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Re: Each piglet in a litter is fed exactly [#permalink]

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09 May 2014, 01:57

PranavChamp wrote:

St 1 : InSuf piglet A fed 1/4 of oats. St 2 : InSuf piglet B fed 1/6 of barley.

St 1+2 : Suff

There are total 10 parts of Oats & Barley Piglet A fed 2 parts out of 10. These 2 parts weigh 0.5 pound. So 10 parts weigh 2.5 pounds. Each piglet fed 0.5 pound so we can say that 2.5/0.5 = 5 piglets

St 1 : InSuf piglet A fed 1/4 of oats. St 2 : InSuf piglet B fed 1/6 of barley.

St 1+2 : Suff

There are total 10 parts of Oats & Barley Piglet A fed 2 parts out of 10. These 2 parts weigh 0.5 pound. So 10 parts weigh 2.5 pounds. Each piglet fed 0.5 pound so we can say that 2.5/0.5 = 5 piglets

How have you come up with 2 parts?

You do not know that oats and barley were mixed in the ratio 4:6 i.e. you cannot say that there are 4 parts of oats and 6 parts of barley. They could be in any ratio and hence we cannot say that piglet A was fed 2 parts of the mix. Look at the explanations given in previous posts.
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Re: Each piglet in a litter is fed exactly [#permalink]

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12 May 2014, 22:55

VeritasPrepKarishma wrote:

Raihanuddin wrote:

PranavChamp wrote:

St 1 : InSuf piglet A fed 1/4 of oats. St 2 : InSuf piglet B fed 1/6 of barley.

St 1+2 : Suff

There are total 10 parts of Oats & Barley Piglet A fed 2 parts out of 10. These 2 parts weigh 0.5 pound. So 10 parts weigh 2.5 pounds. Each piglet fed 0.5 pound so we can say that 2.5/0.5 = 5 piglets

How have you come up with 2 parts?

You do not know that oats and barley were mixed in the ratio 4:6 i.e. you cannot say that there are 4 parts of oats and 6 parts of barley. They could be in any ratio and hence we cannot say that piglet A was fed 2 parts of the mix. Look at the explanations given in previous posts.

Thank you very much. Can you please give two or three variation of this question so that I can practice and familiarize myself with this type of question?

Re: Each piglet in a litter is fed exactly one-half pound of a [#permalink]

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30 Aug 2014, 11:01

VeritasPrepKarishma wrote:

dkj1984 wrote:

Hi Karishma,

I understood your explanation for the general part,however,with reference to this problem,I am still a little confused.

Can u please elaborate on the usage of the weighted average method for this problem.

Thanks!

Regards,

Ok, let me explain using a different example. Say a meal consists of a sandwich and a milkshake. You eat 1/2 of the sandwich and drink 1/2 of the milkshake. Can I say you have had 1/2 of the meal? Sure, right? If you eat only 1/4 of the sandwich and drink 1/4 of the milkshake, then you would have had only 1/4 of the meal. What happens in case you eat 1/2 of the sandwich but drink only 1/4 of the milkshake? In that case, you have had less than 1/2 of the meal but certainly more than 1/4 of the meal, right?

So when piglet A is fed 1/4 of the Oats and 1/6 of the Barley, it is fed less than 1/4 of the total food but more than 1/6 of the total food.

Another thing to consider here is that number of piglets has to be a positive integer, say 'n'. Now, since it is given that each piglet gets the same amount of food and there are n piglets, each piglet will get 1/n of the total food. So piglet A must have got 1/n of the total food too.

This 1/n must lie between 1/4 and 1/6. Only 1/5 lies between 1/4 and 1/6 (such that n is a positive integer). Hence n must be 5.

Hi Karishma,

I was with you until the highlighted statement above. I understand the logic as to why piglet A is fed less than a 1/4 but more than a 1/6. That being said, why is 1/5 the only other variables? Even though piglets have an integer constraint, I fail to see how that translates into your last statement?

