if the stick is broken into 3 parts, what is the probability that the parts form acute angled triangle?
That’s a lot more complicated, I suspect 🙂 A possible approach might be to eliminate all cases whee c^2 > a^2 + b^2, but even that needs to be handled carefully. Shall think about it and reply again if I find a reasonable answer, but from the point of view of aptitude tests, you may safely assume it is out of scope. If you’re writing an olympiad, however…
The graphical method is as always very elegant.
I tried doing it in a different way and landed on 1/4. Can you please let me know if it is legit?
Let the pieces be A,B and C. Let us choose A first. Clearly it cannot be greater than 1/2 of the total length. So probability of choosing an appropriate A which can lead to a triangle is 1/2.
Now for B.
Let the length of A be x. So 1-x is left. Suppose we take half of it for B. So length of B is (1-x)/2. Then length of C will be 1-(x+(1-x)/2) = 1/2 + x/2. Sum of lengths of A and B = x + (1-x)/2 = 1/2+x/2, which is same as that of C and so violates the triangle rule. So length of B has to be less than half of what is left after A. So we have 1/2 probability of choosing B which leads to a triangle. So total probability = 1/2 * 1/2 = 1/4.
I know it looks rather clumsy, but do you think it is correct? Please let me know
No, I think you have made an error in this statement “Then length of C will be 1-(x+(1-x)/2) = 1/2 + x/2”. It will in fact be (1-x)/2 only. You can use this kind of approach too, but to prove its correctness requires integration.
Oh no! I was so thrilled to get the correct answer.
Thanks a lot for the swift reply.
Hi J I have went through all the posts tagged in xat.can you suggest how to plan the next one month for xat preparation.also can we expect some new posts related to xat?
Assuming you have done QA and VA properly for CAT, focus no DM. If you had left something out earlier, though (such as probability or vocab or grammar), well, then you’ll just have to do that as well. And do a little GK every day, can never be fully prepared of course but do the best you can.
And no there aren’t any more posts planned specifically for XAT; the idea of these was just to showcase a few interesting/challenging questions and show how XAT tests the concepts differently (but not different concepts, typically)
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