Two sides of a triangle have lengths 4 and 10. If the third side

[BTGModeratorVI]

Two sides of a triangle have lengths 4 and 10. If the third side has a length of integer x, how many possible values are there for x ?

A. 4
B. 5
C. 6
D. 7
E. 8

Answer: D
Source: Manhattan prep

[Brent@GMATPrepNow]

Two sides of a triangle have lengths 4 and 10. If the third side has a length of integer x, how many possible values are there for x ?

A. 4
B. 5
C. 6
D. 7
E. 8

Answer: D
Source: Manhattan prep

IMPORTANT RULE: If two sides of a triangle have lengths A and B, then |A-B| < third side < A+B

So, for this question, we get: |10 - 4| < third side < 10 + 4
Simplify: 6 < x < 14

Since x is an INTEGER, x can be 7, 8, 9, 10, 11, 12 or 13 (7 possible values)

Answer: D

Cheers,
Brent