I understood your explanation for the general part,however,with reference to this problem,I am still a little confused.

Can u please elaborate on the usage of the weighted average method for this problem.

Thanks!

Regards,

Ok, let me explain using a different example. Say a meal consists of a sandwich and a milkshake. You eat 1/2 of the sandwich and drink 1/2 of the milkshake. Can I say you have had 1/2 of the meal? Sure, right? If you eat only 1/4 of the sandwich and drink 1/4 of the milkshake, then you would have had only 1/4 of the meal. What happens in case you eat 1/2 of the sandwich but drink only 1/4 of the milkshake? In that case, you have had less than 1/2 of the meal but certainly more than 1/4 of the meal, right?

So when piglet A is fed 1/4 of the Oats and 1/6 of the Barley, it is fed less than 1/4 of the total food but more than 1/6 of the total food.

Another thing to consider here is that number of piglets has to be a positive integer, say 'n'. Now, since it is given that each piglet gets the same amount of food and there are n piglets, each piglet will get 1/n of the total food. So piglet A must have got 1/n of the total food too.

This 1/n must lie between 1/4 and 1/6. Only 1/5 lies between 1/4 and 1/6 (such that n is a positive integer). Hence n must be 5.

Hi Karishma,

I was with you until the highlighted statement above. I understand the logic as to why piglet A is fed less than a 1/4 but more than a 1/6. That being said, why is 1/5 the only other variables? Even though piglets have an integer constraint, I fail to see how that translates into your last statement?

We need the solution for 1/n such that n is an integer. It must lie between 1/4 and 1/6 i.e. between .25 and .1666. What integer value can n take? Can it be 7? Will 1/7 lie between 1/6 and 1/4? Can it be 3? Will 1/3 lie between 1/4 and 1/6? n cannot be greater than 6 or less than 4 because it goes out of range. So n must be 5.
_________________

Re: Each piglet in a litter is fed exactly one-half pound of a [#permalink]

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Each piglet in a litter is fed exactly one-half pound...... [#permalink]

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21 Sep 2016, 10:55

Each piglet in a litter is fed exactly one-half pound of a mixture of oats and barley. The ratio of the amount of barley to that of oats varies from piglet to piglet, but each piglet is fed some of both grains. How many piglets are there in the litter?

1) Piglet A was fed exactly 1/4 of the oats today. 2) Piglet A was fed exactly 1/6 of the barley today.

Each piglet in a litter is fed exactly one-half pound of a mixture of oats and barley. The ratio of the amount of barley to that of oats varies from piglet to piglet, but each piglet is fed some of both grains. How many piglets are there in the litter?

1) Piglet A was fed exactly 1/4 of the oats today. 2) Piglet A was fed exactly 1/6 of the barley today.

I'm happy to respond. My friend, you may not be aware of this, but by posting this in a new thread, you have violated the guidelines of GMAT Club. This individual question has been posted numerous times before, for example here: each-piglet-in-a-litter-is-fed-exactly-one-half-pound-of-a-82321.html Whenever you are curious about a math question, ALWAYS search extensively for the question before starting a new thread. Only start a new thread if you are 100% sure that the question has never been posted before on GMAT Club. I believe this question is from GMAT Prep. Every single math question in GMAT Prep has already been posted by someone somewhere in this forum. If you search, you will find a thread, and it may be that one of the posts already existing in that thread will answer your questions. If not, you can always add your own questions to that thread, and all the experts who already posted in that thread will be notified.

Each piglet in a litter is fed exactly one-half pound of a mixture of oats and barley. The ratio of the amount of barley to that of oats varies from piglet to piglet, but each piglet is fed some of both grains. How many piglets are there in the litter?

1) Piglet A was fed exactly 1/4 of the oats today. 2) Piglet A was fed exactly 1/6 of the barley today.

Merging topics. Please refer to the discussion on previous pages.
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Each piglet in a litter is fed exactly one-half pound of a mixture of oats and barley. The ratio of the amount of barley to that of oats varies from piglet to piglet, but each piglet is fed some of both grains. how many piglets are there in the litter?

