If p is the perimeter of a triangle with one side of 7 and another side of 9, what is the range of possible values for p?
(A) 2 < p < 16
(B) 3 < p < 17
(C) 18 < p < 32
(D) 18 < p < 33
(E) 17 < p < 63
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Sandy
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Explanation

From the Third Side Rule, any side of a triangle must be greater than the difference of the other two sides and less than their sum. Since 9 – 7 = 2 and 9 + 7 = 16, the unknown third side must be between 2 and 16, not inclusive.

To get the lower boundary for the perimeter, add the lower boundary of the third side to the other two sides: 2 + 7 + 9 = 18. To get the upper boundary for the perimeter, add the upper boundary for the third side to the other two sides: 16 + 7 + 9 = 32. Thus, p must be between 18 and 32, not inclusive—in other words, 18 < p < 32.
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Sandy
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