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The weights of all dishes of type X are exactly

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The weights of all dishes of type X are exactly

by jjjinapinch » Wed Aug 02, 2017 11:11 am

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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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Source: — Data Sufficiency |

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by ceilidh.erickson » Wed Aug 02, 2017 11:44 am

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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.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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by [email protected] » Tue Mar 27, 2018 3:04 pm

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Hi All,

We're told that 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. We're asked if the weight of 1 dish of type X is LESS than the weight of 1 dish of type Y. This is a YES/NO question. It can be solved with a bit of Arithmetic and TESTing VALUES.

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.

The information in Fact 1 can be 'translated' into....
(3X + 2Y) < (2X + 4Y)
X < 2Y

This tell us that X is less than 2Y, but we don't know for sure whether X is less than Y or not...
IF....
X = 1 and Y = 2, then the answer to the question is YES
X = 1 and Y = 1, then the answer to the question is NO
Fact 1 is INSUFFICIENT

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.

The information in Fact 2 can be 'translated' into....
(4X + 3Y) < (3X + 4Y)
X < Y

This tells us that X is less than Y - which is exactly what the question is asking us. Thus, the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer: B

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Rich
Contact Rich at [email protected]
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by Scott@TargetTestPrep » Thu Mar 29, 2018 4:47 pm

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jjjinapinch wrote: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.
We are given that we have two types of dishes, dish X and dish Y, and each dish of each type has the same weight. We are asked whether the weight of 1 dish of type X is less than the weight of 1 dish of type Y. If we let X and Y denote the weights of dishes X and Y, respectively, then we can restate the question as:

Is X < Y ?

Statement One Alone:

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.

Using the information from statement one we can set up the following inequality:

3X + 2Y < 2X + 4Y

X < 2Y

We see that the weight of 1 dish of type X is less than the combined weight of 2 dishes of type Y. However we can't tell whether the weight of 1 dish of type X is less than the weight of 1 dish of type Y. This is not enough information to answer the question.

Statement Two Alone:

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.

Using the information from statement two we can set up the following inequality:

4X + 3Y < 3X + 4Y

X < Y

We see that this answers the question.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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