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

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Senior Manager
Joined: 02 Apr 2014
Posts: 471
GMAT 1: 700 Q50 V34
Each piglet in a litter is fed exactly one-half pound of a  [#permalink]

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19 Feb 2018, 00:47
Great Question.
Let n = number of piglets.
Let 4x = total oats in pounds, 6y = total barley in pounds
Piglet A: $$x(1/4th) + y(1/6th) = 1.5$$ ----(1)
Remaining piglets: $$3x + 5y = 1.5(n-1)$$
= $$3x + 3y + 2y = 1.5n - 1.5$$
= 3(x+y) + 2y = 1.5n - 1.5
= $$3(1.5) + 2y = 1.5n - 1.5$$ (from --(1))
= $$1.5n = 6 + 2y$$
= $$n = 2(y+3)/1.5$$
=> $$n = 4(y+3)/3$$
Now note, n is an integer, also we have 4, (y+3)/3 which is a fraction,
multiplication of 4 and (y+3)/3 a fraction can yield integer, only if the fraction is multiple of 1.25
if $$(y+3)/3$$ = 1.25 => y = 0.75
if $$(y+3)/3$$ = 2.5 => y = 4.5 (but y cannot be greater than 1.5)
also y cannot be zero and make (y+3)/3 = 1 ((as given prompt, each piglet is fed some grain))
so $$(y+3)/3$$ must be 1.25 and n = 5 => sufficient (C)
Manager
Joined: 10 Apr 2018
Posts: 181
Re: Each piglet in a litter is fed exactly one-half pound of a  [#permalink]

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12 Sep 2018, 11:26
hellosanthosh2k2 wrote:
Great Question.
Let n = number of piglets.
Let 4x = total oats in pounds, 6y = total barley in pounds
Piglet A: $$x(1/4th) + y(1/6th) = 1.5$$ ----(1)
Remaining piglets: $$3x + 5y = 1.5(n-1)$$
= $$3x + 3y + 2y = 1.5n - 1.5$$
= 3(x+y) + 2y = 1.5n - 1.5
= $$3(1.5) + 2y = 1.5n - 1.5$$ (from --(1))
= $$1.5n = 6 + 2y$$
= $$n = 2(y+3)/1.5$$
=> $$n = 4(y+3)/3$$
Now note, n is an integer, also we have 4, (y+3)/3 which is a fraction,
multiplication of 4 and (y+3)/3 a fraction can yield integer, only if the fraction is multiple of 1.25
if $$(y+3)/3$$ = 1.25 => y = 0.75
if $$(y+3)/3$$ = 2.5 => y = 4.5 (but y cannot be greater than 1.5)
also y cannot be zero and make (y+3)/3 = 1 ((as given prompt, each piglet is fed some grain))
so $$(y+3)/3$$ must be 1.25 and n = 5 => sufficient (C)

Hello hellosanthosh2k2,

How did u get this $$x(1/4th) + y(1/6th) = 1.5$$ . shouldn't it be 0.5.

Well i used a approach similar to yours, here is what i did

Say total piglets is x

say piglet a was fed$$\frac{1}{4}$$ of and$$\frac{1}{6}$$ of , then each piglet was fed$$\frac{1}{4}$$+$$\frac{1}{6}$$ = $$\frac{5}{12}.$$

Remaining food is$$\frac{3}{4}+\frac{5}{6}$$ =$$\frac{19}{12}$$

So the Remaining food was equally divided among (x-1) piglets with each getting $$\frac{5}{12}$$

so $$\frac{5}{12}* (x-1)= \frac{19}{12)$$

So x is some value.
Hence C is sufficient.

Probus
Manager
Joined: 10 Apr 2018
Posts: 181
Each piglet in a litter is fed exactly one-half pound of a  [#permalink]

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12 Sep 2018, 11:27
Hello hellosanthosh2k2,

How did u get this $$x(1/4th) + y(1/6th) = 1.5$$ . shouldn't it be 0.5.

Well i used a approach similar to yours, here is what i did

Say total piglets is x

say piglet a was fed$$\frac{1}{4}$$ of oats and$$\frac{1}{6}$$ of barley , then each piglet was fed$$\frac{1}{4}$$+$$\frac{1}{6}$$ = $$\frac{5}{12}.$$

Remaining food is$$\frac{3}{4}+\frac{5}{6}$$ =$$\frac{19}{12}$$

So the Remaining food was equally divided among (x-1) piglets with each getting $$\frac{5}{12}$$

so $$\frac{5}{12}* (x-1)= \frac{19}{12)$$

So x is some value.
Hence C is sufficient.

Probus
Intern
Joined: 16 Sep 2012
Posts: 11
Re: Each piglet in a litter is fed exactly one-half pound of a  [#permalink]

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15 Sep 2018, 04:42
Let's say ratio of oats to total mixture in each piglet A,B,C,D,... be a,b,c,d,.. respectively.
considering condition 1 : (1/2)*a=(1/4)*[(1/2)*(a)+(1/2)*(b)+...so on]
this equation gets down to 3a=b+c+d+..so on -------------(I)
this equation does not restrict us to any number of piglets so condition 1 by itself is not sufficient

considering only condition 2: on similar lines
(1/2)*(1-a)=(1/6)*[(1/2)*(1-a)+(1/2)*(1-b)+...so on]
5(1-a)=(1-b)+(1-c)+...so on -------------------(II)
this equation does not restrict us to any number of piglets so condition 2 by itself is not sufficient
5-2a=[b+c+d+..so on]+[(1-b)+(1-c)+...so on]=1+1+1+1+..so on
As R.H.S of above equation is an integer, L.H.S of above equation gives a=1/2
So there are 5 piglets.
Re: Each piglet in a litter is fed exactly one-half pound of a &nbs [#permalink] 15 Sep 2018, 04:42

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