Question

Question given below has a problem and two statements I & II. Decide if the information given in the statement is sufficient for answering the problem.

Company Z only sells chairs and tables. What percent of its revenue in 2008 did Company Z derive from its sales of chairs ?
(I) In 2008, the price of tables sold by Company Z was 10% higher than the price of chairs sold by Company Z.
(II) In 2008, Company Z sold 20% fewer tables than chairs .

• A. Data in statement I alone is sufficient.
• B. Data in statement II alone is sufficient.
• C. Data in both statements together is sufficient.
• D. Data in both statements together is not sufficient.

Answer 1

The correct option is C Data in both statements together is sufficient.

(C): First of all, notice that the question is only asking for the percent of its revenue the company derived from chairs. The question is asking for a relative value.

The revenue for the company can be expressed by the following equation:

$Revenu{e}_{companyZ}=R_T+R_C$

If you can find the relative value of any two of these revenues, you will have enough information to answer the question.

Also, note that the GMAT will expect you to know that Revenue = Price x Quantity Sold. This relationship is discussed in more detail in Chapter 1 of the Word Problems GMAT Strategy Guide.

The revenue derived from tables is the price per table multiplied by the number of tables sold. The revenue derived from chairs is the price per chair multiplied by the number of chairs sold. You can create some variables to represent these unknown values:

$R_T=P_T\times Q_T$

$R_C=P_C\times Q_C$

(1) INSUFFICIENT: This statement gives you the relative value of the price of tables to the price of chairs. If the price of tables was 10% higher than the price of chairs, then the price of tables was 110% of the price of chairs:

$P_T=1.1P_C$

However, without any information on quantity, this information by itself does not give you the relative value of their revenues.

(2) INSUFFICIENT: If the company sold 20% fewer tables than chairs, then the number of tables sold is 80% of the number of chairs sold:

$Q_T=0.8Q_C$

This information by itself, without any information about price, does not give you the relative value of their revenues.

(1) AND (2) SUFFICIENT: Look again at the equation for revenue derived from the sale of tables:

$R_T=P_T\times Q_T$

Replace $P_T$ with 1.1 $P_C$ and replace $Q_T$ with $0.8Q_C$:

$P_T\times Q_T=\left(1.1P_C\right)\times \left(0.8Q_C\right)$

$P_T\times Q_T=\left(0.88\right)(P_C\times Q_C)$

$R_T=\left(0.88\right)R_C$

Taken together, the two statements provide the relative value of the revenues. No further calculation is required to know that you can find the percent of revenue generated from the sale of chairs. In fact, if you know that you can relate tables to chairs in terms of both quantity and price, it isn't even necessary to calculate revenue at all. The statements together are sufficient.

If you do want to perform the calculation, it would look something like this:

$\frac{R_C}{TotalRevenue}=\frac{R_C}{R_T+R_C}=\frac{R_C}{\left(0.88\right)R_C+R_C}=\frac{R_c}{\left(1.88\right)R_C}=\frac{1}{1.88}\approx 53\%$

The correct answer is (C).