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

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GMAT Instructor
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Each piglet in a litter is fed exactly one-half pound of a [#permalink]  12 Apr 2007, 06:00
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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?

(1) Piglet A was fed exactly 1/4 of the oats today.
(2) Piglet A was fed exactly 1/6 of the barley today.
Intern
Joined: 29 Aug 2005
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since we are asked for number of piglets... we atleast need total amount of mixture fed to all the piglets.

So the statemens are insufficient to answer.
E
CEO
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Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
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E

Let Total Oat = a
Total Barley = b
Total piglets = x
Each piglet gets 1/2 pound

so x*1/2 = a+b
x = 2(a+b).......EQ1

St1: Clearly INSUFF
St2: Clearly INSUFF

Together: a/4 + b/6 = 1/2
3a+2b = 6...EQ2
Using EQ1 and EQ2 we can't get value of x: INSUFF
GMAT Club Legend
Joined: 07 Jul 2004
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Location: Singapore
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I'm not sure if this is a trick, but just reading the question and statements tells us from Piglet A, there is no way we can tell how many piglets there are.

Click E and carry on to the next question.
Director
Joined: 26 Feb 2006
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Re: DS: 3 little piglets (maybe more) [#permalink]  12 Apr 2007, 21:28
kevincan wrote:
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?

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

definitely there are 4 piglets but could be more than 4.
GMAT Instructor
Joined: 04 Jul 2006
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OA=C There must have been 5 piglets
Director
Joined: 14 Jan 2007
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I agree with 'C'.

Statement1: This gives information about the Oats only. We are not sure how much was the Barley's proportion. So INSUFF

Statement2: Same as above. It doesn't give info about the oats' proportion.

Taking them together:

let total number of piglets are p
Total quantity of oat = x
Total quantity of barley= y
Putting the both statements in equation,
for one piglet
x/4+ y/6 = 1/2 it can be written as
9x + 6y = 18 ------------------(1)

remaining piglets = p -1
p-1 piglets are left with 3x/4 of oats and 5y/6 of barley.
putting in eq. 3x/4 + 5y/6 = (1/2)(p-1)
solving it, 9x +10y = 6p -6 ---------(2)

Solving eq 1 and 2
p = (2y/3) + 4

It means the piglets will be more than 4.
as p is a +ve integer, 2y/3 will be +ve integer. possible values of y = 1.5,3,4.5,6....
from equation1 6y < 18
hence y < 3
so y is 1.5.

That means total number of piglets = 1 + 4 = 5
GMAT Instructor
Joined: 04 Jul 2006
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This is fabulous! Another way to is realise that A must get greater than the average quantity of oats and less than the average quantity of barley or vice versa
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