Hi, there. I'm happy to help with this.

Prompt:

How far in miles is city A from city B?

Because these variables will arise, I will introduce

AB = distance from A to B (what the prompt asks for)

AC = distance from A to C

BC = distance form B to C

Statement #1(1) City A is 50 miles away from city C, whereas city B is 30 miles away from city C.

AC = 50 and BC = 30. No information at all given about AB. Statement #1 is

insufficient.

Statement #2(2) City A is 10 more miles far from city C as it is from city B.

(AC) = 10 + (AB)

Here, if we knew (AC), we could find (AB). With only statement #2, though, we don't know anything else. Therefore, statement #2 is

insufficient.

Combined Statements #1 & #2(1) City A is 50 miles away from city C, whereas city B is 30 miles away from city C.

(2) City A is 10 more miles far from city C as it is from city B.

In algebraic form

AC = 50, BC = 30, and (AC) = 10 + (AB)

===> 50 = 10 + (AB) ===> AB = 40

Thus, combining the statements, we are able to determine precisely a numerical answer to the prompt.

Answer = C I believe santu71182 and kys123 are quite correct

Notice, BTW, the three cities form a 3-4-5 right triangle --- a geometrically convenient but geographically unlikely formation.

Here's another free geometry DS question, for more practice.

https://gmat.magoosh.com/questions/1019Does everything I've said make sense? Please let me know if you have any questions.

Mike

_________________

Mike McGarry

Magoosh Test Prep