If cx - bx^3 = 0 where b and c are non-zero numbers, what is the value of b - c ?

[BTGModeratorVI]

If cx - bx^3 = 0 where b and c are non-zero numbers, what is the value of b - c ?

(1) cx = c
(2) bx = b

Answer: D
Source: 800 score

[Brent@GMATPrepNow]

If cx - bx^3 = 0 where b and c are non-zero numbers, what is the value of b - c ?

(1) cx = c
(2) bx = b

Answer: D
Source: 800 score

Given: cx - bx³ = 0

Target question: What is the value of b - c ?

Statement 1: cx = c
Since we know that c ≠ 0, we can safely divide both sides of the equation by c to get: x = 1
Now plug x = 1 into a given equation, cx - bx³ = 0
We get: c(1) - b(1³) = 0
Simplify to get: c - b = 0, which means c = b, which means b - c = 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: bx = b
Since we know that b ≠ 0, we can safely divide both sides of the equation by b to get: x = 1
Now plug x = 1 into a given equation to get: c(1) - b(1³) = 0
Simplify to get: c - b = 0, which means c = b, which means b - c = 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

[deloitte247]

$$If\ cx-bx^3=0$$
Where b and c are non-zero solutions
Target question: What is the value of b-c?
Statement 1: cx=c
$$Where\ c\ne0$$
cx is divisible by x, so, it is either 1 or a prime number where x in both cases=1 as the product=c.
Therefore, c(1) = c
Substituting x=1 into the equation
$$c\left(1\right)-b\left(1\right)^3=0\ \ \ \ \ \ From\ question\ stem$$
c - b = 0
c - 0 = b
-0 = b - c
b - c = 0
Statement 1 is SUFFICIENT

Statement 2: bx = b
This is the same as statement 1 as x=1 and plugging the value will yield b-c=0. Hence, statement 2 is also SUFFICIENT.

Since each statement alone is SUFFICIENT, the correct answer is, therefore, option D