Let u, v, and w denote the lengths of three separate line segments. In

Question

Let u, v, and w denote the lengths of three separate line segments. In order for u, v, and w to represent the lengths of three sides of a triangle, what value must v exceed?

(1) w = u + 5

(2) u = 2 and w = 7

GMATinsight · Accepted Answer

PROPERTY:   For u, v, and w to represent the lengths of three sides of a triangle

SUm of any two numbers must be greater than the third side 
The third side is always greater than difference of other two sides

i.e. |u-w|< v < u+w

Question : What is |u-w| = ?

Statement 1 : w = u + 5

i.e. |u-w| = w-u = 5

SUFFICIENT

Statement 2 : u = 2 and w = 7

i.e. |u-w| = w-u = 5

SUFFICIENT

aNswer: Option D

QuantMadeEasy · Answer

Step 1: Understanding the question 
In a triangle length of third side lie between the difference and sum of the other given sides.
Difference between other two sides < Third Side < Sum of the other two sides 
As u, v and w are the side lengths of a triangle, length of line segment v lies between difference of w and u and sum of w and u
(w-u) < v < (w+v)

Step 2: Understanding statement 1 alone 
(1) w = u + 5
w - v = 5
5 < v 
Sufficient

Step 3: Understanding statement 2 alone 
(2) u = 2 and w = 7
w - v = 5
5 < v 
Sufficient

D is correct

Fighter1095 · Answer

For U,V,W to become the lengths of the sides of the triangle, they must satisfy the two conditions

1). The sum of any two sides of a triangle is always greater than the third side
2). The difference between any two sides of a triangle is less than the third side

statement 1:

u,v,w ==> u,u+5, v

5< v< 2u+5

So, V is always greater than an unique value (5). SUFFICIENT

Statement2:

7-2<v<7+2

5<v<9

So, V is always greater than an unique value (5). SUFFICIENT

Both are sufficient alone. Hence,D

IanStewart · Answer

The sum of two sides of a triangle must exceed the third side. So if one side is u, and the other is u+5, the third side will clearly need to be larger than 5, so that when we add u and the third side, we get something that exceeds u + 5. So I imagine the intended answer is D here.

But that value 5 is not at all unique. Certainly v must exceed 5, but it also must exceed 4, or √2, or 0.01. For information to be sufficient in a DS question asking for a value, you need to be able to find a unique numerical answer for that value, and you can't do that here. I see a lot of prep company DS questions that ask, in various ways, for minimum or maximum values, and that type of question logically doesn't make sense as a DS question. There's a reason no official DS questions are set up this way.

Let u, v, and w denote the lengths of three separate line segments. In

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Let u, v, and w denote the lengths of three separate line segments. In

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards