BTGmoderatorLU wrote:How far is it from town A to town B? Town C is 12 miles east of town A.

1) Town C is south of town B.
2) It is 9 miles from town B and town C.

The OA is C.

From statement 1, we don't have any idea about the distance between A and B.
From statement 2, we got the distance between B and C but no clue about A and B.

Combining we can form a right triangle and the distance is 15 miles between A and B.

Please, can anyone explain another way to solve this DS question? Thanks in advance.

You have done it correctly. With the given information, we have ABC as a rightangled triangle with AB as its hypotenuse, AC as the base (= 12) and BC as the altitude (= 9). Upon solving, we get the unique value of AB = 15. Sufficient.

Hope this helps!

-Jay
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BTGmoderatorLU wrote:How far is it from town A to town B? Town C is 12 miles east of town A.

1) Town C is south of town B.
2) It is 9 miles from town B and town C.

Statement One Alone:

Town C is south of town B.

Since we don't know how far south town B is from town C, we can't determine the distance from town A to town B. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

It is 9 miles from town B and town C.

Since we don't know what direction town B is from town C, we can't determine the distance from town A to town B. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

With both statements, we know that town B is 9 miles south from town C. Since town C is 2 miles east of town A. By the Pythagorean theorem, we have:

9^2 + 12^2 = d^2

81 + 144 = d^2

225 = d^2

15 = d

Answer: C