Number problems

(1) If the product of a number and 4 is 96 more than the number itself, what is the number?

• (a) 25
• (b) 28
• (c) 32
• (d) 33

Answer

Correct Answer: (c) 32

4x = x + 96 \rightarrow 3x = 96 \rightarrow x = 32

(2) The sum of a number and its reciprocal is \( \frac{17}{4} \). What is the number?

• (a) \( \frac{4}{1} \)
• (b) \( \frac{8}{3} \)
• (c) \( \frac{1}{4} \)
• (d) \( \frac{3}{8} \)

Answer

Correct Answer: (b) \( \frac{8}{3} \)

x + \frac{1}{x} = \frac{17}{4} \rightarrow 4x^2 - 17x + 4 = 0 \rightarrow x = \frac{8}{3}

(3) If the difference between six times a number and 11 is equal to the number itself, what is the number?

• (a) 2
• (b) 1.5
• (c) 1.75
• (d) 2.25

Answer

Correct Answer: (a) 2

6x - 11 = x \rightarrow 5x = 11 \rightarrow x = \frac{11}{5} \rightarrow x = 2.2

(4) The sum of two consecutive odd numbers is 44. What are the numbers?

• (a) 22, 22
• (b) 21, 23
• (c) 20, 24
• (d) 19, 25

Answer

Correct Answer: (b) 21, 23

x + (x+2) = 44 \rightarrow 2x + 2 = 44 \rightarrow 2x = 42 \rightarrow x = 21

So, the consecutive odd numbers are 21 and 23.

(5) If the sum of a number and its square is 56, what is the number?

• (a) 7
• (b) 8
• (c) 9
• (d) 10

Answer

Correct Answer: (b) 8

x + x^2 = 56 \rightarrow x^2 + x - 56 = 0 \rightarrow (x + 8)(x - 7) = 0

So, the possible values for x are -8 and 7. Since we are looking for a positive number, x = 7.