Question

Company \(\mathrm{Z}\) spent \(\frac{1}{4}\) of its revenues last year on marketing and \(\frac{1}{7}\) of the remainder on maintenance of its facilities. What fraction of last year's original revenues did company Z have left after its marketing and maintenance expenditures? A. $$\frac{5}{14}$$ B. $$\frac{1}{2}$$ C. $$\frac{17}{28}$$ D. $$\frac{9}{14}$$ E. $$\frac{9}{11}$$

Short answer

\( \frac{9}{14} \).

Step-by-step solution

Calculate marketing expenditure

Let the original revenue of Company Z be denoted by 1 (or 100%). The marketing expenditure is given as \( \frac{1}{4} \) of the original revenue. Therefore, the amount spent on marketing is \( \frac{1}{4} \times 1 = \frac{1}{4} \).

Calculate remaining revenue after marketing

After marketing expenditures, the remaining revenue is the original revenue minus the amount spent on marketing. Thus, the remaining revenue is \( 1 - \frac{1}{4} = \frac{3}{4} \).

Calculate maintenance expenditure

Company Z spends \( \frac{1}{7} \) of the remaining revenue on maintenance. The remaining revenue after marketing is \( \frac{3}{4} \), so the maintenance expenditure is \( \frac{1}{7} \times \frac{3}{4} = \frac{3}{28} \).

Calculate remaining revenue after maintenance

To find the remaining revenue after maintenance, subtract the maintenance expenditure from the revenue left after marketing. Thus, the remaining revenue is \( \frac{3}{4} - \frac{3}{28} \).

Simplify the final expression

To subtract \( \frac{3}{4} \) and \( \frac{3}{28} \), find a common denominator. The least common multiple of 4 and 28 is 28. Express \( \frac{3}{4} \) with a denominator of 28: \( \frac{3}{4} = \frac{21}{28} \). Now, subtract the fractions: \( \frac{21}{28} - \frac{3}{28} = \frac{18}{28} = \frac{9}{14} \).

Key concepts

mathematical reasoning

Mathematical reasoning is fundamental in solving problems involving fractions and percentages. It helps you break down complex problems into simpler steps.

Let's go through the steps:

• First, you need to understand the total revenue is considered as 1.
• Then, calculate the fractions of expenditures.
• At each step, subtract the expenditures to find the remaining revenue.

This structured approach helps in accurate problem-solving.

For example, calculating \(\frac{1}{4}\) of revenue for marketing, then finding the remaining \(\frac{3}{4}\). Next, applying \(\frac{1}{7}\) on the remaining \(\frac{3}{4}\) gives us the maintenance expense of \(\frac{3}{28}\).

GMAT problem solving

GMAT problem solving often requires breaking down the problem into manageable parts. This involves:

• Identifying known values and variables.
• Converting percentages to fractions.
• Carrying out step-by-step calculations.

Remember to work with common denominators when adding or subtracting fractions. It ensures simplicity and accuracy.

For instance, in the marketing and maintenance expenditure example:

- Calculate remaining revenue after marketing: \(\frac{3}{4}\)
- Calculate maintenance: \(\frac{3}{28}\)
- Find common denominators to subtract: \(\frac{21}{28} - \frac{3}{28} = \frac{18}{28}\) which simplifies to \(\frac{9}{14}\).

financial expenditure calculations

Understanding how to calculate financial expenditures is crucial in accounting and finance. It helps determine how much money is spent and what remains. The basic sequence is:

• Calculate the fraction during each expenditure step.
• Subtract the spent amount from the revenue.
• Repeat for all expenditures involved.

For example, if Company Z has initial revenue of 1:

- Marketing: \(\frac{1}{4}\)
- Remaining: \(\frac{3}{4}\)
- Maintenance: \(\frac{1}{7} \times \frac{3}{4} = \frac{3}{28}\)
- Subtract to find remaining: \(\frac{3}{4} - \frac{3}{28} = \frac{18}{28} = \frac{9}{14}\).

Therefore, understanding how to manage fractions and percentages helps accurately assess financial statements.