Carcass wrote:
In an empty square field, n rows of n trees are planted so that the whole field is filled with trees. If k of these trees lie along the boundary of the field, which of the following is a possible value for k?
A. 14
B. 49
C. 86
D. 125
E. 276
320 GRE Math Problems
The total number of trees around the edge (k) will always be a
multiple of 4Here's why:
Notice that we can take this arrangement of trees...
... and divide the trees into
4 groups of 3, and
4 groups of
1So, the total number of trees in this example =
(4)(3) +
(4)(1) = 4(3 + 1) =
4(4)
This means the total number of trees is a multiple of
4Similarly, we can take this arrangement of trees...
... and divide the trees into
4 groups of 5, and
4 groups of
1So, the total number of trees in this example =
(4)(5) +
(4)(1) = 4(5 + 1) =
4(6)
This means the total number of trees is a multiple of
4As you can see, we can use this approach to show that the total number of trees will always be a multiple of
4 When we check the answer choices, only one answer choice (276) is a multiple of
4 So, the correct answer is E