Logical reasoning PrepTest 112 · Section 3 · Question 21

Question prompt

Sandy: I play the Remaining source text redacted.
Why the credited answer is right

Credited answer: B

The notes below walk through why it fits the stem and how to eliminate the rest.

Argument or Facts

Argument/Argument

Valid or Flawed

Flawed/Flawed

Question Type

Errors in Reasoning Questions

Stimulus Summary

Background - The Bigbucks lottery involves picking 5 numbers, and everyone who picks right splits the pot. It rolls over for any week where there’s no winner.
Sandy: It’s best to play after there haven’t been any winners for a few weeks.
Alex: There are fewer people playing when the pot is small, so you’re more likely to win. That’s when it’s best to play.

Answer Anticipation

This question stem asks us to find an error in reasoning in one of the speakers’ arguments, which provides no guidance as to which one we need to focus on! There may be only one speaker who has a flawed argument. We need to analyze both.
Sandy gives us some background on how the Bigbucks lottery works. It’s not too different from what we’d expect from a lottery. The key point here seems to be that the pot gets bigger for each week there isn’t a winner - which seems pretty standard for a lottery.
Both speakers discuss when it’s “best” to play the lottery, but neither really delves into what constitutes the “best” time to play, so they’re both likely making flawed arguments.
Sandy believes that the best time to play is after a few weeks when there aren’t any winners because the money pot is large. However, it’s possible that the number of winners is much higher then, and the split pot is thus lower per person. Failing to consider this possibility makes his argument flawed.
Alex, on the other hand, believes that the chances of winning are highest when the pot is small because fewer people are playing. However, the odds that you pick the correct 5 numbers don’t change with the number of players - those odds are always the same. The only thing that changes are the odds that someone else will also pick the right numbers, thus forcing the pot to be split. Misunderstanding how odds work makes her argument flawed.
Since both arguments are flawed, we need to be on the lookout for either in the answers (and, since only one answer can be correct, the other flaw won’t be mentioned).

Answer choices

  1. A
    Sandy holds that the Remaining source text redacted.
    Why choice A is not credited
    Sandy doesn’t discuss the number of times someone plays, just that it’s best to play when the pot is largest. While this does have implications for how frequently someone plays, he doesn’t attach it to the odds of winning, just the size of any winnings for those who do pick correctly.
  2. B
    Alex holds that the Remaining source text redacted.
    Why choice B matches the stem
    This answer highlights the flaw in Alex’s argument. She believes the odds of winning are highest when there are fewer people playing. However, the odds that the 5 numbers you picked are the winning numbers is the same whether you’re the only one playing, or whether you’re one of a million. What changes based on the number of people playing is the odds there are multiple winners, and thus whether the pot will be shared (and then the size of the individuals shares), not the odds of winning in the first place. Since this answer correctly describes the flaw in Alex’s argument, it’s correct.
  3. C
    Sandy holds that the Remaining source text redacted.
    Why choice C is not credited
    Sandy’s argument is about maximizing the size of the pot, not the odds of winning, so this answer is out of scope of his argument.
  4. D
    Alex holds that the Remaining source text redacted.
    Why choice D is not credited
    Alex doesn’t talk about week-to-week changes in odds, so this answer is out of scope of her argument.
  5. E
    Sandy holds that the Remaining source text redacted.
    Why choice E is not credited
    Similar to (C), Sandy focuses on the size of the pot, not the odds of winning, so this answer is out of scope of his argument.

What this tests

Question analytics

Based on historical answer selection rates for this question.

Answer choice distribution

  1. A 5%
  2. B Credited 55%
  3. C 17%
  4. D 5%
  5. E 17%

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