GRE Multiple Choice Question - Select One or More Answer Choices

Question

GRE Multiple Choice Question.

Question: If $a=3+b$, which of the following is true?

$\left (\mathrm{I} \right ) a>b+2.5$

$\left (\mathrm{II} \right )a<b+2.5$

$\left (\mathrm{III} \right ) a>2+b$

Select One or More Answer Choices:

A. $\mathrm{I}$ only

B. $\mathrm{II}$ only

C. $\mathrm{III}$ only

D. $\mathrm{I}$ and $\mathrm{II}$ only

E. $\mathrm{I}$ and $\mathrm{III}$ only

Clearly $\mathrm{I}$ and $\mathrm{III}$ are true, so I think the answer is E. But GRE Practice Text's answer is A, C, and D and I am entirely not convinced they're correct.

Answer 1

$A$ is wrong, because both I and III are true.

$B$ is wrong.

$C$ is wrong, because both I and III are true.

$D$ is wrong because while $I$ is true, $II$ is not.

$E$ is correct, since two and only two statements are true: $I, III$.

Answer 2

The correct answer is E. The provided answer is wrong.