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The weights of all dishes of type X are exactly

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jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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24 Jul 2017
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The weights of all dishes of type X are exactly

Post Wed Aug 02, 2017 11:11 am
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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