It is currently 26 Jun 2017, 14:28

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 39702
The weights of all dishes of type X are exactly the same [#permalink]

### Show Tags

03 Sep 2012, 06:08
Expert's post
14
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

73% (02:18) correct 27% (01:19) wrong based on 901 sessions

### HideShow timer Statistics

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.

Practice Questions
Question: 33
Page: 277
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 39702
Re: The weights of all dishes of type X are exactly the same [#permalink]

### Show Tags

03 Sep 2012, 06:08
2
KUDOS
Expert's post
3
This post was
BOOKMARKED
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.

_________________
Senior Manager
Joined: 15 Jun 2010
Posts: 361
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Re: The weights of all dishes of type X are exactly the same [#permalink]

### Show Tags

03 Sep 2012, 06:33
3
KUDOS
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.

_________________

Regards
SD
-----------------------------
Press Kudos if you like my post.
Debrief 610-540-580-710(Long Journey): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

Math Expert
Joined: 02 Sep 2009
Posts: 39702
Re: The weights of all dishes of type X are exactly the same [#permalink]

### Show Tags

07 Sep 2012, 05:48
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
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.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15985
Re: The weights of all dishes of type X are exactly the same [#permalink]

### Show Tags

22 Apr 2014, 21:57
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Intern
Joined: 08 Jan 2014
Posts: 20
Location: United States
Concentration: General Management, Entrepreneurship
GMAT Date: 06-30-2014
GPA: 3.99
WE: Analyst (Consulting)
Re: The weights of all dishes of type X are exactly the same [#permalink]

### Show Tags

10 May 2014, 10:40
1
KUDOS
St I )

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

St II) 4x + 3y < 3x +4y, implies
x < y. SUFF. Hence B
Senior Manager
Joined: 29 Oct 2013
Posts: 296
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Re: The weights of all dishes of type X are exactly the same [#permalink]

### Show Tags

23 May 2014, 15:29
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!
_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Intern
Joined: 21 Feb 2015
Posts: 27
Re: The weights of all dishes of type X are exactly the same [#permalink]

### Show Tags

10 Mar 2015, 18:00
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.
Senior Manager
Joined: 28 Feb 2014
Posts: 295
Location: United States
Concentration: Strategy, General Management
Re: The weights of all dishes of type X are exactly the same [#permalink]

### Show Tags

10 Mar 2015, 19:30
1
KUDOS
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
Intern
Joined: 21 Feb 2015
Posts: 27
Re: The weights of all dishes of type X are exactly the same [#permalink]

### Show Tags

10 Mar 2015, 19:52
Thank you it make sense
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15985
Re: The weights of all dishes of type X are exactly the same [#permalink]

### Show Tags

09 May 2016, 14:51
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1158
Location: United States (CA)
Re: The weights of all dishes of type X are exactly the same [#permalink]

### Show Tags

10 May 2016, 07:48
Bunuel wrote:
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.

Solution:

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. We can eliminate answer choices A and D.

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.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15985
Re: The weights of all dishes of type X are exactly the same [#permalink]

### Show Tags

22 Jun 2017, 03:50
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: The weights of all dishes of type X are exactly the same   [#permalink] 22 Jun 2017, 03:50
Similar topics Replies Last post
Similar
Topics:
1 Ed has some fish, and the combined weight of all the fish is 100 pound 1 21 May 2017, 07:26
12 Brand W nut mix contains 24% cashews by weight, and Brand X 6 11 Oct 2016, 22:57
3 A, B and C are assigned the task of making the same type of clay toys. 1 28 Aug 2015, 09:58
2 The total weight of all residents of Ranchville 2 29 Mar 2017, 06:12
24 There are exactly 6 teams in league x. What was the total 10 28 Mar 2017, 08:15
Display posts from previous: Sort by