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
The weights of all dishes of type X are exactly
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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.
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
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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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: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.
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
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