Number problems

user November 18, 2023

(6) The difference between a number and its cube is 63. What is the number?

(a) 5
(b) 4
(c) 3
(d) 6

Correct Answer: (b) 4

$x - x^3 = 63 \rightarrow x^3 - x + 63 = 0$

Using trial and error, you’ll find that x = 4 is the solution.

(7) If twice a number is increased by 18, the result is 42. What is the number?

(a) 12
(b) 10
(c) 12
(d) 6

Correct Answer: (c) 12

$2x + 18 = 42 \rightarrow 2x = 42 - 18 \rightarrow 2x = 24 \rightarrow x = 12$

(8) The product of two consecutive even numbers is 168. What are the numbers?

(a) 12, 14
(b) 14, 16
(c) 12, 14
(d) 16, 18

Correct Answer: (c) 12, 14

$x \cdot (x + 2) = 168 \rightarrow x^2 + 2x - 168 = 0$

Using the quadratic formula, you’ll find that x = 12 and x = -14. Since we are looking for even numbers, x = 12 is the solution.

(9) If the square of a number is 169, what is the number?

(a) 13
(b) 13 or -13
(c) 26
(d) 7

Correct Answer: (b) 13 or -13

$x^2 = 169 \rightarrow x = \pm \sqrt{169}$

So, the possible values for x are 13 and -13.

(10) A number when divided by 3 leaves a remainder of 2. What is the number?

(a) 1
(b) 2
(c) 3
(d) 4

Correct Answer: (b) 2

When a number is divided by 3, it leaves a remainder of 2, which can be represented as $3n + 2$.

So, the number is of the form $3n + 2$, and possible values for n are integers. One of them is 1, so the number is 3 * 1 + 2 = 5.

Post Views: 2