GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Nov 2018, 14:25

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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• Free GMAT Strategy Webinar

November 17, 2018

November 17, 2018

07:00 AM PST

09:00 AM PST

Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
• GMATbuster's Weekly GMAT Quant Quiz # 9

November 17, 2018

November 17, 2018

09:00 AM PST

11:00 AM PST

Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

At a local beach, the ratio of little dogs to average dogs

Author Message
TAGS:

Hide Tags

Manager
Joined: 09 Feb 2013
Posts: 118
At a local beach, the ratio of little dogs to average dogs  [#permalink]

Show Tags

13 Jun 2013, 22:35
6
18
00:00

Difficulty:

95% (hard)

Question Stats:

40% (03:21) correct 60% (03:16) wrong based on 415 sessions

HideShow timer Statistics

At a local beach, the ratio of little dogs to average dogs to enormous dogs is 2:5:8. Late in the afternoon, the ratio of little dogs to average dogs doubles and the ratio of little dogs to enormous dogs increases. If the new percentage of little dogs and the new percentage of average dogs are both integers and there are fewer than 30 total dogs at the beach, which of the following represents a possible new percentage of enormous dogs?

A. 25%
B. 40%
C. 50%
D. 55%
E. 70%

_________________

Kudos will encourage many others, like me.
Good Questions also deserve few KUDOS.

Intern
Joined: 28 Jul 2013
Posts: 7
GMAT 1: 770 Q51 V42
Re: At a local beach, the ratio of little dogs to average dogs  [#permalink]

Show Tags

03 Oct 2013, 05:23
18
6
emmak wrote:
At a local beach, the ratio of little dogs to average dogs to enormous dogs is 2:5:8. Late in the afternoon, the ratio of little dogs to average dogs doubles and the ratio of little dogs to enormous dogs increases. If the new percentage of little dogs and the new percentage of average dogs are both integers and there are fewer than 30 total dogs at the beach, which of the following represents a possible new percentage of enormous dogs?

A. 25%
B. 40%
C. 50%
D. 55%
E. 70%

This problem can be solved with a shortcut which the GMAT typically expects. If you consider the percentage of enormous dogs as x, then the percentage of the rest of the dogs becomes 100-x. Now this percentage is split between the 2 types of dogs in the ratio of 4:5. We also know that the percentages have to be integers. Meaning 100-x will have to be divisible by 9

A quick look at the solutions tells us that 100-x is divisible by 9 only in the case if D.
General Discussion
Intern
Joined: 26 May 2010
Posts: 10
Re: At a local beach, the ratio of little dogs to average dogs  [#permalink]

Show Tags

Updated on: 13 Jun 2013, 23:21
11
2
emmak wrote:
At a local beach, the ratio of little dogs to average dogs to enormous dogs is 2:5:8. Late in the afternoon, the ratio of little dogs to average dogs doubles and the ratio of little dogs to enormous dogs increases. If the new percentage of little dogs and the new percentage of average dogs are both integers and there are fewer than 30 total dogs at the beach, which of the following represents a possible new percentage of enormous dogs?
A)25%
B)40%
C)50%
D)55%
E)70%

Little Dogs(L), Average Dogs(A) and Enormous Dogs (E)
The initial ratio for L:A:E :: 2:5:8
Initial Total dogs = 15X ( x assumed; 2+5+8= 15), Since the total dogs are less than 30 therefore initial total value has to be 15

L = 2, A = 5 E = 8

L:A= 2:5

This ratio doubles

Hence New Dog count is

L= 4 , A = 5 E= X: Also 4+5+x<30

We need to Find X*100/(4+5+X)

Now it says that new percentage of little dogs and Average dogs is an integer

%L = 4*100/(9+x) %A = 5*100/(9+x); Only Value for X is 11 ; 9+x<30 and % integer

Therefore, Enormus Dogs % is = 11*100/(20) = 55%

D is the Ans

Kudos is the Karma

Originally posted by bhuwangupta on 13 Jun 2013, 23:17.
Last edited by bhuwangupta on 13 Jun 2013, 23:21, edited 1 time in total.
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 611
Re: At a local beach, the ratio of little dogs to average dogs  [#permalink]

