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The distance from town A to town B is five miles. C is six

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by varun289 » Wed Apr 24, 2013 3:53 am
The distance from town A to town B is five miles. C is six miles from B. Which of the following could be the distance form A to C?

I 11
II 1
III 7

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, or III.
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by rintoo22 » Wed Apr 24, 2013 4:20 am
The distance from town A to town B is five miles. C is six miles from B. Which of the following could be the distance form A to C?

I 11
II 1
III 7
Answer E. In my opinion.
Traingle Inequality rule satify for option III. And I and II can be on the same line.
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by GMATGuruNY » Wed Apr 24, 2013 4:25 am
varun289 wrote:The distance from town A to town B is five miles. C is six miles from B. Which of the following could be the distance form A to C?

I 11
II 1
III 7

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, or III.
Case 1: In triangle ABC, AB=5 and BC = 6
Here, the length of AC must be LESS THAN THE SUM of other two sides and GREATER THAN THE DIFFERENCE of the other two sides:
6-5 < AC < 6+5
1 < AC < 11.
Thus, it's possible that AC = 7.
Eliminate any answer choice that does not include III (A, B and C).

Case 2: A <--5 miles--> B <--6 miles--> C
Here, AC = 5+6 = 11 miles.
Eliminate D, which does not include I.

The correct answer is E.

In the following case, AC=1:
C <--1 mile--> A <--5 miles--> B.
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by srcc25anu » Wed Apr 24, 2013 4:37 am
For Option 1 and 2 see attached below.

For option 3, if A, B and C form a triangle, then 3rd side is less than sum of other 2 sides and 3rd side is greater than difference of other 2 sides. Following this rule, distance from A to C could be anywhere from (6-5) 1 to (6+5) 11

Hence E
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