Number problems

(31) If a number is decreased by 30% of itself, the result is 42. What is the number?

• (a) 60
• (b) 60 or 70
• (c) 70
• (d) 50

Answer

Correct Answer: (b) 60 or 70

Let the number be \(x\).

Given that \(x – 0.30x = 42\), you can solve this equation to find \(x = 60\). However, \(x\) can also be 70, so both are correct answers.

(32) The sum of two consecutive prime numbers is 24. What are the numbers?

• (a) 11, 13
• (b) 11, 13
• (c) 13, 15
• (d) 7, 17

Answer

Correct Answer: (b) 11, 13

Let the two consecutive prime numbers be \(x\) and \(x+2\).

Given that \(x + (x+2) = 24\), you can solve this equation to find \(x = 11\). So, the numbers are 11 and 13.

(33) If the sum of a number and its cube is 112, what is the number?

• (a) 4
• (b) 5
• (c) 6
• (d) 7

Answer

Correct Answer: (d) 7

Given that \(x + x^3 = 112\), you can solve this equation to find \(x = 7\).

(34) If the product of a number and 9 is 117, what is the number?

• (a) 15
• (b) 13
• (c) 12
• (d) 13 or -13

Answer

Correct Answer: (d) 13 or -13

Given that \(9x = 117\), you can solve this equation to find \(x = 13\). However, \(x\) can also be -13, so both are correct answers.

(35) If a number is divided by 7, the result is 8. What is the number?

• (a) 56
• (b) 56
• (c) 64
• (d) 48

Answer

Correct Answer: (b) 56

Given that \(x/7 = 8\), you can solve this equation to find \(x = 56\).