers is 25, and their difference is 7, what are the numbers?

• (a) 16, 9
• (b) 14, 11
• (c) 13, 12
• (d) 18, 7

Answer

Correct Answer: (a) 16, 9

Let the two numbers be \(x\) and \(y\).

Given that \(x + y = 25\) and \(x – y = 7\), you can solve this system of equations to find \(x = 16\) and \(y = 9\).

(13) If the square of a number is 25, what are the possible values of the number?

• (a) 5 or -5
• (b) 25 or -25
• (c) 4 or -4
• (d) 3 or -3

Answer

Correct Answer: (a) 5 or -5

Given that \(x^2 = 25\), you can take the square root of both sides to find \(x = \pm 5\).

(14) If a number is increased by 25% of itself, the result is 45. What is the number?

• (a) 36
• (b) 36 or 45
• (c) 40
• (d) 32

Answer

Correct Answer: (b) 36 or 45

Let the number be \(x\).

Given that \(x + 0.25x = 45\), you can solve this equation to find \(x = 36\).

(15) If a number is divided by 4, the result is 9. What is the number?

• (a) 45
• (b) 6
• (c) 36
• (d) 18

Answer

Correct Answer: (c) 36

Given that \(x/4 = 9\), you can solve this equation to find \(x = 36\).