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The figure above shows a streetlight that consists of a

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The figure above shows a streetlight that consists of a [#permalink] New post 21 Feb 2012, 02:01
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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.
[Reveal] Spoiler: OA

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Re: PT #3 DS 6 [#permalink] New post 21 Feb 2012, 02:24
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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.
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Re: PT #3 DS 6 [#permalink] New post 21 Feb 2012, 04:12
Bunuel wrote:
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.


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
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Re: PT #3 DS 6 [#permalink] New post 21 Feb 2012, 04:19
Expert's post
boomtangboy wrote:
Bunuel wrote:
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.


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


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.
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Re: The figure above shows a streetlight that consists of a [#permalink] New post 21 Feb 2012, 22:39
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
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Re: The figure above shows a streetlight that consists of a [#permalink] New post 21 Feb 2012, 22:42
Expert's post
boomtangboy wrote:
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


Notice that the sphere is slightly below the top of the pole.
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Re: The figure above shows a streetlight that consists of a [#permalink] New post 24 Feb 2012, 02:32
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:
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Re: The figure above shows a streetlight that consists of a [#permalink] New post 24 Feb 2012, 02:46
Expert's post
eybrj2 wrote:
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:


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.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: The figure above shows a streetlight that consists of a [#permalink] New post 29 Feb 2012, 01:23
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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.
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Re: The figure above shows a streetlight that consists of a [#permalink] New post 02 Feb 2014, 06:04
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Re: The figure above shows a streetlight that consists of a   [#permalink] 02 Feb 2014, 06:04
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