Last visit was: 24 Apr 2024, 18:40 It is currently 24 Apr 2024, 18:40

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
User avatar
Current Student
Joined: 23 Oct 2010
Posts: 235
Own Kudos [?]: 1111 [62]
Given Kudos: 73
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618819 [36]
Given Kudos: 81588
Send PM
avatar
Manager
Manager
Joined: 18 Jun 2010
Posts: 72
Own Kudos [?]: 49 [5]
Given Kudos: 2
 Q48  V30 GMAT 2: 730  Q49  V40
Send PM
General Discussion
avatar
Intern
Intern
Joined: 13 Feb 2012
Status:I will be back!
Posts: 44
Own Kudos [?]: 183 [0]
Given Kudos: 38
Location: India
Send PM
Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
LalaB wrote:
Each member of a pack of 55 wolves has either brown or blue eyes and either a white or a grey coat. If there
are more than 3 blue-eyed wolves with white coats, are there more blue-eyed wolves than brown-eyed
wolves?
(1) Among the blue-eyed wolves, the ratio of grey coats to white coats is 4 to 3.
(2) Among the brown-eyed wolves, the ratio of white coats to grey coats is 2 to 1.


Not able to understand the line " If there are more than 3 blue-eyed wolves with white coats"
avatar
Intern
Intern
Joined: 13 Feb 2012
Status:I will be back!
Posts: 44
Own Kudos [?]: 183 [0]
Given Kudos: 38
Location: India
Send PM
Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
Bunuel wrote:
shadabkhaniet wrote:
Not able to understand the line " If there are more than 3 blue-eyed wolves with white coats"


Each member of a pack of 55 wolves has either brown or blue eyes and either a white or a grey coat. If there are more than 3 blue-eyed wolves with white coats, are there more blue-eyed wolves than brown-eyed wolves?

Look at the matrix below:
Attachment:
Wolves.png
"There are more than 3 blue-eyed wolves with white coats" means that # of wolves which have blue eyes AND white coats is more than 3. The question asks whether there are more blue-eyed wolves (blue box) than brown-eyed wolves (brown box).

(1) Among the blue-eyed wolves, the ratio of grey coats to white coats is 4 to 3. Not sufficient on its own.
(2) Among the brown-eyed wolves, the ratio of white coats to grey coats is 2 to 1. Not sufficient on its own.

(1)+(2) When taken together we get the flowing matrix:
Attachment:
Wolves (1)+(2).png
Notice that x and y must be integers (they represent some positive multiples for the ratios given in the statements).

So, we have that 3y+7x=55. After some trial and error we can find that this equation has only 3 positive integers solutions:
y=2 and x=7 --> 3y+7x=6+49=55;
y=9 and x=4 --> 3y+7x=27+28=55;
y=16 and x=1 --> 3y+7x=48+7=55;

Now, the third solution (x=1) is not valid, since in this case # of wolves which have blue eyes AND white coats becomes 3x=3, so not more than 3 as given in the stem. As for the first two cases, in both of them 7x is more than 3y (49>6 and 28>27), so we can answer definite YES, to the question whether there are more blue-eyed wolves (blue box) than brown-eyed wolves (brown box).

Answer: C.

Hope it's clear.


Thanks Bunnel, excellent explanation. +1 :)
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618819 [1]
Given Kudos: 81588
Send PM
Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
1
Kudos
Expert Reply
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Overlapping Sets:
advanced-overlapping-sets-problems-144260.html
how-to-draw-a-venn-diagram-for-problems-98036.html

All DS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=45
All PS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=65
User avatar
Intern
Intern
Joined: 15 Mar 2012
Posts: 35
Own Kudos [?]: 51 [0]
Given Kudos: 20
Send PM
Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
Bunuel wrote:
shadabkhaniet wrote:
Not able to understand the line " If there are more than 3 blue-eyed wolves with white coats"


Each member of a pack of 55 wolves has either brown or blue eyes and either a white or a grey coat. If there are more than 3 blue-eyed wolves with white coats, are there more blue-eyed wolves than brown-eyed wolves?

