Each piglet in a litter is fed exactly one-half pound of a mixture of

Question

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

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

KarishmaB · Accepted Answer

@subhashghosh: As requested by you, I will try and explain the logic used in this question.

For now, forget the data given in the question. Consider this:

10% of Oats and 20% of Barley was fed to piglet A.

My question is - Of the total food (Oats + Barley) what percentage was fed to piglet A? 
It will depend on the ratio of Oats and Barley. If the mixture had only oats, the piglet was fed 10% of total food. If the mixture had only Barley, the piglet was fed 20% of the mixture. If the mixture had half oats and half barley, the piglet was fed 15% of the mixture. If the mixture had 1 part Oats for every 4 parts Barley, the piglet was fed 18% of the mixture (it is just weighted average). Whatever the case, the piglet was fed more than 10% of total food and less than 20% total food if the mixture had both Oats and Barley.

If this sounds good, consider data given in the question – the piglet was fed 25% Oats and 16.66% Barley (1/4 Oats and 1/6 Barley). So definitely, the piglet was fed more than 1/6 of the total mixture and less than ¼ of the total mixture (as reasoned above). The total food mixture was split equally among all the piglets. Number of piglets has to be an integer, say n. Each piglet gets the same amount of food i.e. 1/n of the total food. But each piglet also gets less than ¼ of total food and more than 1/6 of total food. The only integral value for n such that 1/6 < 1/n < ¼ is 5.

KarishmaB · Answer

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.

IanStewart · Answer

Neither statement is sufficient alone. Together, if the pig had 1/6 of the barley and 1/4 of the oats, the fraction of the total food it had was somewhere between 1/6 and 1/4. Since each pig gets an equal amount of food, each pig gets 1/n of the total amount of food, where n must be an integer. So 1/6 < 1/n < 1/4, and n must be 5.

samrus98 · Answer

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

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

SOL:

St1:
Just knowing how much of the oats Piglet A was fed today is not sufficient to answer how many piglets are there in the litter. If Piglet A was fed 1/4 of the barley as well then we could conclude that there are a total of 4 piglets. But if the amount of barley is more or less then we can't be sure.
 => NOT SUFFICIENT

St2:
By similar reasoning,
 => NOT SUFFICIENT

St1 & St2 Together:
Since Piglet A was fed 1/4 of the Oats and 1/6 of the barley, we can say for sure that there can be a minimum of 4 piglets and a maximum of 6 piglets.

Using statements 1 & 2 we get the equation => 1/4*O + 1/6*B = 1/2
=> 3O + 2B = 6 ................... I

We know that the number of piglets is between 4 and 6 and that for every piglet the total of (O + B) required is 0.5 pound where O & B cannot be zero. With this knowledge and the  assumption that nothing of oats and barley should be left  after the piglets have been fed, lets form another equation:
If number of piglets is 4, we would require (O + B)*4 = 0.5 * 4 = 2
=> O + B = 2 ...................... IIA
Solving I & IIA we get,
O = 2, B = 0 => Not valid since B cannot be 0.

If number of piglets is 5, we would require (O + B)*5 = 0.5 * 5 = 2.5
=> O + B = 2.5 .................... IIB
Solving I & IIB we get,
O = 1, B = 1.5 => Valid

If number of piglets is 6, we would require (O + B)*6 = 0.5 * 6 = 3
=> O + B = 3 ...................... IIC
Solving I & IIC we get,
O = 0, B = 3 => Not valid since O cannot be 0.
 => SUFFICIENT

ANS: C

PS: If all the oats and barley doesnt need to be fed to the piglets then the answer to this question would be E, as the number of piglets could be 4 or 5.

dhushan · Answer

Hi everyone,

Looking over the answer to the solution, I am confused as to why their needs to be a minimum and maximum of 4 to 6 piglets respectively. Given that their is 3/4 of the Oats and 5/6 of the Barley, why could their not be 7 piglet where each received 3/28 of the Oats and 5/42 of the Barley? Or following the same logic, even more than 7 piglets?

