Problem Solving

Hi guys

Who knows the answer for sure ?

Of the 60 animals on a certain farm, 2/3 are either pigs or cows. How many of the animals are cows ?

(1) The farm has more than twice as many cows at it has pigs

(2) The farm has more than 12 pigs

I hesitated between C and E

Xbond wrote:Hi guys

Who knows the answer for sure ?

Of the 60 animals on a certain farm, 2/3 are either pigs or cows. How many of the animals are cows ?

(1) The farm has more than twice as many cows at it has pigs

(2) The farm has more than 12 pigs

I hesitated between C and E

You're certainly correct that neither statement alone is sufficient.

A great way to approach data sufficiency is to pick numbers. If you can pick numbers that satisfy the rules you're given and still get more than 1 answer to the question, then you don't have enough information.

(1) c > 2p

We have a total of 40 cows and pigs (2/3 of 60). If c > 2p, we could have:

39 cows and 1 pig
or
38 cows and 2 pigs
(or lots of other breakdowns).

Since we can get more than one value for "number of cows", (1) is insufficient.

(2) p > 12

We could have 27 cows and 13 pigs
or
13 cows and 27 pigs
(or lots of other breakdowns).

Since we can get more than one value for "number of cows", (2) is insufficient.

Together:

from (2), we know that the smallest value we can choose for p is 13. If we have 13 pigs, we have 27 cows.

let's try to increase the number of pigs to 14. If we have 14 pigs, we have 26 cows. However, now we've violated (1) that says that we need more than twice as many cows as pigs.

So, to satisfy both rules, we know that p=13 and c=27. We have a definite value for the number of cows, so together the statements are sufficient: choose (C).

Stuart Kovinsky wrote:

Xbond wrote:Hi guys

Who knows the answer for sure ?

Of the 60 animals on a certain farm, 2/3 are either pigs or cows. How many of the animals are cows ?

(1) The farm has more than twice as many cows at it has pigs

(2) The farm has more than 12 pigs

I hesitated between C and E

You're certainly correct that neither statement alone is sufficient.

A great way to approach data sufficiency is to pick numbers. If you can pick numbers that satisfy the rules you're given and still get more than 1 answer to the question, then you don't have enough information.

(1) c > 2p

We have a total of 40 cows and pigs (2/3 of 60). If c > 2p, we could have:

39 cows and 1 pig
or
38 cows and 2 pigs
(or lots of other breakdowns).

Since we can get more than one value for "number of cows", (1) is insufficient.

(2) p > 12

We could have 27 cows and 13 pigs
or
13 cows and 27 pigs
(or lots of other breakdowns).

Since we can get more than one value for "number of cows", (2) is insufficient.

Together:

from (2), we know that the smallest value we can choose for p is 13. If we have 13 pigs, we have 27 cows.

let's try to increase the number of pigs to 14. If we have 14 pigs, we have 26 cows. However, now we've violated (1) that says that we need more than twice as many cows as pigs.

So, to satisfy both rules, we know that p=13 and c=27. We have a definite value for the number of cows, so together the statements are sufficient: choose (C).

"We have a total of 40 cows and pigs (2/3 of 60)."

Stuart, how are you interpreting 2/3 are either pigs or cows? Your interpretation implies 2/3 are pigs AND cows. I am thinking it should be either 40 pigs or 40 cows.

I kind of agree with Stuart, I think it says "out of the total lot" 2/3 are either pigs or cows.

dtweah wrote: Stuart, how are you interpreting 2/3 are either pigs or cows? Your interpretation implies 2/3 are pigs AND cows. I am thinking it should be either 40 pigs or 40 cows.

I'm just using a normal interpretation of how "either a or b" is used in this context.

When we say something like "I ate either fish or chicken 5 days last week", we usually mean we there were 5 days on which we ate fish/chicken, not worrying about which one we ate. Interpreting that as "I ate either fish 5 days last week or chicken 5 days last week" is counter-intuitive.

Stuart Kovinsky wrote:

dtweah wrote: Stuart, how are you interpreting 2/3 are either pigs or cows? Your interpretation implies 2/3 are pigs AND cows. I am thinking it should be either 40 pigs or 40 cows.

I'm just using a normal interpretation of how "either a or b" is used in this context.

When we say something like "I ate either fish or chicken 5 days last week", we usually mean we there were 5 days on which we ate fish/chicken, not worrying about which one we ate. Interpreting that as "I ate either fish 5 days last week or chicken 5 days last week" is counter-intuitive.

