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

Without "The ratio of the amount of barley to that of oats varies from piglet to piglet," one would wonder how piglet A got 1/4th of one grain and 1/6th of another.

If each piglet were given 1/5th of the total grains (as mentioned that each piglet got the same amount) in the same ratio of oats:barley, and if each piglet were given 1/4th oats and 1/6th barley, this would mean that we would fall short of oats and have excess barley left. We would need to distribute 1/5th oats and 1/5th barley to each piglet if the ratio were to be kept the same. So if there were 5 pounds of oats and 10 pounds of barley, each piglet would get 1 pound of oats and 2 pounds of barley.

But we are given that the ratio of oats and barley varies among the piglets. So if piglet A got 1/4th oats (extra oats) and 1/6th barley (less barley), another piglet could have got less oats and more barley. Hence it clarifies that each piglet got the same total amount of grains but in different combinations. Hence 1/4 oats and 1/6 barley for piglet A is possible.

VeritasKarishma - are any of these viable scenarios or does every pig only have to be 20 % only ?

scenario # 1
piglet A) 19 %
piglet B) 21 %
piglet C 19 %
Piglet D) 21 %
piglet E) 20 %

scenario # 2
piglet A) 19 %
piglet B) 21 %
piglet C 19 %
Piglet D) 21 %
piglet E) 10 %
Piglet F) 10 %

Not possible. We are given:
"Each piglet in a litter is fed exactly one-half pound of a mixture of oats and barley."
so each piglet got the same quantity.

Hi VeritasKarishma - how does

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

TRANSLATE into every pig has to have the same % of total food ?

The statement in pink is talking about a specific amount, not a percentage.

Why do think this statement in pink implies every pig has to have the same % of total food ?

That is where I am struggling.

If I have n students in my class and I brought in some books and distributed all of them giving exactly 3 books to each student, what percentage of the book did you get?
It depends on how many students were there but the least you can say is that each student, including you, got the same percentage of books.

If there were 5 students, each got 20% of the books.
If there were 10 students, each got 10% of the books.
and so on.

When each receives exactly the same amount, it means each got exactly the same percentage of the total distributed.

Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1

Each statement alone is clearly insufficient.

Statements combined.
Let \(O =\) the total amount of oats, \(B =\) the total amount of barley, and \(N =\) the number of piglets.

Piglet A's amount of feed \(= \frac{O}{4} + \frac{B}{6}\)
Amount of feed per piglet \(= \frac{total-oats-and-barley-combined}{number-of-piglets} = \frac{O+B}{N} = \frac{O}{N} + \frac{B}{N}\)

The resulting expressions each represent the amount of feed for Piglet A and thus must be equal:
\(\frac{O}{N} + \frac{B}{N}=\frac{O}{4} + \frac{B}{6}\)

Clearly, the left side will not equal the right side if N=4 or N=6.

If N<4, then each fraction on the left side will be greater than its analogue on the right.
For example, if N=3:
\(\frac{O}{3}\) will be greater than \(\frac{O}{4}\), and \(\frac{B}{3}\) will be greater than \(\frac{B}{6}\).
As a result, the sum on the left side will be GREATER than the sum on the right.

If N>6, then each fraction on the left side will be smaller than its analogue on the right.
For example, if N=7:
\(\frac{O}{7}\) will be smaller than \(\frac{O}{4}\), and \(\frac{B}{7} \)will be smaller than \(\frac{B}{6}\).
As a result, the sum on the left side will be LESS than the sum on the right.

For the two sums to be EQUAL, only one option remains:
N=5
SUFFICIENT.

An alternate approach for combining the two statements:

Let \(O\) = the amount of oats fed to Piglet A and \(B\) = the amount of barley fed to Piglet A.

Since the \(O\) pounds of oats fed to Piglet A constitute 1/4 of all the oats, the total amount of oats = \(4O\)
Since the \(B\) pounds of barley fed to Piglet A constitute 1/6 of all the barley, the total amount of barley = \(6B\)
Thus, the total amount of feed \(= 4O+6B\)

Since each piglet receives the same amount of feed, the amount of feed per piglet = the amount fed to Piglet A = \(O+B\)
Thus:
Number of piglets = \(\frac{total-feed}{feed-per-piglet} = \frac{4O+6B}{O+B}\)

The resulting expression represents the WEIGHTED AVERAGE for \(O\) and \(B\).
If \(O=100\) and \(B=0\) so that the average is weighted completely toward \(O\), we get:
weighted average = \(\frac{4O+6B}{O+B}= \frac{400}{100} = 4\)
If \(O=0\) and \(B=100\) so that the average is weighted completely toward B, we get:
weighted average \(= \frac{4O+6B}{O+B} = \frac{600}{100} = 6\)

In the posted problem, O and B must be positive values, since the feed contains both oats and barley.
As a result, the weighted average cannot actually be equal to 4 or 6 but must be BETWEEN these two values.
Since 5 is the only integer between 4 and 6, the number of piglets = 5.
SUFFICIENT.

I was also confused about this question, and didn't really understand the explanations so came up with my own. Hope this helps.

We know that each piglet has to each 1/2 pound of a mixture, regardless of the ratio of barley to oat. That's it really.

Then, we got the statements, which I will convert to equations.

Let's say x is the total oat given today and y is the total barley given today.

In that case,

x/4 + y/6 = 1/2 (Piglet A gotta eat 1/2 pound).

If you simplify the equation a bit, you get the following:

3x + 2y = 6

Now this doesn't help all that much, since what I need to know is x + y. If I knew this, I would divide this by 1/2 (how many each piglet consumes exactly) and find the total number of piglets. So I'll try to approximate instead.

Dividing both sides by 3, we get
x + (2/3)y = 2 ( This figure is slightly smaller than x + y. So this is our lower bound for x + y )

Dividing both sides by 2, we get
(3/2)x + y = 3 ( This figure is slightly larger than x + y. So this is our upper bound for x + y )

Combining them, we get
2 < x + y < 3

Since we need to divide the total by the total mixture by 1/2 pound to get the piglet number, we get the following
4 < Piglet Number < 6 (only logical number can be 5)