Look at the matrix below:
Attachment:
Wolves.png
"There are more than 3 blue-eyed wolves with white coats" means that # of wolves which have blue eyes AND white coats is more than 3. The question asks whether there are more blue-eyed wolves (blue box) than brown-eyed wolves (brown box).

(1) Among the blue-eyed wolves, the ratio of grey coats to white coats is 4 to 3. Not sufficient on its own.
(2) Among the brown-eyed wolves, the ratio of white coats to grey coats is 2 to 1. Not sufficient on its own.

(1)+(2) When taken together we get the flowing matrix:
Attachment:
Wolves (1)+(2).png
Notice that x and y must be integers (they represent some positive multiples for the ratios given in the statements).

So, we have that 3y+7x=55. After some trial and error we can find that this equation has only 3 positive integers solutions:
y=2 and x=7 --> 3y+7x=6+49=55;
y=9 and x=4 --> 3y+7x=27+28=55;
y=16 and x=1 --> 3y+7x=48+7=55;

Now, the third solution (x=1) is not valid, since in this case # of wolves which have blue eyes AND white coats becomes 3x=3, so not more than 3 as given in the stem. As for the first two cases, in both of them 7x is more than 3y (49>6 and 28>27), so we can answer definite YES, to the question whether there are more blue-eyed wolves (blue box) than brown-eyed wolves (brown box).

Answer: C.

Hope it's clear.


There could be another solution to the equation:
y=11 and x=3 --> 3y+7x=33+21=55; and in this case, 7x < 3y => A & B together are insufficient => E is the answer
Am I missing something here?
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618819 [0]
Given Kudos: 81588
Send PM
Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
Expert Reply
divineacclivity wrote:
Bunuel wrote:

Each member of a pack of 55 wolves has either brown or blue eyes and either a white or a grey coat. If there are more than 3 blue-eyed wolves with white coats, are there more blue-eyed wolves than brown-eyed wolves?

Look at the matrix below:
Attachment:
Wolves.png
"There are more than 3 blue-eyed wolves with white coats" means that # of wolves which have blue eyes AND white coats is more than 3. The question asks whether there are more blue-eyed wolves (blue box) than brown-eyed wolves (brown box).

(1) Among the blue-eyed wolves, the ratio of grey coats to white coats is 4 to 3. Not sufficient on its own.
(2) Among the brown-eyed wolves, the ratio of white coats to grey coats is 2 to 1. Not sufficient on its own.

(1)+(2) When taken together we get the flowing matrix:
Attachment:
Wolves (1)+(2).png
Notice that x and y must be integers (they represent some positive multiples for the ratios given in the statements).

So, we have that 3y+7x=55. After some trial and error we can find that this equation has only 3 positive integers solutions:
y=2 and x=7 --> 3y+7x=6+49=55;
y=9 and x=4 --> 3y+7x=27+28=55;
y=16 and x=1 --> 3y+7x=48+7=55;

Now, the third solution (x=1) is not valid, since in this case # of wolves which have blue eyes AND white coats becomes 3x=3, so not more than 3 as given in the stem. As for the first two cases, in both of them 7x is more than 3y (49>6 and 28>27), so we can answer definite YES, to the question whether there are more blue-eyed wolves (blue box) than brown-eyed wolves (brown box).

Answer: C.

Hope it's clear.


There could be another solution to the equation:
y=11 and x=3 --> 3y+7x=33+21=55; and in this case, 7x < 3y => A & B together are insufficient => E is the answer
Am I missing something here?


Arithmetic: 33+21=54 not 55.
avatar
Intern
Intern
Joined: 14 Apr 2015
Posts: 13
Own Kudos [?]: [0]
Given Kudos: 0
Send PM
Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
Bunuel wrote:
shadabkhaniet wrote:
Not able to understand the line " If there are more than 3 blue-eyed wolves with white coats"


Each member of a pack of 55 wolves has either brown or blue eyes and either a white or a grey coat. If there are more than 3 blue-eyed wolves with white coats, are there more blue-eyed wolves than brown-eyed wolves?

Look at the matrix below:
Attachment:
Wolves.png
"There are more than 3 blue-eyed wolves with white coats" means that # of wolves which have blue eyes AND white coats is more than 3. The question asks whether there are more blue-eyed wolves (blue box) than brown-eyed wolves (brown box).

