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WHY are these statements valid or invalid? (some and most qualifiers)

matiecena83matiecena83 Member
edited April 2021 in Logical Reasoning 62 karma

1) Some customers prefer vanilla to chocolate and no customer has no preference in the matter. Therefore, most customers prefer chocolate.

2) Most customers order chocolate ice cream, and most customers get toppings. All customers who get toppings get a free hat. So, some people who order chocolate ice cream get a free hat.

3) Everyone who orders a sundae gets offered a free extra cherry, and most people say yes to the free extra cherry. Some people who order the banana split get offered a free extra cherry, and less than half of those people say yes. Therefore, more customers get a free cherry with a sundae than they do with a banana split.

4) Everyone who orders a sundae gets offered a free extra cherry, and most people say yes to the free extra cherry. Some people who order the banana split get offered a free extra cherry, and less than half of those people say yes. So, people who order a sundae are more likely to say yes to a free extra cherry than are people who order a banana split.

Solutions
Valid: 2 & 4
Invalid: 1 & 3

Overall, I'm having difficulty mapping out the solutions with some, most, all... Thank you very much for your help in advance!

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Comments

  • matiecena83matiecena83 Member
    edited April 2021 62 karma

    I got these questions from: http://www.thelsattrainer.com/assets/31-lsat-vocabulary-sample-chapter.pdf

    There are more sample questions here if anyone is interested

  • mattscrappymattscrappy Member
    138 karma

    Hi!
    1) is invalid because it assumes the "some" statement of vanilla is definitely less than half. LSAT "some" can literealy mean 1-100%, so, while it could be true that most people (51-100%) prefer chocolate, it isn't necessarily true.
    2) is valid becuase it links two most premises to a some inference. Mathematically, it means that, at minimum, 51% of people order chocolate and 51% get toppings. That means that, to satisfy both conditions, at lease one person must do both and would mean that that at least that one person gets a free hat.
    3) is invalid because it assumes that both sample sizes are the same, a.k.a it confuses numbers and percentages. Yes its true that higher % of people would receive a cherry from a sundae than a split, but what if there are only 10 people ordering sundaes and 10,000 ordering splits? There could then be 100 splits with cherries, and even if everyone orders a cherry with their sundae it still isn't enough to be "more than they do with a banana split"
    4) is valid because it's the opposite of 3), and correctly ignores samples size. Its conditions in the premises prove the same thing - that a higher percentage of people order cherries with sundaes than spilts, and then states that as it's conclusion.

    The hardest part for me in getting good at these was learning, and internalizing, how the LSAT specifically treats "all", "most", and "some." The makers rely on a portion (a some assumption, fyi!) of test takers not knowing the logical difference and will ask questions that target that. Internalizing these differences really improved my ability to get quicker and more accurate.
    Hope any of this helps!

  • matiecena83matiecena83 Member
    62 karma

    @mgscaptura said:
    Hi!
    1) is invalid because it assumes the "some" statement of vanilla is definitely less than half. LSAT "some" can literealy mean 1-100%, so, while it could be true that most people (51-100%) prefer chocolate, it isn't necessarily true.
    2) is valid becuase it links two most premises to a some inference. Mathematically, it means that, at minimum, 51% of people order chocolate and 51% get toppings. That means that, to satisfy both conditions, at lease one person must do both and would mean that that at least that one person gets a free hat.
    3) is invalid because it assumes that both sample sizes are the same, a.k.a it confuses numbers and percentages. Yes its true that higher % of people would receive a cherry from a sundae than a split, but what if there are only 10 people ordering sundaes and 10,000 ordering splits? There could then be 100 splits with cherries, and even if everyone orders a cherry with their sundae it still isn't enough to be "more than they do with a banana split"
    4) is valid because it's the opposite of 3), and correctly ignores samples size. Its conditions in the premises prove the same thing - that a higher percentage of people order cherries with sundaes than spilts, and then states that as it's conclusion.

    The hardest part for me in getting good at these was learning, and internalizing, how the LSAT specifically treats "all", "most", and "some." The makers rely on a portion (a some assumption, fyi!) of test takers not knowing the logical difference and will ask questions that target that. Internalizing these differences really improved my ability to get quicker and more accurate.
    Hope any of this helps!

    Thanks so much for your help!

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