Hi Rich,
So here is how i solved, yet it took from me some time. I hope you can give me an easier way/short cut to solve it.
Step 1: all possible ways to choose 3 from 8 is 8C3 = 56
Step 2: break rule: I listed the 8 numbers as shown: 1 2 3 4 5 6 7 and determined that the first number has 7 possibilities of not making a triangle, the second has 6, the third has 5 and so on until reaching the seventh which has one possibility.
Step 3: add all possibilities: 7+6+5+4+3+2+1= 3.5x8 = 28
Step 4= 52/52 - 28/52 = 22/52 = 11/26.
Is there another way to solve it faster or is this the only way?
Please advise.. thanks
[email protected] wrote:Hi amrabdelnaby,
I'm going to give you some 'hints' so that you can try this question again on your own:
1) This question is based on the Triangle Inequality Theorem - the idea that if you add up any 2 sides of a triangle, THAT sum MUST be greater than the length of the third side (for example, a triangle can have sides of 3, 4 and 5 since 3+4 > 5, 3+5 > 4 and 4+5 > 3....but a triangle CANNOT have sides of 1, 2 and 4 since 1+2 is NOT > 4).
2) Since we're choosing 3 DIFFERENT integers, and the 'order' of the 3 integers does not matter, we can use the Combination formula to figure out the TOTAL number of possible groups of 3 integers.
3) You will probably find it easier to find the number of groups that do NOT create an actual triangle than the number that DO.
GMAT assassins aren't born, they're made,
Rich
