If k is an integer and 2 < k < 7, for how many different

[BTGModeratorVI]

If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2, 7, and k?

(A) one
(B) two
(C) three
(D) four
(E) five

Answer: A
Source: Official guide

[ssrivastava]

K can have 3,4,5,6 as
For a triangle, sum of two sides should always be greater than the third site.
One side is 2. 2+3(K's value) = 5 <7 (given side of triangle). thus, a triangle is not possible.
The only value which satisfies this condition is K=6.Thus, a is the answer

[Brent@GMATPrepNow]

If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2, 7, and k?

(A) one
(B) two
(C) three
(D) four
(E) five

Answer: A
Source: Official guide

IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
DIFFERENCE between A and B < length of third side < SUM of A and B

So, if a triangle has sides 2, 7 and k, we can write: 7 - 2 < k < 7 + 2
Simplify to get: 5 < k < 9

We're told that k is an INTEGER, and that 2 < k < 7.
So, the only possible value of k that satisfies the inequality 5 < k < 9 is k = 6

Answer: A