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# The weights of all dishes of type X are exactly the same

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The weights of all dishes of type X are exactly the same [#permalink]  03 Sep 2012, 05:08
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The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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.

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Question: 33
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Difficulty: 600

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Re: The weights of all dishes of type X are exactly the same [#permalink]  03 Sep 2012, 05:08
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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 ?

Say the weight of 1 dish of type X is $$x$$ and the weight of 1 dish of type Y is $$y$$. The question asks whether $$x<y$$.

(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 --> $$3x+2y<2x+4y$$ --> $$x<2y$$. If $$x=1$$ and $$y=2$$, then the answer is YES but if $$x=3$$ and $$y=2$$, then the answer is NO. Not sufficient.

(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 --> $$4x+3y<3x+4y$$ --> $$x<y$$. Sufficient.

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Re: The weights of all dishes of type X are exactly the same [#permalink]  03 Sep 2012, 05:33
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Bunuel 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.

Let X & Y are respective weights of Dish 1 & Dish 2. So Question reduces to is X<Y?

St 1: Insufficient: 3X + 2Y < 2X + 4Y,
=> X<2Y, Insufficient, X=4 & Y=5 or X=5 & Y=4 both conditions satisfy the equation.

St 2: Sufficient: 4X + 3Y < 3X + 4Y
=> X < Y, clearly sufficient.

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Re: The weights of all dishes of type X are exactly the same [#permalink]  07 Sep 2012, 04:48
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SOLUTION

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 ?

Say the weight of 1 dish of type X is $$x$$ and the weight of 1 dish of type Y is $$y$$. The question asks whether $$x<y$$.

(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 --> $$3x+2y<2x+4y$$ --> $$x<2y$$. If $$x=1$$ and $$y=2$$, then the answer is YES but if $$x=3$$ and $$y=2$$, then the answer is NO. Not sufficient.

(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 --> $$4x+3y<3x+4y$$ --> $$x<y$$. Sufficient.

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Re: The weights of all dishes of type X are exactly the same [#permalink]  22 Apr 2014, 20:57
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Re: The weights of all dishes of type X are exactly the same [#permalink]  10 May 2014, 09:40
St I )

3x + 2y < 2x + 4y
Implies x<2y . INSUFF

St II) 4x + 3y < 3x +4y, implies
x < y. SUFF. Hence B
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Re: The weights of all dishes of type X are exactly the same [#permalink]  23 May 2014, 14:29
Statement1: For those who hate picking numbers just like me: 3X + 2Y < 2X + 4Y --> x<2y --> x/2<y --> Thus y could be less than x, equal to x or greater than x. Not sufficient
St2: is quite straight forward. Sufficient

B it is!
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Re: The weights of all dishes of type X are exactly the same [#permalink]  10 Mar 2015, 17:00
I don't get it. x<2y, if x =2, and y=3 then 2<2(3) = 2 <6 thus y is greater than x
on the other hand, if x=3 and y = 2 then 3<2(2) = 3<4 thus y is still greater than x. M I missing the point ? I don't understand why you thing if x=3, and y=2 will make the first statement insufficient.
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Re: The weights of all dishes of type X are exactly the same [#permalink]  10 Mar 2015, 18:30
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mawus wrote:
I don't get it. x<2y, if x =2, and y=3 then 2<2(3) = 2 <6 thus y is greater than x
on the other hand, if x=3 and y = 2 then 3<2(2) = 3<4 thus y is still greater than x. M I missing the point ? I don't understand why you thing if x=3, and y=2 will make the first statement insufficient.

Statement 1:
X < 2Y

if x=2, and y=3
3 < 2*3 true
2<3 true

if x=3 and y=2
3 < 2*2 true
but 3 is not < 2

we have 2 conflicting pieces of information, so Statement 1 is insufficient
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Re: The weights of all dishes of type X are exactly the same [#permalink]  10 Mar 2015, 18:52
Thank you it make sense
Re: The weights of all dishes of type X are exactly the same   [#permalink] 10 Mar 2015, 18:52
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