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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...

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by AAPL » Fri Aug 14, 2020 4:51 am

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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

OA C
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Source: — Data Sufficiency |

[b]Given that:[/b] Total food mixture of oat and barley = 0.5 pound
Let the number of oats = o
Let the number of barley = b
o + b = 0.5


[b]Target question =>[/b]How many piglets are in the litter?


[b]Statement 1 =>[/b] Piglet A was fed exactly 1/4 of the oats today
The proportion of barley in the mixture is unknown. Statement 1 is NOT SUFFICIENT


[b]Statement 2 =>[/b] Pig A was fed exactly 1/6 of the barley today
The proportion of oats in the food mixture is unknown and statement 2 is NOT SUFFICIENT


[b]Combining both statements together =>[/b]
Let the total number of piglets = x
From statement 1 and 2 => 1/4 o + 1/6 b = 8/2
3o + 2b/12 = 1/2
3o + 2b = 6 .......eqn 1
For total food
o + b = 0.5 * x
o/0.5 + b/0.5 = 0.5x/0.5
2o + 2b = x ......eqn 2
Subtracting eqn 2 from 1
3o + 2b = 6 - 2o + 2b = x
o = 6 - x
x = 6 - 0


Since oatmeal(o) cannot be 0 and x is expected to be a positive integer
The least possible value of o = 1
if o = 1 then x is 5
Check: 3o + 2b = 6
3(1) + 2b = 6
2b/2 = 6 - 3 = 3/2
b = 1.5
o = 1 and b = 1.5
But if ''o''=2 then x is 4
check 3o + 2b = 6
3(2) + 2b = 6
2b = 6-6
b = 0


This is not possible because the food mixture is expected to have a proportion of barley and oatmeal hence ''o'' cannot be 2 since ''o'' is confirmed to be 1 and x = 5. Both statements together ARE SUFFICIENT


[b]Answer = C[/b]
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[b]Given that:[/b] Total food mixture of oat and barley = 0.5 pound
Let the number of oats = o
Let the number of barley = b
o + b = 0.5


[b]Target question =>[/b]How many piglets are in the litter?


[b]Statement 1 =>[/b] Piglet A was fed exactly 1/4 of the oats today
The proportion of barley in the mixture is unknown. Statement 1 is NOT SUFFICIENT


[b]Statement 2 =>[/b] Pig A was fed exactly 1/6 of the barley today
The proportion of oats in the food mixture is unknown and statement 2 is NOT SUFFICIENT


[b]Combining both statements together =>[/b]
Let the total number of piglets = x
From statement 1 and 2 => 1/4 o + 1/6 b = 8/2
3o + 2b/12 = 1/2
3o + 2b = 6 .......eqn 1
For total food
o + b = 0.5 * x
o/0.5 + b/0.5 = 0.5x/0.5
2o + 2b = x ......eqn 2
Subtracting eqn 2 from 1
3o + 2b = 6 - 2o + 2b = x
o = 6 - x
x = 6 - 0


Since oatmeal(o) cannot be 0 and x is expected to be a positive integer
The least possible value of o = 1
if o = 1 then x is 5
Check: 3o + 2b = 6
3(1) + 2b = 6
2b/2 = 6 - 3 = 3/2
b = 1.5
o = 1 and b = 1.5
But if ''o''=2 then x is 4
check 3o + 2b = 6
3(2) + 2b = 6
2b = 6-6
b = 0


This is not possible because the food mixture is expected to have a proportion of barley and oatmeal hence ''o'' cannot be 2 since ''o'' is confirmed to be 1 and x = 5. Both statements together ARE SUFFICIENT


[b]Answer = C[/b]
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