(1) Among the blue-eyed wolves, the ratio of grey coats to white coats is 4 to 3. Not sufficient on its own.
(2) Among the brown-eyed wolves, the ratio of white coats to grey coats is 2 to 1. Not sufficient on its own.

(1)+(2) When taken together we get the flowing matrix:
Attachment:
Wolves (1)+(2).png
Notice that x and y must be integers (they represent some positive multiples for the ratios given in the statements).

So, we have that 3y+7x=55. After some trial and error we can find that this equation has only 3 positive integers solutions:
y=2 and x=7 --> 3y+7x=6+49=55;
y=9 and x=4 --> 3y+7x=27+28=55;
y=16 and x=1 --> 3y+7x=48+7=55;

Now, the third solution (x=1) is not valid, since in this case # of wolves which have blue eyes AND white coats becomes 3x=3, so not more than 3 as given in the stem. As for the first two cases, in both of them 7x is more than 3y (49>6 and 28>27), so we can answer definite YES, to the question whether there are more blue-eyed wolves (blue box) than brown-eyed wolves (brown box).

Answer: C.

Hope it's clear.


Hello Bunel ,
why should i see x only as integer , why can't it be fraction with denominator as 7 eg:18/7 ?
SVP
SVP
Joined: 20 Mar 2014
Posts: 2362
Own Kudos [?]: 3626 [1]
Given Kudos: 816
Concentration: Finance, Strategy
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Send PM
Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
1
Kudos
divya517 wrote:
Bunuel wrote:
shadabkhaniet wrote:
Not able to understand the line " If there are more than 3 blue-eyed wolves with white coats"


Each member of a pack of 55 wolves has either brown or blue eyes and either a white or a grey coat. If there are more than 3 blue-eyed wolves with white coats, are there more blue-eyed wolves than brown-eyed wolves?

Look at the matrix below:
Attachment:
Wolves.png
"There are more than 3 blue-eyed wolves with white coats" means that # of wolves which have blue eyes AND white coats is more than 3. The question asks whether there are more blue-eyed wolves (blue box) than brown-eyed wolves (brown box).

(1) Among the blue-eyed wolves, the ratio of grey coats to white coats is 4 to 3. Not sufficient on its own.
(2) Among the brown-eyed wolves, the ratio of white coats to grey coats is 2 to 1. Not sufficient on its own.

(1)+(2) When taken together we get the flowing matrix:
Attachment:
Wolves (1)+(2).png
Notice that x and y must be integers (they represent some positive multiples for the ratios given in the statements).

So, we have that 3y+7x=55. After some trial and error we can find that this equation has only 3 positive integers solutions:
y=2 and x=7 --> 3y+7x=6+49=55;
y=9 and x=4 --> 3y+7x=27+28=55;
y=16 and x=1 --> 3y+7x=48+7=55;

Now, the third solution (x=1) is not valid, since in this case # of wolves which have blue eyes AND white coats becomes 3x=3, so not more than 3 as given in the stem. As for the first two cases, in both of them 7x is more than 3y (49>6 and 28>27), so we can answer definite YES, to the question whether there are more blue-eyed wolves (blue box) than brown-eyed wolves (brown box).

Answer: C.

Hope it's clear.


Hello Bunel ,
why should i see x only as integer , why can't it be fraction with denominator as 7 eg:18/7 ?


Because if x = fraction , lets say =18/7, then 3x = NUMBER OF WOLVES with white coats = 54/7 = fraction . How can number of wolves be fraction? It does not make any sense to say we have 3/4 wolves or 22/7 wolves etc. Thus, x can only take integer values.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10161
Own Kudos [?]: 16594 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Each member of a pack of 55 wolves has either brown or blue [#permalink]
1
Kudos
Expert Reply
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.
Remember equal number of variables and independent equations ensures a solution.

Each member of a pack of 55 wolves has either brown or blue eyes and either a white or a grey coat. If there are more than 3 blue-eyed wolves with white coats, are there more blue-eyed wolves than brown-eyed wolves?

