Dogs

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manik11: Master | Next Rank: 500 Posts; Posts: 113; Joined: Wed Dec 07, 2011 7:20 am; Thanked: 3 times

by manik11 » Fri Jan 22, 2016 3:55 am

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%

OA : D
Source : Veritas Prep

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Source: Beat The GMAT — Problem Solving | Fri Jan 22, 2016 3:55 am

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Fri Jan 22, 2016 4:54 am

manik11 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%

OA : D
Source : Veritas Prep

L:A:E = 2:5:8

New, L:A = 2*(2:5)= 4:5
New, L:E > 2:8 i.e. L:E > 1:4 (i.e. Numerator should increase or denominator should decrease

Min value of New no. of Little dogs = 4x (where x must be Integer)
Min value of New no. of Average dogs = 5x (where x must be Integer)
Min value of New no. of Enormous dogs < 4*4x i.e. <16x (where x must be Integer)

Min total No. of Dogs = 4x+5x+(<16x) i.e. <25x which must be less than 30 and must be Integer as well for x to be Integer

i.e. Total Dogs may be 24, 23, 22, 21, 20 etc. (Given: It should be fewer than 30)

i.e. x must be 1

% of Little dogs = (4/total dogs)*100 = 400/total
% of Average dogs = (5/total dogs)*100 = 500/total

i.e. Total dogs should be factor of 400 and 500 both.

As per given information 20 fits best

Total Dogs = 20
Little = 4
Average = 5
Enourmous = 11

% of enormous = (11/20)*100 = 55%

Answer: option D

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manik11: Master | Next Rank: 500 Posts; Posts: 113; Joined: Wed Dec 07, 2011 7:20 am; Thanked: 3 times

by manik11 » Fri Jan 22, 2016 5:03 am

Hi GMATinsight,
Could you please explain this step in your solution?

GMATinsight wrote: Min value of New no. of Enormous dogs < 4*4x i.e. <16x (where x must be Integer)

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Fri Jan 22, 2016 5:11 am

manik11 wrote:Hi GMATinsight,
Could you please explain this step in your solution?

GMATinsight wrote: Min value of New no. of Enormous dogs < 4*4x i.e. <16x (where x must be Integer)

CURRENT RATIO OF L:E = 2:8 = 1:4

As questions says, the ratio must increase

The ratio increases if either numerator increases or Denominator decreases.

Numerator is 4x (Fixed) i.e.Denominator must be LESS THAT 4*4x i.e. LESS THAN 16x for Ratio of L:E to increase

therefore, Max value of New no. of Enormous dogs < 4*4x i.e. <16x (where x must be Integer)

(Please read Min as Max there)

I hope this helos

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Fri Jan 22, 2016 4:32 pm

If we start with

L/A = 2/5

L/E = 1/4

After the changes, we have

L/A = 4/5

L/E > 1/4

From L/A = 4/5, we know that (L + A) is a multiple of 9. Since L + A + E < 30, we must have L + A = 9, 18, or 27, which would give L = 4, 8, or 12.

Let's consider each case.

If (L + A) = 9, then L = 4, A = 5, and E < 16. (If E â‰¥Â 16, then L/E â‰¤Â 1/4.) Since L / (L + A + E) and A / (L + A + E) are both integers, we must have (L + A + E) be divisible by 4 and (L + A + E) be divisible by 5. One choice is (L + A + E) = 20.

If (L + A + E) = 20, we have E = 11. That gives us E / (L + A + E) = 11 / (4 + 5 + 11) = 55%; success!

Since our first case worked, we don't have to check anything else.

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