Show Tags

13 Jun 2013, 23:18
3
emmak wrote:
At a local beach, the ratio of little dogs to average dogs to enormous dogs is 2:5:8. Late in the afternoon, the ratio of little dogs to average dogs doubles and the ratio of little dogs to enormous dogs increases. If the new percentage of little dogs and the new percentage of average dogs are both integers and there are fewer than 30 total dogs at the beach, which of the following represents a possible new percentage of enormous dogs?
A)25%
B)40%
C)50%
D)55%
E)70%

Given ratio of Little Dogs:Average Dogs = 2:5. When this ratio doubles, it becomes 4:5. Ratio between Little dogs: Enormous dogs = 2:8.

Also, this increases from 2:8-->1:4 to 4:(8+x) , where x is an non-negative integer(Maximum value which x can assume is 7, under the given conditions)

New % of little dogs =$$\frac{4}{(4+5+8+x)}*100$$= $$\frac{4}{(17+x)}*100$$ The minimum value of x, for which this is an integer ; x = 3.

Similarly, % of average dogs =$$\frac{5}{(17+x)}*100$$. Again, x = 3 for an integral value.

Thus, the new percentage of enormous dogs =$$\frac{(8+3)}{20}*100$$= 55 %

D.
_________________
Manager
Joined: 29 Aug 2013
Posts: 74
Location: United States
GMAT 1: 590 Q41 V29
GMAT 2: 540 Q44 V20
GPA: 3.5
WE: Programming (Computer Software)
Re: At a local beach, the ratio of little dogs to average dogs  [#permalink]

Show Tags

08 Oct 2013, 08:10
7
1
emmak wrote:
At a local beach, the ratio of little dogs to average dogs to enormous dogs is 2:5:8. Late in the afternoon, the ratio of little dogs to average dogs doubles and the ratio of little dogs to enormous dogs increases. If the new percentage of little dogs and the new percentage of average dogs are both integers and there are fewer than 30 total dogs at the beach, which of the following represents a possible new percentage of enormous dogs?

A. 25%
B. 40%
C. 50%
D. 55%
E. 70%

I like to go straight forward and with the question stem. This is how I solved analyzing the question sentence by sentence.

1) Initially the ratio of Local : Average : Enormous is 2:5:8.
2) After afternoon ratios become :- 4:5:x (since we do not know in what ratio are enormous dogs in)
3) Initially Local : Enormous ratio is 1:4. Now, Ques stem says that this ratio increases. Therefore new ratio i.e. 4:x > 1:4 ; this gives us x < 16.

4) Now, percentage of Local dogs in afternoon is $$\frac{(4*100)}{(9+x)}$$ and average dogs is $$\frac{(5*100)}{(9+x)}$$

5) These ratios will be integers only when the denominators of these terms are common factors of 400 and 500 and the multiplication of those factors such as 2,5,10,20,50 etc. Since x is less than 16, x can only be 1 and 11 so that the denominators are 10 and 20 respectively.

6) Therefore the possible percentages of Enormous dogs can be 10% (i.e. (1/(9+1))*100 considering x = 1) and 55% (i.e. (11/(9+11))*100 considering x = 11)

Only 55% is in the options hence D

Consider Kudos if the post helped!!
Senior Manager
Joined: 07 Apr 2012
Posts: 370
Re: At a local beach, the ratio of little dogs to average dogs  [#permalink]

Show Tags

31 Aug 2014, 10:08
2
bhuwangupta wrote:
Now it says that new percentage of little dogs and Average dogs is an integer

%L = 4*100/(9+x) %A = 5*100/(9+x); Only Value for X is 11 ; 9+x<30 and % integer

Kudos is the Karma

Why is this true?
Why can't x=1?
Am I missing something here?
Non-Human User
Joined: 09 Sep 2013
Posts: 8791
Re: At a local beach, the ratio of little dogs to average dogs  [#permalink]

Show Tags

12 Apr 2018, 12:16
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: At a local beach, the ratio of little dogs to average dogs &nbs [#permalink] 12 Apr 2018, 12:16
Display posts from previous: Sort by