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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.

Practice Questions Question: 33 Page: 277 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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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.

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.

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

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This post received KUDOS

Expert's post

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.

Answer: B.

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Re: The weights of all dishes of type X are exactly the same [#permalink]
22 Apr 2014, 20:57

Hello from the GMAT Club BumpBot!

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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.

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.

Based on your example,

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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