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In a comprehensive study of corporate productivity, companies that transitioned from a five-day to a four-day workweek reported an average 15 percent increase in total weekly output. However, these companies simultaneously experienced a 20 percent increase in total operational costs, largely because they had to hire additional part-time staff to maintain continuous customer service on the fifth day. Despite these added expenses, the vast majority of the companies reported significantly higher annual net profits following the transition. During this period, these companies did not alter their pricing structures, introduce new products, or experience changes in non-operational costs.

Based on the information above, is it true or false that for the vast majority of these companies, the additional revenue resulting from the 15 percent increase in total weekly output exceeded the absolute dollar amount of the 20 percent increase in total operational costs?

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True
The correct answer is True because it is mathematically necessitated by the stimulus. If net profit increased while costs increased, revenue must have increased by an absolute amount greater than the cost increase. With other revenue drivers held constant, the 15 percent output increase is the sole source of this revenue, strongly supporting the claim that its absolute value exceeded the cost increase.

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1
Analyze the components of net profit as described in the stimulus.
Net profit is implicitly understood as total revenue minus total costs (operational plus non-operational).
Establishing the mathematical relationship is necessary to deduce how changes in output and costs affect profit.
2
Evaluate the changes in costs and profits.
Total operational costs increased by 20 percent and non-operational costs were unchanged, yet net profits still increased for the vast majority of companies.
This indicates that total revenue must have increased by an absolute dollar amount greater than the absolute dollar increase in total costs.
3
Identify the exclusive source of the increased revenue.
Since prices and product lines remained stable, the revenue increase must have been generated solely by the 15 percent increase in total weekly output.
This links the stated output increase to the required revenue increase.
4
Synthesize the findings to evaluate the statement.
The absolute financial value generated by the 15 percent output increase must have been larger than the absolute dollar cost of the 20 percent operational cost increase.
This confirms that the statement is a necessary deduction from the provided premises.

Anahtar Kavram

Synthesizing proportional relationships and absolute numbers to draw a mathematically necessary inference.
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