Question:
Armtech, a temporary-employment agency, previously gave its employees 2.5 paid vacation days after each 700 hours worked. Armtech's new policy is to give its employees 5.0 paid vacation days after each 1,200 hours worked. Therefore, this new policy is more generous to Armtech employees in giving them more vacation days per hour worked than the old policy did.
Which of the following is an assumption on which the argument depends?
Armtech, a temporary-employment agency, previously gave its employees 2.5 paid vacation days after each 700 hours worked. Armtech's new policy is to give its employees 5.0 paid vacation days after each 1,200 hours worked. Therefore, this new policy is more generous to Armtech employees in giving them more vacation days per hour worked than the old policy did.
Which of the following is an assumption on which the argument depends?
Which of the following is an assumption on which the argument depends?
Show Hint
For assumption questions, look for the logical leap. The argument here jumps from a mathematical rate to a real-world quality ("generous"). The assumption must bridge that gap, connecting the calculation to its practical application. The negation test is a powerful tool to confirm the correct answer.
Updated On: Oct 4, 2025
- Most current Armtech employees approve of the company's new vacation policy.
- A few Armtech employees leave the company before having worked 700 hours.
- Most Armtech employees were not aware that the company planned to change its vacation policy until after it had already done so.
- A significant portion of Armtech employees stay with the company long enough to work for 1,200 hours.
- Armtech's new vacation policy closely matches the vacation policies of competing temporary employment agencies.
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
This is a critical reasoning question that asks for a necessary assumption in an argument. An assumption is an unstated premise that must be true for the conclusion to follow logically from the stated premises. The argument concludes that the new policy is "more generous" based on a mathematical calculation of vacation days per hour.
Step 2: Key Formula or Approach:
1. Analyze the argument's structure: Premise → Conclusion.
2. Calculate the rates to verify the premise.
3. Identify the logical gap between the mathematical generosity and the practical generosity implied by the conclusion.
4. Use the "negation test": the correct assumption, when negated, will destroy the argument.
Step 3: Detailed Explanation:
Argument Analysis:
- Old Policy Rate: \( \frac{2.5 \text{ days}}{700 \text{ hours}} \approx 0.00357 \) days per hour.
- New Policy Rate: \( \frac{5.0 \text{ days}}{1200 \text{ hours}} \approx 0.00417 \) days per hour.
- Premise: The new rate (0.00417) is indeed higher than the old rate (0.00357).
- Conclusion: Therefore, the new policy is more generous.
Logical Gap: The argument equates a higher mathematical rate with being "more generous." However, a policy's generosity in the real world depends on employees actually being able to benefit from it. The new policy requires employees to work much longer (1,200 hours) to receive any benefit, compared to the old policy's 700-hour threshold. The argument implicitly assumes this higher threshold is achievable.
Evaluating the Options:
- (A) Employee approval is about perception, not the objective generosity of the policy. The argument would stand even if they disapproved.
- (B) This is irrelevant. The policy's generosity is for those who stay, not those who leave.
- (C) Employee awareness is irrelevant to the terms of the policy itself.
- (D) This addresses the logical gap. For the new policy to be genuinely "more generous," employees must actually reach the 1,200-hour mark to receive the 5 vacation days. If a significant portion of employees do not stay that long, then for them, the policy is effectively less generous, as they might have earned vacation under the old 700-hour rule but earn nothing under the new rule.
Negation Test on (D): Let's negate the assumption. "A significant portion of Armtech employees do NOT stay long enough to work for 1,200 hours." If this is true, then for many employees, the new policy provides zero vacation days, whereas the old one provided 2.5. This would make the new policy less generous for them, destroying the original conclusion. Since the negation destroys the argument, (D) is a necessary assumption.
- (E) Competitors' policies are irrelevant to the internal comparison between Armtech's old and new policies.
Step 4: Final Answer:
The argument assumes that the conditions for receiving the new, higher benefit are actually met by a significant number of employees, making the policy's generosity a practical reality rather than just a theoretical calculation.
This is a critical reasoning question that asks for a necessary assumption in an argument. An assumption is an unstated premise that must be true for the conclusion to follow logically from the stated premises. The argument concludes that the new policy is "more generous" based on a mathematical calculation of vacation days per hour.
Step 2: Key Formula or Approach:
1. Analyze the argument's structure: Premise → Conclusion.
2. Calculate the rates to verify the premise.
3. Identify the logical gap between the mathematical generosity and the practical generosity implied by the conclusion.
4. Use the "negation test": the correct assumption, when negated, will destroy the argument.
Step 3: Detailed Explanation:
Argument Analysis:
- Old Policy Rate: \( \frac{2.5 \text{ days}}{700 \text{ hours}} \approx 0.00357 \) days per hour.
- New Policy Rate: \( \frac{5.0 \text{ days}}{1200 \text{ hours}} \approx 0.00417 \) days per hour.
- Premise: The new rate (0.00417) is indeed higher than the old rate (0.00357).
- Conclusion: Therefore, the new policy is more generous.
Logical Gap: The argument equates a higher mathematical rate with being "more generous." However, a policy's generosity in the real world depends on employees actually being able to benefit from it. The new policy requires employees to work much longer (1,200 hours) to receive any benefit, compared to the old policy's 700-hour threshold. The argument implicitly assumes this higher threshold is achievable.
Evaluating the Options:
- (A) Employee approval is about perception, not the objective generosity of the policy. The argument would stand even if they disapproved.
- (B) This is irrelevant. The policy's generosity is for those who stay, not those who leave.
- (C) Employee awareness is irrelevant to the terms of the policy itself.
- (D) This addresses the logical gap. For the new policy to be genuinely "more generous," employees must actually reach the 1,200-hour mark to receive the 5 vacation days. If a significant portion of employees do not stay that long, then for them, the policy is effectively less generous, as they might have earned vacation under the old 700-hour rule but earn nothing under the new rule.
Negation Test on (D): Let's negate the assumption. "A significant portion of Armtech employees do NOT stay long enough to work for 1,200 hours." If this is true, then for many employees, the new policy provides zero vacation days, whereas the old one provided 2.5. This would make the new policy less generous for them, destroying the original conclusion. Since the negation destroys the argument, (D) is a necessary assumption.
- (E) Competitors' policies are irrelevant to the internal comparison between Armtech's old and new policies.
Step 4: Final Answer:
The argument assumes that the conditions for receiving the new, higher benefit are actually met by a significant number of employees, making the policy's generosity a practical reality rather than just a theoretical calculation.
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