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Each piglet in a litter is fed exactly one-half pound of a mixture of 02 Sep 2020, 13:05
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VeritasKarishma
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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,

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.
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hello,
I appreciate the way you crafted the answer. For this, since the ratios are 1/4 and 1/6 and that the n is an integer, we got n=5. But what if it were some other ratios, such as 1/4 and 1/7, wouldn't n equal to 5 or, 6? I mean what's the reasoning here.

Best,
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Each piglet in a litter is fed exactly one-half pound of a mixture of 23 May 2021, 13:36
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VeritasKarishma - what is the significance of this statement in the question stem ?

The ratio of the amount of barley to that of oats varies from piglet to piglet.

Because of above statement - I did not believe you could assume that each pig ate 20 % of the entire food

Maybe pig A ate 18 % | Pig B ate 21 % | Pig C ate 23 % (As long as it is between 16.67 % and 25 %)
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Each piglet in a litter is fed exactly one-half pound of a mixture of 24 May 2021, 00:51
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raaz8522

hello,
I appreciate the way you crafted the answer. For this, since the ratios are 1/4 and 1/6 and that the n is an integer, we got n=5. But what if it were some other ratios, such as 1/4 and 1/7, wouldn't n equal to 5 or, 6? I mean what's the reasoning here.

Best,
Show more

raaz8522 - Please tag me if a question is directed to me. I try to get to all "mentions".

Though late, here is the reply - If we were given that 1/7 < 1/n < 1/4, n could be 5 or 6 and hence we would not get a unique answer. In that case, answer would be (E).

The way the question is worded, you cannot find the exact number of piglets except if there is only one integer value within the given range.

We know that food is equally distributed among all so each piglet gets 1/n of the food.
If piglet A gets 1/4 of oats and 1/7 of barley (your hypothetical case), piglet 1 got a total of 1/n of the grains such that 1/7 < 1/n < 1/4. This is all the info we have.
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Each piglet in a litter is fed exactly one-half pound of a mixture of 24 May 2021, 00:59
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VeritasKarishma - what is the significance of this statement in the question stem ?

The ratio of the amount of barley to that of oats varies from piglet to piglet.

Because of above statement - I did not believe you could assume that each pig ate 20 % of the entire food

Maybe pig A ate 18 % | Pig B ate 21 % | Pig C ate 23 % (As long as it is between 16.67 % and 25 %)
Show more

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.
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Each piglet in a litter is fed exactly one-half pound of a mixture of 24 May 2021, 07:33
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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 %
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Each piglet in a litter is fed exactly one-half pound of a mixture of 25 May 2021, 00:12
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jabhatta2
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 %
Show more

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.
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Each piglet in a litter is fed exactly one-half pound of a mixture of 25 May 2021, 04:29
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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.
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Each piglet in a litter is fed exactly one-half pound of a mixture of 25 May 2021, 23:34
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jabhatta2
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.
Show more

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.
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Each piglet in a litter is fed exactly one-half pound of a mixture of 15 Jun 2021, 06:30
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Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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Each piglet in a litter is fed exactly one-half pound of a mixture of 13 Jul 2022, 04:01
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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
Show more

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.

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Each piglet in a litter is fed exactly one-half pound of a mixture of 14 Jul 2022, 05:23
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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.

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Each piglet in a litter is fed exactly one-half pound of a mixture of 31 Jul 2023, 12:18
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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)
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Each piglet in a litter is fed exactly one-half pound of a mixture of 05 Nov 2024, 02:12
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My solution is slightly different than the ones posted on the forum.

When you combine both statements we are given that Piglet A was fed 1/4 of the Oats & 1/6 of the Barley

So let's say that the total quantity of oats is 4X & the total quantity of Barley is 6Y (I try to avoid fractions when it is possible...). So basically, we are given that piglet A was fed 1X + 1Y = 0.5 pounds

Also, 4X + 4Y = 2 (0.5 * 4) pounds & similarly 6X + 6Y = 3 pounds

Therefore, 4X + 4Y (2 pounds) < 4X + 6Y (actual quantity given) < 6X + 6Y (3 pounds)

The Total Quantity MUST BE 2.5 pounds because it is the only possible value between 2 and 3 pounds AND is a multiple of 0.5 pounds. 4X + 6Y has to be a multiple of 0.5 because each piglet was fed exactly 0.5 pounds.

Since we now know that the total quantity is 2.5 pounds and each piglet was fed 0.5 pounds, there are 5 piglets in total (2.5/0.5 = 5)

I hope my solution was not too confusing.
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Each piglet in a litter is fed exactly one-half pound of a mixture of 18 Dec 2024, 09:02
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After reviewing all the approaches above, I find my method very intuitive.
Please refer to the attachment for the details. The basic idea is to handle the problem using lines in a Cartesian coordinate system.
I wrote some simple explanation in the pic, if you need further explanation, please let me know.
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File comment: Intuitive Solution
photo_2024-12-18_23-30-11.jpg
photo_2024-12-18_23-30-11.jpg [ 271.77 KiB | Viewed 585 times ]

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