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Another way, perhaps easier in calculation, is this.

5sqrt(2) is app 7. Therefore the triangle has a side 7, and 12 (=5+7). And we know the long side would be 13. However we know the two short sides are really a little longer than 7 and 12, so the long side must be a little longer than 13. Therefore 14.

I'd be sure about this answer if there isn't a choice of 15. However since there ARE two answers above 13, I'd use this as a sanity check for my other answer, or I'd useing this technique to make a quick guess if I'm short of time.

I think the rule being tested here is that the side of a triangle cannot be greater than the (sum of the other two sides) and cannot be less than the difference of the other two sides.

given that
what is the smallest possible value thats in between 15 and 5, is 11?

cant 11 be the answer....again we dont know what angle southeast it is...

if we have a 45-45-90 triangle then there is no way that one side can be 10! it has sqrt(2)*5 which is less than 10.

This is also same as finding the larger diagnal of a parellelogram where the sides are a and b.
I think it is something like this(I am not sure of the exact formula.Please correct me if you know ithe formula).
larger diagnal = sqrt(a^2+b^2+2abCosB). In our case, a=5,b=10 and B=90+45 degrees.

I think the rule being tested here is that the side of a triangle cannot be greater than the (sum of the other two sides) and cannot be less than the difference of the other two sides.

given that what is the smallest possible value thats in between 15 and 5, is 11?

cant 11 be the answer....again we dont know what angle southeast it is...

if we have a 45-45-90 triangle then there is no way that one side can be 10! it has sqrt(2)*5 which is less than 10.

You know that was the first thing that came to my mind and i do believe that is what's being tested. Based on the options, i would have picked D anyways since it is less than 15.

Now can someone please backup the theory that southeast is 45degrees? Please don't mislead us to memorize unfounded rules. thanks

"city B is 5 miles east of city A. city C is 10 miles southeast of city B. which of the following is the closest to distance from city A to city C? "

who stated that Southeast means : 45*. I don t agree. I would say 12.

12^2 is the closest of 125 and following that C is still southeast of B B is still east of A

Besides I doubt that such question will pop up during the quest

I will love to believe this kinda of complexity won't pop up on the test. I know trignomerty is not tested and it seems a couple of people used trig to solve it thus i won't even waste my time internalizing this

Now can someone please backup the theory that southeast is 45degrees?

Please look at my post just before yours. It is the definition from the dictionary.

Folaa3 wrote:

I will love to believe this kinda of complexity won't pop up on the test. I know trignomerty is not tested and it seems a couple of people used trig to solve it thus i won't even waste my time internalizing this.

It may be a little stretched from the GMAT level. Or perhaps we could say this would be a hard level GMAT question. However you do not need to know trignomerty to solve this question. In other words, this is not totally out of scope of GMAT.

I think this is a good question. First, it tests your attention level. (Yes, can you correctly draw the triangle out? Did you notice it was southeast instead of south?) Second, it tests your understanding about straight triangles. (c^2=a^2+b^2) Third, it tests your arithmatic abilities. (The level of calculation is a little bit harder than a GMAT question normally requires, I believe. But if you can do it correctly, it means you would not have arithmatic problems for the eaiser level questions.)

Now can someone please backup the theory that southeast is 45degrees? Please don't mislead us to memorize unfounded rules. thanks[/quote]

Southeast is actually 45degees. It's a fact in trignometry/bearing. If it were something else, say 60 degrees, it will have been stated that Point C is 60 degrees due south of B. This question actually seems to need trignomery, since we are given one angle as 135 degrees and two sides (0.5 A * B sin C). I also guessed between 14 and 15, and my guess was 14.