How far in miles is city A from city B?

(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.

Statement 1 is insufficient,

A_____________B_________________C
30 km
50 km

OR

A___________________C_________________B
50 km 30 km

Statement 2 is also insufficient
rather in this , city A could be in any direction, north, south ,east west
BTW same case with option 1 also
must say something wrong with the question, as the first statement says A is 50 km far and the second says 10 kms far from city C
what u say??
IMO E
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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
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Mike McGarry
Magoosh Test Prep