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kaulnikhil
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1) A few seconds with a pen and pad will rule this one insufficient. If we put A and B as far apart as possible--with C directly in the middle--we'll get a straight line, and a value of AB of exactly 10. Our answer to the question would be No. If we move B anywhere else, we have a triangle. Since each side of a triangle must be shorter than the other two sides, AB must be less that 10 and our answer is Yes. Since we can answer this Yes/No question with a "maybe", we know (1) is insufficient, and answers (A) and (D) are eliminated.
2) Here, picking numbers is easier than playing with the geometry. Since there is no restriction on the location of any of the points, we can have AB and AC both have length of 7, or AB and AC both equal 500. (B) is eliminated, and we now need to combine our statements to evaluation whether the answer is (C) or (E)
Combined, we still don't know. Go back to that straight line--if we set AB = 10, AC = 5 and BC = 5
AC + BC = 10
AB + AC = 15 > 10
Then we can follow both rules with an AB of 10.
On the other hand, draw the point in almost the same relation, but this time add a slight angle. We get a isosceles triangle--AC = 5, BC = 5, and AB = 9.
AC + BC = 10
AB + AC = 14 > 10
So, following both rules, we can get a value of 10 which is not less than 10, or 9 which is. The answer is (E), the choices are not sufficient even together.
