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so there are total 40 animals that are either cow or pigs. st - 1==> you can have 8 pigs and 32 cows OR 10 pigs and 30 cows OR 12 pigs and 28 cows OR 13 pigs and 27 cows ... so not sufficient. st - 2 not sufficient ==> if pigs are more than 12 it could be that pigs are 13 or 14 or whatsoever ... and remaining cows.

if you consider together... basically you noticed that in st - 1, you need something to restrict # of pigs which is provided by st - 2. so considering both, you can just have 1 case - pigs 13 and cows 27. Answer C.

Together, the only (C, P) combination that meets the sum is (13, 27). C
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DS - If negative answer only, still sufficient. No need to find exact solution. PS - Always look at the answers first CR - Read the question stem first, hunt for conclusion SC - Meaning first, Grammar second RC - Mentally connect paragraphs as you proceed. Short = 2min, Long = 3-4 min

Re: Of the 60 animals on a certain farm, 2/3 are either cows or [#permalink]

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15 Jul 2012, 08:43

The question tells us that: \(p + c = 40\)

Restrictions: \(p\) and \(c\) must be non-negative integers. (We can't have -2 pigs or 1.5 cows.)

(1) \(c > 2p\)

Let's say that \(c = 2p\). Then: \(p + c = 40\) \(p + (2p) = 40\) \(p = 13.33\)

If \(p\) were an integer greater than 13.33, then \(p + c\) would be greater than 40 (for example, if \(p = 14\), then \(p + c > (14) + 2(14)\), \(p + c > 42\)). But \(p + c\) cannot be greater than 40, since the question says that \(p + c = 40\). Therefore: \(p < =13.33\)

Insufficient because \(p\) could be one of a number of non-negative integers less than 13.33 (for example, 13 or 2), and thus \(c\) could be one of a number of non-negative integers (\(c\) = 40 minus whatever \(p\) is).

(2) \(p > 12\)

Insufficient because \(p\) could be one of a number of integers (for example, 13 or 39), and thus \(c\) could be one of a number of integers (\(c\) = 40 minus whatever \(p\) is).

(1) and (2) together are sufficient because: (1) \(p <= 13.33\) (2) \(p > 12\) Therefore: \(12 < p <= 13.33\) \(p\) must equal 13 since 13 is the only integer that is greater than 12 and less than or equal to 13.33.

Re: Of the 60 animals on a certain farm, 2/3 are either cows or [#permalink]

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08 Feb 2013, 07:01

HI all I am facing little difficulty in interpretation of the question, My specifc doubts are:- 1. Here either or means C+p = 40 , since a pig cannot be a cow at the same time. What if the question had a scenario, where a case of both was possible.....should we consider c+p- both = 40 in that case. I am haveing a doubt with either or statement 2. In case of question stating "What was the number of cows", what should we infer that it requires number of only cow ie cow - both or only cow + both, i am facing difficulty...... 3."I. The farm has more than twice as many cows as it has pigs " Can we interpret this as 'For every pig there were more than twice cow" ie c/p>2/1

HI all I am facing little difficulty in interpretation of the question, My specifc doubts are:- 1. Here either or means C+p = 40 , since a pig cannot be a cow at the same time. What if the question had a scenario, where a case of both was possible.....should we consider c+p- both = 40 in that case. I am haveing a doubt with either or statement 2. In case of question stating "What was the number of cows", what should we infer that it requires number of only cow ie cow - both or only cow + both, i am facing difficulty...... 3."I. The farm has more than twice as many cows as it has pigs " Can we interpret this as 'For every pig there were more than twice cow" ie c/p>2/1

Pls help me in clearing my doubts...

Regards Archit

Responding to a pm:

Either A or B means either A or B or both. If they mean to say that both should not be included then they will say 'Either A or B but not both'

What is the number of A? implies all A (including those who can be B too) What is the number of only A ? implies those A who are B too are not to be counted.

3."I. The farm has more than twice as many cows as it has pigs " Can we interpret this as 'For every pig there were more than twice cow" ie c/p>2/1

Yes, that's correct. You can write it as c/p > 2 or as c > 2p (same thing)
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I thought this to be a very interesting approach - even better than picking numbers. But something is quite confusing when one tries to develop statement (1) and (2) together to find the solution. There isn't an algebraically proof? Is it pick numbers the only method? Here is my puzzle:

- Statement (1): Not sufficient C > 26

- Statement (2): Not sufficient P > 12

Or, substituting variables:

40 - C >12 C < 38

- Statement (1) and (2) together:

26 < C < 38 ----> ??? Why is this not the right approach?

