Question

What is the monthly rent for a certain apartment?
(1) The monthly rent per person for 4 people to share the rent for the apartment is \$375.
(2) The monthly rent per person for 4 people to share the rent of the apartment is \$125 less than the monthly rent per person for 3 people to share the rent.

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• D. EACH statement ALONE is sufficient.
• E. Statements (1) and (2) TOGETHER are NOT sufficient

Hint:

In Data Sufficiency, you don't need to actually solve the problem completely if you can see that a unique solution exists. For Statement (2), once you set up the equation \(\frac{R}{4} = \frac{R}{3} - 125\), you can recognize it's a linear equation with one variable and conclude that it's solvable for R, making the statement sufficient.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This is a Data Sufficiency question where we need to determine if the given statements provide enough information to find a unique value for the total monthly rent. Let R be the total monthly rent.
Step 2: Detailed Explanation:
Evaluating Statement (1) Alone:
"The monthly rent per person for 4 people to share the rent... is \$375."
This can be written as an equation:
\[ \frac{R}{4} = \$375 \] We can solve this equation for R by multiplying both sides by 4:
\[ R = 375 \times 4 = \$1500 \] Since we can find a single, unique value for the rent, Statement (1) alone is sufficient.
Evaluating Statement (2) Alone:
"The monthly rent per person for 4 people... is \$125 less than the monthly rent per person for 3 people..."
The rent per person for 4 people is \(R/4\).
The rent per person for 3 people is \(R/3\).
The statement translates to the equation:
\[ \frac{R}{4} = \frac{R}{3} - 125 \] This is a single equation with one variable, R. We can solve for R.
To eliminate the fractions, multiply the entire equation by the least common multiple of 4 and 3, which is 12:
\[ 12 \left( \frac{R}{4} \right) = 12 \left( \frac{R}{3} \right) - 12(125) \] \[ 3R = 4R - 1500 \] \[ 1500 = 4R - 3R \] \[ R = \$1500 \] Since we can find a single, unique value for the rent, Statement (2) alone is sufficient.
Step 3: Final Answer:
Both Statement (1) and Statement (2) are sufficient on their own to determine the total monthly rent. Therefore, the correct answer is (D).