Solution for Problem 1:

Length of arc BCD = 2*r [given]
We already know,
[2*pie*r / 360] = 2*r / Angle BAD

which gives, Angle BAD = 120
For the Triangle BAD the two arms are equal (radius) BA = AD
So, x = 180 - 120 / 2 = 30

Let me know if this helps,

Choose, B


Solution for Problem 2:

Cogs and Wheel problem -

Total circumference / the cog size = 2*pie*3 / (pie/16) = 96
The number 96 gives for cogs and cog space in between, divide by 2 = 48
Choose C.

Let me know if this helps,

How did you get

length of arc BCD = 2r

I agree with your solution for the second one OpenGmat. I did it a different way, but your solution is a lot smoother and shorter.

Roy, arc BCD is given as 2r. It's a bit tricky at first glance though. It says AB=BC=CD. Well AB is the radius of the circle (A is the center of the circle and B is a point on the circle). Now BC is half of the whole arc BCD and CD is the other half of arc BCD. SO:

AB=r because it's the radius
BC=r because it's equal to AB
CD =r because it's equal to AB

So arc BCD is really BC+CD, which is r+r, which equals 2r

Hope that helps a bit