Twice a number is 3 times the square of the number less than one. If the number is positive, what is the value of the

[VJesus12]

Twice a number is 3 times the square of the number less than one. If the number is positive, what is the value of the number?

(A) 1

(B) 1/2

(C) 1/3

(D) 2/3

(E) 3/2

[spoiler]OA=C[/spoiler]

Source: Magoosh

[deloitte247]

Let the number = x
$$2x=1-\left(3x^2\right)$$
$$2x=1-3x^2$$
$$3x^2+2x-1=0$$
$$3x^2+3x-1x-1=0$$
$$3x\left(x+1\right)-1\left(x+1\right)=0$$
$$3x-1=0\ or\ x+1=0$$
$$x=\frac{1}{3}\ or\ x=-1$$
Given that the number is positive, x cannot be negative
$$so\ x\ne-1$$
$$x\ =\ \frac{1}{3}$$

Answer = C

[Scott@TargetTestPrep]

Twice a number is 3 times the square of the number less than one. If the number is positive, what is the value of the number?

(A) 1

(B) 1/2

(C) 1/3

(D) 2/3

(E) 3/2

[spoiler]OA=C[/spoiler]

Solution:

The rather odd wording “3 times the square of the number less than one” actually means to subtract 3 times the square of the number from one. Thus, we can create the equation:

2n = 1 - 3n^2

3n^2 + 2n - 1 = 0

(3n - 1)(n + 1) = 0

n = -1 or n = 1/3

Since n is positive, n = 1/3.

Answer: C