vinaymimani wrote:
Is the area of the triangle ABC more than 12 sq. units?
I. The GCD of the sides AB and AC is 2.
II. The LCM of the sides AB and AC is 12.
OA and OE after some brainstorming.
A is not sufficient as we will have a Number of AB, AC lengths that can have a GCD of 2. For Eg: 4,6 8,10. For Different AB AC values, the range of the third side will vary.
B is also not sufficient as we will have a number of AB AC lengths that can have LCM 12. For Eg: 4,3 6,12 1,12
If we take A and B together we will have : AB * AC=24. Now if AB and AC are Base and height of the triangle, then we will have the Area as 12. which is not more than 12(as per question)
if we do not have AB and AC Base and height then, AB and AC should be 4 and 6 respectively. That means AC should lie between 2 and 10. If we take AC=8, then using sqrt [s(s-a)(s-b)(s-c)] formula we will have area less than 12. If we have AC =3, then we will have the area nearly 5. IE, always, the area will be less than 12.
There fore the answer should be C. Let me know if that the correct answer