Question:

Critical Reasoning -- Assumption Argument: 
"Flexible working hours will increase employee productivity because people perform best during the hours when they feel most energetic." 

Which of the following is a necessary assumption? 

  1. Employees can accurately identify the hours when they are most productive. 
  2. Productivity depends only on the time of day. 
  3. Employees dislike rigid schedules.
  4. Flexible hours reduce overall work time. 

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A necessary assumption is something that must be true for the argument to work. Try using the negation test: if negating the statement weakens the argument, it is a necessary assumption.
Updated On: Jul 4, 2026
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Approach Solution - 1

Approach: A necessary assumption is the unstated bridge the argument cannot survive without. Use the negation test: if negating an option destroys the argument, it is the necessary assumption.

Step 1: Map the argument. Premise: people perform best during their most energetic hours. Conclusion: flexible hours will raise productivity. The hidden gap is whether employees can actually line up their work with those energetic hours.

Step 2: Test option 1. "Employees can accurately identify the hours when they are most productive." Negate it: if employees could NOT identify their peak hours, flexibility would not help them work during those hours, and the productivity gain collapses. The argument depends on this, so it is necessary.

Step 3: Reject the rest. Option 2 ("productivity depends only on time of day") is too extreme \(--\) the argument needs time-of-day to matter, not to be the sole factor. Option 3 (employees dislike rigid schedules) is about preference, irrelevant to whether output rises. Option 4 (flexible hours reduce total work time) actually works against higher productivity, so it cannot be an assumption the argument relies on.

Necessary assumption: \( \text{Option 1} \)
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Approach Solution -2

Approach: Draw a straight line from stated premise to stated conclusion, and see exactly where the argument jumps without support, the assumption must sit precisely in that gap, no negation-testing needed.

Step 1: State premise and conclusion side by side. Premise: people perform best in their most energetic hours. Conclusion: flexible hours will raise productivity.

Step 2: Find the missing link. Going from "people have energetic hours" to "flexibility raises output" silently assumes that people know when their own energetic hours are, otherwise flexibility just lets them choose randomly, with no guaranteed link to their peak energy.

Step 3: Match this gap to the options. Option 1 ("employees can accurately identify... most productive [hours]") is exactly this missing link. Options 2 to 4 either overreach ("only"), discuss an unrelated preference (liking flexibility), or point in a direction that would undercut, not support, the conclusion (reduced work time).

Necessary assumption: Option 1.
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