Logical reasoning PrepTest 122 · Section 2 · Question 16

Incorrect. not Time for leisure activities → Work 18+ hours/day. This is a reversal of statement #2, and while not logically supported, reversals are potentially true, so this answer can be eliminated.

Incorrect. Work 18+ hours/day -some-Successful. We can reverse a most statement if (and only if) we drop it down to a some statement, so this answer is supported by the stimulus.

Incorrect. Happy-some-Successful. We inferred that most successful entrepreneurs are not happy, but that leaves open the possibility that some are.

Correct. Argument or Facts:
Facts

Question Type:
Cannot Be True

Stimulus Summary:
(1) Successful-most-Work 18+ hours/day
(2) Work 18+ hours/day → not Time for leisure activities
(3) Happy → Time for leisure activities

Answer Anticipation:
Four of the answers here can be true; the fifth and correct one cannot, making this a Cannot Be True question.

Answers cannot be true when they contradict information (or inferences) from the stimulus. When we have conditional logic in a Cannot Be True question, we're looking for an answer that establishes the sufficient condition of a statement but says the necessary condition isn't present. When we have quantifiers in a Cannot Be True question, we're looking for an answer that denies the quantified inferences. So let's get to work making chains and inferences!

Let's start with the two conditionals, since they have an overlapping term. To get them to chain together, we need to take the contrapositive of one of the statements. We're going to take the contrapositive of statement #3 and then combine it with statement #2. Why? Because statement #2 already shares a term with statement #1, and so we don't want to lose that (though we will still take the contrapositive):
Work 18+ hours/day → not Time for leisure activities → not Happy
(Happy → Time for leisure activities → not Work 18+ hours/day)

The combined statement can be combined with statement #1 using our quantifier rules. Since the sufficient condition of the conditional overlaps with either term in the quantified statement, we can combine them. And since it's the second term in the most statement that overlaps, we can get a most inference—the one exception to our normal limit of getting a some inference:
Successful-most-not Time for leisure activities
Successful-most-not Happy

Note that we made both inferences along the chain—since each term guarantees the next, we can make the same inferences for each "downstream" term.

Let's find an answer that contradicts one of these inferences.

Answer Explanation:
Work 18+ hours/day-some-Happy. The conditional chain allows us to infer that any entrepreneur working 18+ hours/day has no time for leisure activities and thus isn't happy, so this answer contradicts the conditional. Since it contradicts an inference from the stimulus, this is the correct answer.

Key Takeaway:
Cannot Be True questions need an answer that contradicts a statement or inference from the stimulus. When the stimulus has conditional statements, this means the answer will establish the presence of the sufficient condition when the necessary condition is absent.

Incorrect. Successful-some-not Work 18+ hours/day. Statement #1 establishes that most successful entrepreneurs work at least 18 hours/day, leaving room for there to be some who don't.