Number problems

user November 18, 2023

(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

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

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

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

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?