Question 200548
There are 15 blue jays and 14 orioles perched in 3 trees . each tree has at least 4 blue jays, and 2 orioles, if no tree has more orioles than blue jays, then the largest number of birds that can be in one tree is 
a)11 b) 12 c) 13 d) 14 e) 15
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Pretend we have three trees, TREES 1, 2, and 3 and 
we are going to place the birds in the trees so that 
TREE 1 will have as many birds as possible, under the 
given conditions.

Make this chart


                     TREE 1         TREE 2               TREE 3    
No. of Blue Jays
No. of Orioles

We start by placing 4 bluejays and 2 orioles in each tree,
since each tree must have that:

                     TREE 1         TREE 2               TREE 3    
No. of Blue Jays       4              4                    4 
No. of Orioles         2              2                    2

So 

1. Now we have accounted for 12 of the 15 blue jays, leaving 
3 more blue jays to place.

and

2. We have accounted for 6 of the 14 orioles, leaving 8 more orioles
to place. 
  
Now since we're letting Tree 1 have the most birds, let's put all 
three of the remaining blue jays in TREE 1, making there be 7 Blue 
Jays there.

                     TREE 1         TREE 2               TREE 3    
No. of Blue Jays       7              4                    4 
No. of Orioles         2              2                    2

Now we have placed all the Blue Jays.  We still have 8 more orioles
to place.  We can only put 5 more orioles in TREE 1, because TREE 1
can't have more orioles than blue jays.  So we have

                     TREE 1         TREE 2               TREE 3    
No. of Blue Jays       7              4                    4 
No. of Orioles         7              2                    2

That leaves 3 more orioles and so we can put two of them in in TREE 2 
and 1 in TREE 2, or vice-versa.  So we either end up with THIS:

                     TREE 1         TREE 2               TREE 3    
No. of Blue Jays       7              4                    4 
No. of Orioles         7              4                    3 

OR with THIS:

                     TREE 1         TREE 2               TREE 3    
No. of Blue Jays       7              4                    4 
No. of Orioles         7              3                    4  

Either way TREE 1 has 14 birds.  So that's the answer d).

Edwin</pre>