I am not sure of the answer choice I would have marked.. but I can try..
Centered @ (0, 0)... and also A > B > 0 this means both A and B are positive and both lie inside the Quad I
so we dont care for the remaining Quads and we get the probability of both being positive as (1/4).
prob of A > B, this I am not sure how to figure out..
very frankly.. if I would have not known the correct answer from you, I would have suggested option B only, since A > B > 0 can be percieved as a way of saying that both A and B are greater than 0.
Lemme know if you get the means to figure out the correct answer..
You just draw the line x=y.And for all the points below the line x=y ,x>y.These occupies half of the I quardrant.
You can observe that only in the first quadrant the coordinates are positive ie. A>0 and B>0 as given in the condition. Also there are total 8 patitions in which we can divide the xy plane which i cant draw here to explain. Also A>B in I quadrant below line x=y. Hence probability is 1/8 obviously.I think u have not checked for the condition th is both coordiantes should be positive.
one qq... hows do you divide a XY plane into 8 parts..??.. I knew of only 4 quads and I would really appreciate if you could explain me this 8 parts thing.. ;)
I dont recall all the co-ordinate geometry fundas, but as far as I remember, it used to have only 4 quads in xy plane.. plz share your thoughts..
Let the radius be 2units... X can be 2units and Y can be 0.00000000001unit, or vice versa...
How did you reach the conclusion highlighted above conclusion..??..
See varun. take a graph paper and draw lines two lines x=y passing through origin these two lines you will observe will divivde the x,y plane in 8 equal area sections. Now by prniciple of geometry the x coordinate is greater than y in half of I quadrant only for x>y>0. I hope you understood.
The four sides of a parallelogram all have the same length. If the angle between two of the sides is 60 degrees, what is the ratio of the shorter diagonal to the longer diagonal? A. 1 : 3 B. 1 : 3 C. 3 : 2 D. 3 : 4 E. 2 : 3
The four sides of a parallelogram all have the same length. If the angle between two of the sides is 60 degrees, what is the ratio of the shorter diagonal to the longer diagonal? A. 1 : 3 B. 1 : 3 C. 3 : 2 D. 3 : 4 E. 2 : 3
Any idea how to solve this?
Sol: It is a rhombus.So if all sides be equal to a. Now,cos 60=1/2=2a^2-l1^2/2*a^2=>a^2=2a^2-l1^2=>a^2=l1^2...i
And cos 120=-1/2=2a^2-l1^2/2*a^2=>-a^2=2a^2-l1^2=>3a^2=l2^2...ii i and ii=>l1^2/l2^2=1/3=>l1/l2=1/3
The four sides of a parallelogram all have the same length. If the angle between two of the sides is 60 degrees, what is the ratio of the shorter diagonal to the longer diagonal? A. 1 : 3 B. 1 : 3 C. 3 : 2 D. 3 : 4 E. 2 : 3
Any idea how to solve this?
let say diagonals are d1,d2 Lets say one of the daigonal facing 60 degree angle is d1.this forms equilateral triangle so d1=4. Total area of parralelegram=2*sqrt(3)*4*4/4=1/2*d1*d2 d2=sqrt(3) d1:d2=1:sqrt(3)
the triangle formed by the intersection of will have angles as 30 deg, 60 deg and 90 deg. So d1/2 = x cos 60 = x/2, d1 = x d2/2 = x sin 60 = xsqrt(3)/2, d2 = x sqrt(3)
i keep visiting this thread and share some of the good questions from my old GMAT notes. here is another one.
5 chairs, 2 couple and one single person. What is the probability that no couple sit together.
The Total ways to arrange 5 people=!5 case1. When first couple is sitting together=!4*!2 cas2.When second couple sitting together=!4*!2 case3.when both couples sitting together=!3*!2*!2 so the number of ways when couples are sitting together=case1+case2-case3 =96-24=72 so probability=72/120=3/5
