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

Question

Each piglet in a litter is fed exactly one-half pound of a mixture of oats and barely. The ratio of the amount of barely 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 barely today

Please explain your answer!
Thanks

x97agarwal · Answer

lets the total amount of oats = x 
and the amount of barley = y

S1. Piglet A was fed x/4; not enough information AD out

S2. Piglet A was fed y/6; not enough information B is out

Combining: x/4 + y/6 = 1/2 ; 
 3x + 2y = 6
x and y cannot be -ve or zero
Hence for this equation to hold: x = 1 and y = 1.5 (3+3 = 6)
6kg of total feed; since each piglet is give 0.5kg the total number should be 6/0.5 = 12

IMO C

tarek99 · Answer

nope

you're wrong!

x97agarwal · Answer

I possibly found my error and edited my answer. IMO C

tarek99 · Answer

Although C is the OA, you didn't give the total number of piglets. According to your variables, X and Y are the amounts of oat and barely respectively, but they are   NOT   the number of piglets. So what's the number of piglets?

x97agarwal · Answer

Sorry I forgot.
6kg of total feed; since each piglet is give 0.5kg the total number should be 6/0.5 = 12

tarek99 · Answer

but then for some reason, the explanation says that the number of piglets should be 5??? here's how:

We know that each piglet is fed  1/2  pound of oats and barely, so each piglet receives either an above average amount of oats and a below average amount of barely, vice versa, or even an average amount of both grains. Neither (1) nor (2) is sufficient by itself, but together, we see that piglet A got a larger share of that oats and a below average amount of barely. (1) tells us that there are more than 4 piglets and (2) tells us that there are fewer than 6 piglets.  Thus there are  5  piglets .

More mathematically, suppose there are x piglets sharing a total of B pounds of barely and O pounds of oats. Each piglet then receives  (B+O)/x  pounds of grain. Piglet A received received  O/4 + B/6  pounds of grain.

Therefore,  (B+O)/x = (3O+2B)/12  and  x/(B+O) = 12/(3O+2B)

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

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