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The weights of all dishes of type X are exactly

This topic has 1 expert reply and 0 member replies
jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
Joined
24 Jul 2017
Posted:
83 messages

The weights of all dishes of type X are exactly

Post Wed Aug 02, 2017 11:11 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    The weights of all dishes of type X are exactly the same, and the weights of all dishes of type Y are exactly the same. Is the weight of 1 dish of type X less than the weight of 1 dish of type Y ?
    (1) The total weight of 3 dishes of type X and 2 dishes of type Y is less than the total weight of 2 dishes of type X and 4 dishes of type Y.
    (2) The total weight of 4 dishes of type X and 3 dishes of type Y is less than the total weight of 3 dishes of type X and 4 dishes of type Y.

    Official Guide question
    Answer: B

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    Post Wed Aug 02, 2017 11:44 am
    Let x = the weight of one type X dish, and y = the weight of one type Y dish.

    Target question: x < y ?

    (1) The total weight of 3 dishes of type X and 2 dishes of type Y is less than the total weight of 2 dishes of type X and 4 dishes of type Y.
    Translate:
    3x + 2y < 2x + 4y
    x < 2y
    This does not answer our target question: is x < y ? Insufficient.

    For proof, you could test numbers:
    x = 3
    y = 2
    x < 2y --> 3 < 4 --> keeps statement true
    x < y ? --> 3 < 2 --> No.

    x = 3
    y = 4
    x < 2y --> 3 < 8 --> keeps statement true
    x < y ? --> 3 < 4 --> Yes.

    2) The total weight of 4 dishes of type X and 3 dishes of type Y is less than the total weight of 3 dishes of type X and 4 dishes of type Y.
    Translate:
    4x + 3y < 3x + 4y
    x < y
    This exactly matches our target question. Sufficient.

    The answer is B.

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