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# If p is the perimeter of a triangle with one side of 7 and another sid

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Math Expert
Joined: 02 Sep 2009
Posts: 49916
If p is the perimeter of a triangle with one side of 7 and another sid  [#permalink]

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21 Sep 2018, 01:11
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Difficulty:

35% (medium)

Question Stats:

70% (01:09) correct 30% (00:41) wrong based on 36 sessions

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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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Re: If p is the perimeter of a triangle with one side of 7 and another sid  [#permalink]

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21 Sep 2018, 01:17
1
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

Property: For a triangle to exist Sum of any two sides of the triangle MUST be greater than the third side

For gives sides of length 7 and 9

let, third side = x

Now, x+7 > 9 i.e. x > 2
and 9+7 > x i.e. x < 16

i.e. Perimeter, p = 7+9+x

i.e. 7+9+2 < p < 7+9+16
i.e. 18 < p < 32

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If p is the perimeter of a triangle with one side of 7 and another sid  [#permalink]

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21 Sep 2018, 05:24
I answered in less than 30sec and got caught by the answer trap A.
So careful with the twist a the end of the question we are looking for the perimeter not the missing side.
C indeed it is.
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 365
Re: If p is the perimeter of a triangle with one side of 7 and another sid  [#permalink]

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21 Sep 2018, 08:00
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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Re: If p is the perimeter of a triangle with one side of 7 and another sid &nbs [#permalink] 21 Sep 2018, 08:00
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