1) There is a larger number of hydrophilic molecules on the outside of a cell than on the inside. Identify the conditions that could equalize the intracellular and extracellular concentrations of this molecule.

A. not inserting any transport proteins in the membrane
B. placing only intracellularly‑directed pumps in the membrane
C. placing carrier proteins in the membrane
D. placing intracellularly‑directed and extracellularly‑directed pumps in the membrane

2) Which of the conditions would be the most metabolically efficient way for a cell to equalize the intracellular and extracellular concentrations of this molecule?

A. not inserting any transport proteins in the membrane
B. placing only intracellularly-directed pumps in the membrane
C. placing carrier proteins in the membrane
D. placing intracellularly directed and extracellularly directed pumps in the membrane

Explanation:

If there is no barrier preventing molecules from moving molecules, then there will be large movement of molecules  from an area of high concentration to an area of low concentration. This passive process is known as diffusion. The phospholipid bilayer of a cell's membrane works as a barrier to large molecules, ions, and most hydrophilic molecules. Whereas small hydrophobic molecules can pass freely through the phospholipid bilayer, other molecules and ions are transported across the cell membrane with the help of transport proteins. Some transport proteins, allowing hydrophilic molecules and ions to passively move through them and across the cell membrane.

Examples: carrier proteins and channel proteins.

Placing carrier proteins in the cell membrane will allow the molecule to reach equal concentrations on the both the sides of the membrane and maintain that way over long time. In contrast, transport proteins known as pumps will use cellular energy, usually in the form of ATP, to transport molecules.

Placing equal numbers of intracellularly directed and extracellularly directed pumps would also equalize the concentrations of a molecule long over time. Pumps are to transport molecules against their concentration gradient, such as the sodium-potassium pump continuously moves sodium ions out of a cell.  

Through the use of carrier proteins, there is equalization of  concentrations of a hydrophilic molecule. This equalize the numbers of molecules on the inside and outside of the cell, but the pumps would continue moving the molecule inward, eventually resulting in more molecules inside of the cell than out.