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

Detailed answers please!
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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.
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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

Thanks, I totally overlooked the fact that the amount of B and O for each pig had to add up to 0.5lbs.

Finding the limit of the number of pigs to be between 4 and 6 was key.

This is how I read the problem.
O + B = t ( Let t be the total weight of Oats and Barley, this has to be multiple of 1/2lb, since each piglet require 1/2 lbs ... ratio may be different )
3O + 2B = 6 ( comming from o/4 + b/6 = 1/2 )
Now, here is the meat,
O can be multiple of 1/2 and B can be multiple of 1/2 ONLY since O+B = Multiple of 1/2
Now the only way to make o and b multiples of 1/2 is by,
O = 1 and B = 3/2
Total max number of Pigs = 2(from O) + 3( from B ) = 5

@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.
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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,

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.
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