Stuart, " 2/3 of 60 animals are either pigs or cows", means there are either 40 cows or there are 40 pigs. To interpret this to mean that the" sum of pigs and cows among the animals is 2/3 of 60 =40" is indeed counterintuitive to me. I stand to be corrected on the actual GMAT since this is math language I learned since about middle school. Also, there is nothing in that problem that suggests there are only cows or pigs. There could be other animals.

"40 animals are either pigs or cows" is different from "40 animals are pigs and cows"

This is my last word.

If the statement had been worded "either 2/3 of the animals are pigs or they are cows", then your interpretation would be correct.

dtweah wrote:

Stuart Kovinsky wrote:

Xbond wrote:Hi guys

Who knows the answer for sure ?

Of the 60 animals on a certain farm, 2/3 are either pigs or cows. How many of the animals are cows ?

(1) The farm has more than twice as many cows at it has pigs

(2) The farm has more than 12 pigs

I hesitated between C and E

You're certainly correct that neither statement alone is sufficient.

A great way to approach data sufficiency is to pick numbers. If you can pick numbers that satisfy the rules you're given and still get more than 1 answer to the question, then you don't have enough information.

(1) c > 2p

We have a total of 40 cows and pigs (2/3 of 60). If c > 2p, we could have:

39 cows and 1 pig
or
38 cows and 2 pigs
(or lots of other breakdowns).

Since we can get more than one value for "number of cows", (1) is insufficient.

(2) p > 12

We could have 27 cows and 13 pigs
or
13 cows and 27 pigs
(or lots of other breakdowns).

Since we can get more than one value for "number of cows", (2) is insufficient.

Together:

from (2), we know that the smallest value we can choose for p is 13. If we have 13 pigs, we have 27 cows.

let's try to increase the number of pigs to 14. If we have 14 pigs, we have 26 cows. However, now we've violated (1) that says that we need more than twice as many cows as pigs.

So, to satisfy both rules, we know that p=13 and c=27. We have a definite value for the number of cows, so together the statements are sufficient: choose (C).

"We have a total of 40 cows and pigs (2/3 of 60)."

Stuart, how are you interpreting 2/3 are either pigs or cows? Your interpretation implies 2/3 are pigs AND cows. I am thinking it should be either 40 pigs or 40 cows.

2/3 are pigs or cows.

2/3 are men or women.

2/3 are mbas or ba's

2/3 are pigs and cows would mean that pigs + cows = 2/3.

I can see what you're saying but then the wording would be 2/3 are either pigs or cows.

I agree with Stuart.

doclkk wrote:

dtweah wrote:

Stuart Kovinsky wrote:

Xbond wrote:Hi guys

Who knows the answer for sure ?

Of the 60 animals on a certain farm, 2/3 are either pigs or cows. How many of the animals are cows ?

(1) The farm has more than twice as many cows at it has pigs

(2) The farm has more than 12 pigs

I hesitated between C and E

You're certainly correct that neither statement alone is sufficient.

A great way to approach data sufficiency is to pick numbers. If you can pick numbers that satisfy the rules you're given and still get more than 1 answer to the question, then you don't have enough information.

(1) c > 2p

We have a total of 40 cows and pigs (2/3 of 60). If c > 2p, we could have:

39 cows and 1 pig
or
38 cows and 2 pigs
(or lots of other breakdowns).

Since we can get more than one value for "number of cows", (1) is insufficient.

(2) p > 12

We could have 27 cows and 13 pigs
or
13 cows and 27 pigs
(or lots of other breakdowns).

Since we can get more than one value for "number of cows", (2) is insufficient.

Together:

from (2), we know that the smallest value we can choose for p is 13. If we have 13 pigs, we have 27 cows.

let's try to increase the number of pigs to 14. If we have 14 pigs, we have 26 cows. However, now we've violated (1) that says that we need more than twice as many cows as pigs.

So, to satisfy both rules, we know that p=13 and c=27. We have a definite value for the number of cows, so together the statements are sufficient: choose (C).

"We have a total of 40 cows and pigs (2/3 of 60)."

Stuart, how are you interpreting 2/3 are either pigs or cows? Your interpretation implies 2/3 are pigs AND cows. I am thinking it should be either 40 pigs or 40 cows.

2/3 are pigs or cows.

2/3 are men or women.

2/3 are mbas or ba's

2/3 are pigs and cows would mean that pigs + cows = 2/3.

I can see what you're saying but then the wording would be 2/3 are either pigs or cows.

I agree with Stuart.

On the GMAT treat either as a combined sum and don't separate them.
2/3 of 60 animals are either pigs or cows. What one animal is chosen at random, what is the probability it is either a pig or a cow. If GMAT ask you the above Choose

40/60 which is consistent with your definition above. Good Luck.

Many thks