The lengths of three line segments are 6, (d + 3), and (2d - 4). Which

Question

The lengths of three line segments are 6, (d + 3), and (2d - 4). Which of the following describes all values of d for which a triangle can be created with given three line segments ?

A.  \frac{3}{7} < d < 11

B.  \frac{5}{3} < d < 12

C.  \frac{7}{3} < d < 13

D.  \frac{8}{3 }< d < 13

E.  \frac{10}{3 }< d < 13

GMATinsight · Answer

For a triangle to be formed, the sum of two sides must be greater than the third side Sides are 6, (d + 3), and (2d - 4) i.e. Case 1: 6 + (d + 3) > (2d - 4) i.e. d < 13 Case 2: 6 + (2d - 4) > (d + 3) i.e. d > 1 Case 3: (2d - 4) + (d + 3) > 6 i.e. d > 7/3 i.e. 7/3 < d < 13 Answer: Option C

sanjitscorps18 · Answer

let a = 6, b = (d + 3), and c = (2d - 4) To create a triangle the following must be satisfied (i) a < b + c => 3d - 1 > 6 => 3d > 7 => d > 7/3 (ii) a > b - c |2d - 4 - d - 3| < 6 => | d - 7 | < 6 => either d < 13 or d > 1 Combining both we get \frac{7}{3} < d < 13 Option C

KarishmaB · Answer

Plug in from the options:
Looking at the range of d in the options, we see that the lowest integer value of d could be 1, 2, 3 or 4.
Put d = 2, sides are 6, 5, 0. We cannot make a triangle with side 0. Since options (A) and (B) include d = 2, they don't work. 
Put d = 2.5, sides are 6, 5.5, 1. We can make a triangle with these sides because sum of each pair is greater than the third side (in other words, difference between any two sides is less than the third side). So d = 2.5 should be a part of the range. It is included in (C) but not in (D) and (E).

Answer (C)

$!vakumar.m · Answer

Simplest approach is to apply the  Triangle inequality property  
difference of (any) two sides < third side < sum of the two sides

the three sides given here are 6, d+3, 2d-4
so we can write the inequality equation as 
 (2d-4) - (d+3) < 6 < (2d-4) + (d+3) 
=>  d-7 < 6 < 3d -1 
lets solve  d-7 < 6 
we get  d<13  .............(1)

and from  6<3d -1  
we get  \frac{7}{3 }< d ...........(2)

from inequalities 1 n 2, we get  \frac{7}{3} < d < 13

Answer: C

The lengths of three line segments are 6, (d + 3), and (2d - 4). Which

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GMAT Problem Solving (PS) Questions

The lengths of three line segments are 6, (d + 3), and (2d - 4). Which

Prep Toolkit

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My Rewards