Thanks,

Dhushan

chetan2u · Answer

restricting the no between 4 and 6 because some piglet has 1/4 of oats and 1/6 of something else does not make senseand cannot be correct 
can someone post OA..
from 2 statements one can get 3o+2b=6..(i)
 and if t is total no of piglets total food=t*1/2=t/2 pounds..
 also total food=b+o=t/2....(ii)
 two eq but three variables o,b and t so ans should be E

IanStewart · Answer

You're not using one crucial piece of information - each pig ate the same total amount of food. We know that one pig had 1/4 of the oats and 1/6 of the barley. If each other pig had 3/28 of the oats, then each other pig had less oats than the first pig, and if each other pig had 5/42 of the barley, then each other pig had less barley than the first pig. If the other pigs had less oats and less barley than the first pig, there's no way they could have had the same total amount of food.

You aren't using one crucial piece of information: t must be an integer (and o and b must be positive). When you have restrictions on your unknowns, then counting equations and unknowns can be very misleading (see Q123 in the DS section of OG12 for another example). If the solution I posted above doesn't make sense to you, you can proceed algebraically, using the equations you wrote above. First, multiply the equation b + o = t/2 by 2 on both sides, and subtract from the equation 3o + 2b = 6:

3o+2b = 6
-  2o + 2b = t 
o = 6 - t

Now, o is clearly positive, so the right side of the equation above must be positive, and t < 6.

Next, multiply the equation b + o = t/2 by 3 on both sides, and subtract the equation 3o + 2b = 6 from it:

3o + 3b = 3t/2
-  3o + 2b = 6  
b = 1.5t - 6
2b/3 = t - 4

Now b is clearly positive, so the right side of the above equation must be positive, and t > 4.

Since 4 < t < 6, and t is an integer, t = 5. The answer is C.

KieuPhuong · Answer

Another way to find the No of pig is 5:
We need to know how much (O + B) there is (in pounds).

As 1/4 O + 1/6 B = 1/2 => O + 2/3 B = 2 (both sides multiplied with 4) but O + 2/3 B < O + B, then O + B > 2, which means there must be more than 4 pigs to eat more than 2 pounds.

Similarly, 1/4 O + 1/6 B = 1/2 => 3/2 O + B = 3 (both sides multiplied with 6) but 3/2 O + B > O + B, then O + B < 3, which means that the food is not enough for 6 pigs.

The No of pigs must be integer, then it is definitely 5.

However this explanation also uses the same method as in above posts.

PranavChamp · Answer

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

dkj1984 · Answer

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,

bhandariavi · Answer

1/4 + 1/6 = half pound ....(1)
Combination of half pounds are : (1/4, 1/6) (1/4, 1/6) (1/4, 1/6) (1/4, 1/6) Remaining is (1/6,1/6)
1/6 in itself is not half pound (refer 1). Therefore, 1/6 barley + 1/6 barley must be half pound. Therefore, 5 combination of half pounds. C is the answer.
However, dont assume that the last piglet is going to eat barley only. Just look for how many half pounds you can make in total - that must be no. of piglets.

Raihanuddin · Answer

How have you come up with 2 parts?

KarishmaB · Answer

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.

russ9 · Answer

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?

KarishmaB · Answer

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.

mikemcgarry · Answer

Dear ishanmechno , 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. I will ask Bunuel to merge topics. Mike :-)

ccooley · Answer

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

Leuro · Answer

Hi  VeritasKarishma ,

solving the problem like this, you are assuming that all the grains available must be fed to piglets. This is not highlighted in the question stem. If this assumption were relaxed, you cannot be sure about the total amount of piglets (which can be from 1 to 5).

What am I getting wrong?

Thank you very much!

KarishmaB · Answer

Hi Leuro,

No, we are not assuming that all the available grains must be fed. Look, it has to do with the wording of the question.

"Each piglet in a litter is fed exactly one-half pound of a mixture of oats and barley." - So this means that 1/2 pound is fed to each piglet. So if there are 10 piglets, 5 pounds in total is fed today. This 5 pounds will be a mix of oats and barley perhaps 2 pounds oats and 3 pounds barley or whatever.

(1) Piglet A was fed exactly 1/4 of the oats today
So we have a fixed amount of 5 pounds that was fed today out of which 2 pounds was oats. Piglet A was fed 1/4 of the oats. 
There is no question of anything remaining. We don't have that total there is 100 pounds of mix etc. Since everyday 1/2 pound is fed to each piglet, that is the quantity we are talking about.

I hope this helps.

Each piglet in a litter is fed exactly one-half pound of a mixture of

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Each piglet in a litter is fed exactly one-half pound of a mixture of

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