(1) Piglet A was fed exactly 1/4 of the oats today (2) Piglet A was fed exactly 1/6 of the barley today

What bothers me is that it's unclear whether the statements are referring to the total amount of oats/barley fed to all of the piglets, or the total amount of oats/barley in the mixture. The original answer implies that we should assume those are the same (i.e. 100% of the mixture is fed to the piglets every day), but that seems far from obvious to me.

If you don't make that assumption, here's a solution where there are four piglets:

total mixture - 1.8 lbs oats, 0.3 lbs barley, 2.1 lbs total each piglet (including piglet A) gets 0.45 lbs of oats and 0.05 lbs of barley four piglets in total 0.1 lbs of the mixture goes uneaten
_________________

Chelsey Cooley | Manhattan Prep Instructor | Seattle and Online

Each piglet in a litter is fed exactly one-half pound of a [#permalink]

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19 Jul 2017, 21:28

The answer seems to be quite a lot simpler than the people are explaining. Think of it like this

(a) if 1/4 the pig ate that day was oats then maybe he had 100% oats and now there is 1.5 of oats left and an unlimited amount of barley. There could be 0.5 barley there could be 600 (b) Same logic for (b)

Now (C) which people seem to be over complicate

(1) If Oats was greater than 2 then that would mean the pig ate more than 0.5 of food so we know oats can't be bigger than 2 (2) If barley was greater than 3 we know the pig would eat more than 0.5 of food so we know the maximum number of Oats + Barley is 5

So if we know the maximum number of oats + Barley is 5 there can be a maximum of 10 pigs. But we know that the pig has a mix so now we know there are less than 10 pigs.

We also know as mentioned that there has to be greater than 4 Pigs because Oats can't be below 2. Because if oats were 2 and a pig ate 1/4 of it he would have no room left over for Barley.

So you know that the amount of food has to be >2 and less than <5. So from this we know the amount of pigs can be 5,6,7,8 or 9. We can try a couple of amounts to guess.

Let's try 9 first

A+B=4.5 (4.5=9/2.. 9 pigs so each pigs eats 0.5) 1/4 A + 1/6B = 0.5

A+B=4.5 A + 4/6B =2 Cancelling 2/6 B = 2.5 X 3 implies B =7.5 so this does not get a solution.

Let's try 8 pigs A+B=4 1/4A+1/6 B =0.5

A+B=4 A+4/6B =2 2/6 B = 2. Again implying B =6! Not possible as 6 >4

NOW LET'S PICK A LOWER NUMBER SAY 6 PIGS

We get A= oats B= Barley A+B=3 1/4A + 1/6B = 0.5.

Let's solve for B.

A+B =3 A + 4/6B = 2

2/6B = 1 . B =3. We know this amount isn't possible as the pig has to eat some oats!

From this let's try to guess a lower amount say 2.5

A+B = 2.5 1/4A + 1/6 B = 0.5

A+B =2.5 A + 4/6 B =2

2/6 B =0.5 . 1/6 B = 0.25 and B = 1.5. From this we would get X = 1 and this equation works at these numbers.

We already know 4 pigs is impossible because that would imply they only ate oats. A+B=2 1/4A + 1/6 B =0.5

A+B=2 A+4/6 = 2

2/6 B = 0. We know this is not possible

To go even quicker you can use the logic some of the experts used above. For instance, if we had 3 pounds of food and one pig got 1/6 of it that would mean it ate 0.5 pounds. If there were 4 pounds of food than 1/6 would be 4/6 above 0.5 so that is too high. So we know there are less than 6 pigs. If we had 2 pounds of food we know that 1/4 is consumed or 0.5. But any less than 4 pounds would be too low a number. As you guys can see 2 pounds of food would imply the pig only ate oats and 6 pounds would imply a pig only ate barley therefore the only integer that works is 5. You can then check 5 to see if it works which it does.

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