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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

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

Step by step solution

01

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 \( \frac{1}{4} \times 1 = \frac{1}{4} \).
02

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 \( 1 - \frac{1}{4} = \frac{3}{4} \).
03

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 \( \frac{1}{7} \times \frac{3}{4} = \frac{3}{28} \).
04

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 \( \frac{3}{4} - \frac{3}{28} \).
05

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: \( \frac{21}{28} - \frac{3}{28} = \frac{18}{28} = \frac{9}{14} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

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