Bunuel wrote:

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

\(?\,\,\,:\,\,\,a + b + c\,\, = \,\,16 + c\,\,\,\,{\text{possibilities}}\)

GMATinsight´s approach is perfect, but to avoid two inequalities done separately, we may present the result in its "full version":

Given a,b,c > 0, a triangle with (lengths of) sides a,b,c exists if, and only if, each side is greater than the difference and less than the sum of the other two.Hence:

\(9 - 7 < c < 9 + 7\,\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{a + b\,\, = \,\,7 + 9\,\, = \,\,\boxed{16}} \,\,\,\,\,\,\,\boxed{16} + 2 < \boxed{a + b} + c < \boxed{16} + 16\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,18 < p < 32\)

The right answer is therefore (C).

This solution follows the notations and rationale taught in the GMATH method.

Regards,

Fabio.

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)

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