How far in miles is city A from city B?

I think it meant city C is 10 miles further than city B. ABC could be a triangle and since you know 3 of the vertices u can solve. Although It is a much simpler question. A to C is 50m, so if AC is the miles more than AB the length of AB is 40.

Need both pieces of info, C

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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.


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/1019

Does everything I've said make sense? Please let me know if you have any questions.

Mike