1. We are given the standard Gibbs energy change:

$\Delta_r G^\circ = A - BT$

where $A$ and $B$ are constants.

2. Use the thermodynamic relation:

$\Delta_r G^\circ = \Delta_r H^\circ - T\Delta_r S^\circ$

Comparing with

$\Delta_r G^\circ = A - BT$

we identify:

$\Delta_r H^\circ = A, \qquad \Delta_r S^\circ = B$

3. Now determine when the reaction is exothermic or endothermic.

• Exothermic reaction means:

$\Delta_r H^\circ < 0$

So here, exothermic means:

$A < 0$

• Endothermic reaction means:

$\Delta_r H^\circ > 0$

So here, endothermic means:

$A > 0$

4. Therefore, the sign of $B$ is irrelevant for deciding whether the reaction is exothermic or endothermic. Only $A$ matters.

5. Evaluate the options:

• A: Exothermic if $B<0$
  False, because exothermicity depends on $A$, not $B$.

• B: Endothermic if $A>0$
  True, because $\Delta_r H^\circ = A$.

• C: Exothermic if $A>0$ and $B<0$
  False, since $A>0$ implies endothermic, not exothermic.

• D: Although the printed option appears truncated as “Endothermic if $A\ 0$”, the meaningful correct statement from thermodynamics is clearly option B.

6. Hence, the correct answer is:

$\boxed{\text{B}}$