swerve wrote:$$If\ \ \ 0 < x < 2,$$ which of the following must be greatest?

(A) x
(B) x^2
(C) 2x
(D) x + 2
(E) 2^x

The key word here is MUST.
That is, the correct answer must yield the biggest value for ALL values of x between 0 and 2
So, let's TEST one of the possible x-values.
Let's test x = 1

We get....

(A) x = 1
(B) x^2 = 1^2 = 1
(C) 2x = (2)(1) = 2
(D) x + 2 = 1 + 2 = 3
(E) 2^x = 2^1 = 2

Since D yields the biggest value, then the correct answer MUST be D

Cheers,
Brent

swerve wrote:$$If\ \ \ 0 < x < 2,$$ which of the following must be greatest?

(A) x
(B) x^2
(C) 2x
(D) x + 2
(E) 2^x

The OA is D.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

If x = 1, we see that the given answer choices become 1, 1, 2, 3, and 2, respectively. Therefore, D is the correct answer.

Answer: D