eybrj2 wrote:
The figure above shows a streetlight that consists of a glass sphere, with center O, placed on top of a vertical pole that is 4 meters high. What is the height QR of the streetlight?
(1) The radius of the pole is 6 centimeters.
(2) The radius OQ of the sphere is 24 centimeters.
There is absolutely no need to actually calculate the height QR. Just notice that the height of a pole (given) and the radius of the pole completely defines (fixes) it. The same way the radius of a sphere completely defines (fixes) it. So, only if we have defined (fixed) pole and defined (fixed) sphere we can be able to say
how much below the top of the pole the sphere goes, and we'll be able to calculate QR.
Both statements together provide us with the info needed: the radius of the pole and the radius of the sphere. Hence when taken together statements are sufficient.
Answer: C.
P.S. When dealing with DS problems try to avoid calculations as much as possible. Remember DS problems do not ask you to solve, but rather to determine if you are ABLE to solve and in many cases you can determine that a statement is sufficient without working out all of the math.
Hope it's clear.
If the sphere sits on the pole its one point would touch the pole, hence the height of street lamp would be pole height + sphere diameter