The figure above shows a streetlight that consists of a

Question

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.

pradeepss · Accepted Answer

See that attached picture. We need both radius of the glass sphere and the pole in order to calculate the total height of the combined structure.

ANSWER: C

sahilvijay · Answer

Ans is C

1) Radius of pole = 6
We dont know the radius of light => unknown for calculating height above pole
A,D eliminated

2) Radius of light known but radius of pole unknown => unknown for calculating how much light is inside of pole ie the lower part of sphere
B eliminated

Combine

radius light =24
radius pole = 6
then how much centre of light above pole can be found by pythogoras theorm

Ht of centre above pole = √ ( 24^2-6^2 = h
Ht of light RQ = 400+h+24 
sufficient
C is the Answer

Bunuel · Answer

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.

boomtangboy · Answer

Hi Bunuel, I'm slightly confused with why do we need the radius of the pole ? 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 Thus B should be sufficient correct? Thanks in advance :-D

Bunuel · Answer

No, it does't "sit" on the pole it's placed IN the circular top of the pole (notice that the sphere is slightly below the top of the pole). Now, consider extreme case when the radius of the pole is more than the radius of the sphere, in that case the sphere will just fall into it.

Hope it's clear.

boomtangboy · Answer

Hi Bunuel,

Thanks for your reply but I have this question, may be its even silly but in your reply you assumed the pole to be hollow i.e a steel pipe but the question says pole i.e solid pole like a vaulting pole hence the chance of the sphere going into the pole is nil.

I dont know how the GMAT defines such terms cause both possibilities exist

Bunuel · Answer

Notice that the sphere is slightly below the top of the pole.

eybrj2 · Answer

I was also confused the part that boomtangboy mentioned above.

Bunuel says that the sphere slightly goes into the pole in the picture, but should we solve the problem with the information in the Q, not the picture. The question doesn't say that the sphere slightly goes into the pole.

So confusing.... :cry:

Bunuel · Answer

But the question doesn't say the opposite either: why are you assuming that the sphere and the pole have only one tangent point?

In addition if it were the case then the whole point of the drawing and the radius of the pole makes little sense, because the question just becomes about adding two quantities: length of the pole and the diameter of the sphere.

carcass · Answer

Only with what Bunuel says we have the answer C, whereas if the two figures touch each other in one point the solution was D, but when I look at this kind of statement I think that something is behind the scenes.

Too simple a question like this to say: we have the radi x 2 + height ...........this is not wonderland, this is Mordor Land.

Too simple a question like this to say: we have the radi x 2 + height ...........this is not wonderland, this is Mordor Land.

annie2014 · Answer

I am still confused how the information is sufficient.

How do we calculate the  c  shown above? We only know that  a  is 6. What is the value of  b ?

annie2014 · Answer

Bunnel, can you help me?

pradeepss · Answer

i updated the picture...please take a look.

basically, we know that radius of pole is 6 and radius of the sphere is 24. so we can calculate the partial portion part of the radius of sphere. We can then find the needed information.

hope this helps.

Rebaz · Answer

The picture is very confusing, coz if we blieve the first picture that is placed under the question, the sphere sits on top of the pole and certianly not in.

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