DS ratio

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pm; Thanked: 165 times; Followed by:70 members

DS ratio

by karthikpandian19 » Sun Jun 10, 2012 6:23 pm

At the end of 2004, a certain farm had 24 hens, 12 cows, 30 sheep,and 14 pigs. By the end of 2005, 22 new animals-each either a hen, cow, sheep or pig-were brought to the farm. No animals left the farm. How many pigs were there on the farm at the end of 2005?
1. The ratio of cows to pigs and the ratio of hens to sheep were the same at the end of 2004 and 2005.
2. The number of sheep increased by 1/6 from the end of 2004 to the 2005

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Source: Beat The GMAT — Data Sufficiency | Sun Jun 10, 2012 6:23 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Sun Jun 10, 2012 6:35 pm

karthikpandian19 wrote:At the end of 2004, a certain farm had 24 hens, 12 cows, 30 sheep,and 14 pigs. By the end of 2005, 22 new animals-each either a hen, cow, sheep or pig-were brought to the farm. No animals left the farm. How many pigs were there on the farm at the end of 2005?
1. The ratio of cows to pigs and the ratio of hens to sheep were the same at the end of 2004 and 2005.
2. The number of sheep increased by 1/6 from the end of 2004 to the 2005

(1) The ratio of cows to pigs and the ratio of hens to sheep were the same at the end of 2004 and 2005.

At the end of 2004, ratio of cows to pigs = 12/14 = 6/7
Now for the ratio to be the same at the end of 2005, either cows and pigs should be added in the same ratio or should not be added.
So, the possible number of new cows and pigs are: (0, 0) or (6, 7).

At the end of 2004, ratio of hens to sheep = 24/30 = 4/5.
So, possible number of new hens and sheep are: (0, 0), (4, 5) or (8, 10).

It can be seen that only one combination gives a total of 22 animals: (6, 7) and (4, 5), as 6 + 7 + 4 + 5 = 22
So, 7 new pigs were brought to the farm.
At the end of 2005, number of pigs = 14 + 7 = 21; SUFFICIENT.

(2) The number of sheep increased by 1/6 from the end of 2004 to the end of 2005.
5 sheep were brought to the farm, but there is no info on the remaining 17 animals; NOT sufficient.

The correct answer is A.

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eagleeye: Legendary Member; Posts: 520; Joined: Sat Apr 28, 2012 9:12 pm; Thanked: 339 times; Followed by:49 members; GMAT Score:770

by eagleeye » Sun Jun 10, 2012 6:45 pm

Hi karthikpandian19:

The correct answer should be A. Let me explain:

We are given, numbers for hens, cows, sheep and pigs. We need to find no. of pigs at the end of 2005, after adding 22 new animals.

1) We are given that cows/pigs and hens/sheep ratio remains the same after the new animals came.

Cows/Pigs=12/14 = 6:7, to maintain this ratio we can only add animals in multiples of (6+7=13).
The only possibility is 0 or 13 animals to be added to this group since the higher multiples of 13 (such as 26, 39) are greater than 22.
For the other group, Hens/Sheep = 24/30=4:5, by the same logic, there can be added only the following new animals: 0, 9, or 18.
Of these options only 9+13 =22 gives the correct answer. Hence we know there were 7 pigs added. SUFFICIENT.

2) Here we are told hat sheep increased by 1/6. Hence new number of sheep = 7/6*30=35. But we know nothing about how the rest of animals are distributed. INSUFFICIENT.

Hence the final answer is A.

Let me know if this helps