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Difficulty: Very hardIdentifying the Apparent Discrepancy

A financial institution recently implemented a restrictive automated screening protocol in its high-frequency algorithmic trading division, aiming to limit capital risk. Following this implementation, the total volume of trades executed daily by the division decreased by 15 percent. Additionally, financial audits confirm that the average profit generated per successful trade has remained entirely unchanged compared to the period preceding the new protocol. Nevertheless, the division’s total daily profit derived from high-frequency trading has increased by 20 percent since the protocol took effect.

Evaluate whether the following statement is true or false:

The assertion that 'the average profit generated per successful trade has remained entirely unchanged' and the assertion that 'the division’s total daily profit derived from high-frequency trading has increased by 20 percent' together constitute a genuine logical discrepancy.

Answer: Answer

Answer

False
The statement is false because the two identified assertions do not contradict one another. A flat average profit per successful trade combined with a 20 percent increase in total profit simply implies that more successful trades were made. The actual discrepancy requires the inclusion of the third fact—that the total volume of all trades executed decreased—which makes the increase in successful trades surprising.

Step-by-Step Solution

1
Isolate the two specific assertions presented in the statement.
Assertion 1: Average profit per successful trade is unchanged. Assertion 2: Total daily profit increased by 20 percent.
The question specifically asks if this pair of assertions constitutes a genuine discrepancy, requiring them to be evaluated independently of the other facts.
2
Determine if there is any inherent logical conflict between these two assertions.
There is no conflict. Total profit equals the average profit per successful trade multiplied by the number of successful trades. If the average remains flat, total profit can easily increase by simply executing a higher number of successful trades.
A genuine apparent discrepancy must consist of facts that are mutually counter-intuitive or logically contradictory.
3
Identify what is missing that creates the actual discrepancy in the stimulus.
The paradox only exists because a third fact (the total volume of all trades decreased by 15 percent) restricts the obvious explanation that trade volume increased.
Recognizing that the tension depends entirely on the omitted third fact proves that the two provided assertions do not constitute a discrepancy on their own.

Key Concept

Recognizing that a logical discrepancy requires mutually counter-intuitive facts, and carefully distinguishing between averages and absolute totals.
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Topics

Identifying the Apparent Discrepancy

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