(1) Among the blue-eyed wolves, the ratio of grey coats to white coats is 4 to 3.
(2) Among the brown-eyed wolves, the ratio of white coats to grey coats is 2 to 1.

Transforming the original condition and the question, we have the below 2by2 question which is a typical question in GMAT test.

There are 4 variables (a,b,c,d), 2 equations (a+b+c+d=55, b>3) and we need 2 more equations to match the number of variables and equations. Since there is 1 each in 1) and 2), there is high probability that C is the answer, and it actually turns out that C is the answer.
Attachments

GC DS LalaB Each member of a pack of (20150913).png
GC DS LalaB Each member of a pack of (20150913).png [ 3.07 KiB | Viewed 15296 times ]

Manager
Manager
Joined: 09 Oct 2015
Posts: 174
Own Kudos [?]: 61 [0]
Given Kudos: 28
Send PM
Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
Bunuel wrote:
AmoyV wrote:
Each member of a pack of 55 wolves has either brown or blue eyes and either a white or a grey coat. If there
are more than 3 blue-eyed wolves with white coats, are there more blue-eyed wolves than brown-eyed
wolves?
(1) Among the blue-eyed wolves, the ratio of grey coats to white coats is 4 to 3.
(2) Among the brown-eyed wolves, the ratio of white coats to grey coats is 2 to 1.


Merging topics.

Please refer to the discussion above.


If we do it by taking fractions, i.e. 3/7 X , 4/7 X , 2/3Y AND 1/3 Y, we do not get the same answer. Could you please advice?

3x/7>3 --> 3x>21--x>7
Director
Director
Joined: 12 Nov 2016
Posts: 569
Own Kudos [?]: 118 [0]
Given Kudos: 167
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Send PM
Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
Bunuel wrote:
shadabkhaniet wrote:
Not able to understand the line " If there are more than 3 blue-eyed wolves with white coats"


Each member of a pack of 55 wolves has either brown or blue eyes and either a white or a grey coat. If there are more than 3 blue-eyed wolves with white coats, are there more blue-eyed wolves than brown-eyed wolves?

Look at the matrix below:



"There are more than 3 blue-eyed wolves with white coats" means that # of wolves which have blue eyes AND white coats is more than 3. The question asks whether there are more blue-eyed wolves (blue box) than brown-eyed wolves (brown box).

(1) Among the blue-eyed wolves, the ratio of grey coats to white coats is 4 to 3. Not sufficient on its own.
(2) Among the brown-eyed wolves, the ratio of white coats to grey coats is 2 to 1. Not sufficient on its own.

(1)+(2) When taken together we get the flowing matrix:



Notice that x and y must be integers (they represent some positive multiples for the ratios given in the statements).

So, we have that 3y+7x=55. After some trial and error we can find that this equation has only 3 positive integers solutions:
y=2 and x=7 --> 3y+7x=6+49=55;
y=9 and x=4 --> 3y+7x=27+28=55;
y=16 and x=1 --> 3y+7x=48+7=55;

Now, the third solution (x=1) is not valid, since in this case # of wolves which have blue eyes AND white coats becomes 3x=3, so not more than 3 as given in the stem. As for the first two cases, in both of them 7x is more than 3y (49>6 and 28>27), so we can answer definite YES, to the question whether there are more blue-eyed wolves (blue box) than brown-eyed wolves (brown box).

Answer: C.

Hope it's clear.

Attachment:
Wolves (1)+(2).png

Attachment:
Wolves.png


Yes- if we combine both statements then we can inevitably solve for X- there is only one such value that can satisfy the ratios in this matrix- I plugged in numbers and serendipitously arrived at the answer- we know that, for example, the value of x must be somewhere between 4-20 and can thus plug in values.
Intern
Intern
Joined: 25 Jul 2018
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 16
Send PM
Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
I feel like everyone here got it wrong.

C is not the solution.

They clearly state that the number of blue eyed wolfs with white coat is MORE than 3.
This means it can only be 4 and up.
If we use the proportions we will find out that the minimum number of Blue eyed wolfs possible is
4x3+4x4=28
55 - 28 = 27
The number of blue eyed wolfs will be higher than brown eyed no matter what. Hence A is sufficient.