I thought this to be a very interesting approach - even better than picking numbers. But something is quite confusing when one tries to develop statement (1) and (2) together to find the solution. There isn't an algebraically proof? Is it pick numbers the only method? Here is my puzzle:

- Statement (1): Not sufficient C > 26

- Statement (2): Not sufficient P > 12

Or, substituting variables:

40 - C >12 C < 38

- Statement (1) and (2) together:

26 < C < 38 ----> ??? Why is this not the right approach?

From \(40 - c > 12\) you get \(c < 28\) not \(c < 38\). Thus when we combine we get \(26<c<28\) --> \(c=27\).

Could we add across inequalities as I did below? If not, when is it allowed to add across inequalities? (1) c > 2p NS

(2) p > 12 NS

(1) + (2) c + p > 2p + 12 40 > 2p + 12 2p < 28 p < 14 Because (2) gives p > 12, with the above statement, p = 13 and we can solve for c. S

You can add inequalities as long as both the inequalities have the same sign. a > b c > d gives a+c > b + d Think logically: a is greater than b and c is greater than d so a+c will be greater than b+d because you are adding the larger numbers together. So what you have done above is correct.

If the inequality signs are different, you cannot add them.

Also, you can subtract inequalities when they have opposite signs but prefer not to do that to avoid confusion. Just flip the sign of one inequality by multiplying it by -1 and then add them up.
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Question stem says that 2/3 of 60 are pigs or cows. That means 40 animals are pigs or cows. So all we need to have sufficiency is either number of pigs or number of cows.

1) Farm has more than 2 cows for 1 pig (at least 26.6 animals of the 40 are cows). This just tells us that the farm has at least 27 pigs and that the max number of cows is 13. For example the farm could have 30 pigs and 10 cows. Not a definitive number. Insufficient.

2) Farm has more than 12 pigs. Again not enough info. Insuff

1+2) Statements together tell us: 12 < number of pigs is <=13 Which means number pigs = 13 Number of cows = 27.

ANSWER = C.

I do agree with 'yangsta8' that the answer is 'C' but (if I am NOT wrong), Stmnt#1 says the number of Cows are more than twice than the pigs. Thus, the cows could be 27 and Pigs could be 13; and For example, the farm could have 30 cows and 10 pigs. ------------------------------- Hi Bunuel and Yangsta8 - Please correct me if I am wrong (which is very much possible)!

c+p=40

(1) c>2p --> min # of cows is 27 and max # pigs is 13, so there can be any combination not violating this and totaling 40. Not sufficient (2) p>12 Not sufficient

(1)+(2) p>12 but max of p is 13, hence p=13 --> c=27

You are right there can be 27 cows (min) and 13 pigs (max) or 30 cows and 10 pigs.

Think there was simple typo from yangsta8.

Hi bunnel,

I need clarification here

2/3 are either pigs or cows

i am understanding (2/3)*60 = 40 (cows or pigs) how it can be c+p = 40 question is saying either cow or pig so this can be c or p but not C+P

i am understanding (2/3)*60 = 40 (cows or pigs) how it can be c+p = 40 question is saying either cow or pig so this can be c or p but not C+P

Please clarify.

Thanks.

If I may add, 40 are either pigs or cows does not mean that either all 40 are pigs or all 40 are cows. It means of all the 40, some are pigs and the rest are cows.

Say, if you say that 90% of the students are either from Michigan or Ohio, it means that the rest of the 10% are from other states but 90% belong to these two states. How many of the 90% are from Michigan and how many are from Ohio, we don't know but we know that together they account for 90% of the class.
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Of the 60 animals on a certain farm, 2/3 are either cows or [#permalink]

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11 Jul 2014, 10:25

What about the 20 extra animals ? Why can't they be cows or pigs as well within that set ? Nothing is mentioned about these 20 animals. We just know that 40 animals are either pigs or cows. Does anyone get my point ?

Having 13 pigs, 27 cows, and 20 other animals is a possiblity.

Having 14 pigs, 30 cows and 16 other animals is another possibility.

What about the 20 extra animals ? Why can't they be cows or pigs as well within that set ? Nothing is mentioned about these 20 animals. We just know that 40 animals are either pigs or cows. Does anyone get my point ?

Having 13 pigs, 27 cows, and 20 other animals is a possiblity.

Having 14 pigs, 30 cows and 16 other animals is another possibility.

Following that logic, E is the right answer.

Of the 60 animals on a certain farm, 40 are either pigs or cows means that from the remaining 20 animals neither is either pig or cow.
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