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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] New post 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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Re: The weights of all dishes of type X are exactly the same [#permalink] New post 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.

Answer: B.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

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Re: The weights of all dishes of type X are exactly the same [#permalink] New post 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.

Hence Answer is Option B.
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Re: The weights of all dishes of type X are exactly the same [#permalink] New post 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.

Answer: B.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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