Somehow people lost track of the question.

Or may be its just me who is crazy :roll:
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618819 [0]
Given Kudos: 81588
Send PM
Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
Expert Reply
nobilisrex wrote:
I feel like everyone here got it wrong.

C is not the solution.

They clearly state that the number of blue eyed wolfs with white coat is MORE than 3.
This means it can only be 4 and up.
If we use the proportions we will find out that the minimum number of Blue eyed wolfs possible is
4x3+4x4=28
55 - 28 = 27
The number of blue eyed wolfs will be higher than brown eyed no matter what. Hence A is sufficient.

Somehow people lost track of the question.

Or may be its just me who is crazy :roll:


For (1) we get that z + 7x = 55, where z is the number of brown-eyed wolves and 7x is the number of blue-eyed wolves. The question asks whether 7x > z. From z + 7x = 55, we can have that say 7x = 14 and z = 41 (answer NO) or 7x = 28 and z = 27 (answer YES).

C is correct.

P.S. You can check correct answer under the spoiler in the original post.
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5957
Own Kudos [?]: 13387 [2]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
2
Kudos
Expert Reply
LalaB wrote:
Each member of a pack of 55 wolves has either brown or blue eyes and either a white or a grey coat. If there are more than 3 blue-eyed wolves with white coats, are there more blue-eyed wolves than brown-eyed wolves?

(1) Among the blue-eyed wolves, the ratio of grey coats to white coats is 4 to 3.
(2) Among the brown-eyed wolves, the ratio of white coats to grey coats is 2 to 1.


Please find below the video solution of this question. The solution comprises of two important take aways...
1) Never miss an information given in question
2) How to find solutions of linear equations

Manager
Manager
Joined: 09 Jun 2014
Posts: 229
Own Kudos [?]: 280 [0]
Given Kudos: 205
Location: India
Concentration: General Management, Operations
Send PM
Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
rahulkashyap wrote:
Bunuel wrote:
AmoyV wrote:
Each member of a pack of 55 wolves has either brown or blue eyes and either a white or a grey coat. If there
are more than 3 blue-eyed wolves with white coats, are there more blue-eyed wolves than brown-eyed
wolves?
(1) Among the blue-eyed wolves, the ratio of grey coats to white coats is 4 to 3.
(2) Among the brown-eyed wolves, the ratio of white coats to grey coats is 2 to 1.


Merging topics.

Please refer to the discussion above.


If we do it by taking fractions, i.e. 3/7 X , 4/7 X , 2/3Y AND 1/3 Y, we do not get the same answer. Could you please advice?

3x/7>3 --> 3x>21--x>7



I tried a similar approach .But I guess the catch here is that the ratios 3/7x ..2/3y will be integers so we need assume x as multiple of 7 and y as multiple of 3
So even if u take fractions here ..

You can imagine end equations as 7x+3y = 55 and look for values of x and y ..(keeping in mind that x>7 from your earlier deduction )

Chetan2u,GMATPrepNow

Please advise if my line of thought is correct!!
Manager
Manager
Joined: 23 May 2020
Posts: 171
Own Kudos [?]: 235 [0]
Given Kudos: 143
Concentration: Statistics, Finance
GPA: 3.41
WE:Advertising (Advertising and PR)
Send PM
Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
(1) Not sufficient
(2) Not sufficient
(1) & (2) ⇒ 7a + 3b = 55 ⇒ b = (55 - 7a) / 3 = (54 - 6a + 1 - a)/3 = 18 - 2a + (1 - a)/3
b must be an integer: (1 - a) must divisible by 3:
a = 4 → (1 - a)/3 = - 1, → 18 - 2x4 - 1 = 9 → Yes→ 7a = 28 > 3b = 27
a = 7 → (1 - a)/3 = - 2, → 18 - 2x7 - 2 = 2 → Yes → 7a = 49 > 3b = 6
a = 10 → (1 - a)/3 = -3 → 18 - 2x10 - 3 < 0 → No → Stop trying a >10

In 2 results, we have 7a > 3b ⇒ Sufficient.
=> C
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 32655
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
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.
GMAT Club Bot
Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
Moderator:
Math Expert
92900 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne