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Let the three points be anywhere. Since it is not mentioned that it is a triangle therefore we cannot use only Statement 1 using Statement 1 and 2 AB > AC and AB > 10 -BC the second is more interesting as we can start by having A,B and C in a straight line and as we move point B (or C, or A) we get various values of a triangle with values like AB > 10, AB>9 AB>8... so forth which makes both statements not sufficient
Since A, B and C are three different point, AB, BC,and AC are all positive values. so AC will have a value defines as 0 < AC < 10. because if AC> 10, AB becomes negative. SO this inturn gives the value of AB as : 10 > AB > 0. So AB is less than 10.
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the answer is E, and a quick dirty way to do it is by plugging in numbers. First thing to note is that it the original question does not say A B or C are distinct, implying that A could equal B and so on. Also, the way the equations are set up it is just easier to think about the points as numbers.
so is stmt 1 enough? AC + BC = 10. plug in A=2, B=0, C=5 in this case AB<10 now plug in A = 5, B =5, C=1 in this case AB>10. Therefore stmnt 1 is not enough.
is stmt 2 enough? AB +AC >10 A = 11, B = 1, C = 1 and AB >10 A = 1, B = 1, C =10 and AB<10 therefore stmnt 2 is not enough
Together? AC + BC = 10 and AB+AC>10 A=3, B = 2, C =2 and AB<10 A=18, B = 2, C =.5 and AB>10
My pick is also E. If we have been provided with some additional information on the location of the points, for example whether it is a triangle, a straight line or something then provided statements could have been sufficient. _________________
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But if we solve for the inequality in equation 2, we get AB>10-AC. Since AC cannot be negative or zero, AB will be < 10 no matter if the points are in a triangle or collinear. Isn't the second statement enough and answer B?