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mahiGMAT
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A ladder of fixed length is stacked against a wall. The wall is perpen Updated on: 25 Mar 2015, 03:08
Originally posted by mahiGMAT on 25 Mar 2015, 02:49.
Last edited by Bunuel on 25 Mar 2015, 03:08, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
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17% (01:44) correct 83% (02:11) wrong based on 18 sessions

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A ladder of fixed length is stacked against a wall. The wall is perpendicular to the floor, so that the ladder makes a right angled triangle while placed on the floor leaning against the wall. What is the area of the circumcircle of the triangle (the one the ladder makes with the floor and the wall), when the ladder subtends a 60 degree angle with the floor?

(1) The height of the point of contact of the ladder on the wall is 1m when the ladder subtends an angle of 30 degrees with the floor.

(2) The area of the circumcircle of the triangle formed when the ladder subtends an angle of 30 degrees with the floor is (3*pi)/4

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A ladder of fixed length is stacked against a wall. The wall is perpen 25 Mar 2015, 07:43
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mahiGMAT
A ladder of fixed length is stacked against a wall. The wall is perpendicular to the floor, so that the ladder makes a right angled triangle while placed on the floor leaning against the wall. What is the area of the circumcircle of the triangle (the one the ladder makes with the floor and the wall), when the ladder subtends a 60 degree angle with the floor?

(1) The height of the point of contact of the ladder on the wall is 1m when the ladder subtends an angle of 30 degrees with the floor.

(2) The area of the circumcircle of the triangle formed when the ladder subtends an angle of 30 degrees with the floor is (3*pi)/4
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hi Bunuel,
shouldn't the statement one also be sufficient...
when the ladder makes an angle of 30 degrees , we have 30-60-90 triangle in which we know one side ...
thus we can know other two sides including the length of ladder...
now in Q stem, it is given that ladder is making 60 degree angle, thus again making a 30-60-90 triangle, in which we know one side, hypotenuse which is equal to ladder..
so other two sides can be found, and accordingly the area of circumcircle...

also..
the circumcircle area would be same irrespective of what angle the ladder makes as the ladder is nothing but the diameter, which will remain the same everytime...
ans D...
however the OA added is B....
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A ladder of fixed length is stacked against a wall. The wall is perpen 26 Mar 2015, 10:55
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can anyone share the explanation please ...

thanks ...

i tried googling this question and found just one other forum that has taken up this question but does bot share any explanation ... has this question been disused here on the GMAT club already???


is this really 600 - 700 level??

much obliged ...
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A ladder of fixed length is stacked against a wall. The wall is perpen 26 Mar 2015, 11:42
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Hi mahiGMAT,

What is the source of this question? I ask because while the basic Geometry concepts involved could show up on your Official GAMT, this question is written in a way that doesn't quite 'match up' with how the GMAT writers craft their questions.

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A ladder of fixed length is stacked against a wall. The wall is perpen 26 Mar 2015, 15:49
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I do not believe OA can be B, St 1 by itself is sufficient. If the angle subtended is 30*, and as the triangle is a 30-60-90 triangle we can say that the sides will be in 1:3(1/2):2 in proportion. From that we can easily calculate the length of the sides.

Same again for B when the value of the side is known we can calculate the other sides.

Can the maths experts tell me where am i going wrong with my understanding.

IMO D
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A ladder of fixed length is stacked against a wall. The wall is perpen 29 Mar 2015, 00:31
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Experts, please share your thoughts. Even I think the answer should be D instead of B.

Thanks
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A ladder of fixed length is stacked against a wall. The wall is perpen 29 Mar 2015, 23:36
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chetan2u
mahiGMAT
A ladder of fixed length is stacked against a wall. The wall is perpendicular to the floor, so that the ladder makes a right angled triangle while placed on the floor leaning against the wall. What is the area of the circumcircle of the triangle (the one the ladder makes with the floor and the wall), when the ladder subtends a 60 degree angle with the floor?

(1) The height of the point of contact of the ladder on the wall is 1m when the ladder subtends an angle of 30 degrees with the floor.

(2) The area of the circumcircle of the triangle formed when the ladder subtends an angle of 30 degrees with the floor is (3*pi)/4

hi ]Bunuel,
shouldn't the statement one also be sufficient...
when the ladder makes an angle of 30 degrees , we have 30-60-90 triangle in which we know one side ...
thus we can know other two sides including the length of ladder...
now in Q stem, it is given that ladder is making 60 degree angle, thus again making a 30-60-90 triangle, in which we know one side, hypotenuse which is equal to ladder..
so other two sides can be found, and accordingly the area of circumcircle...

also..
the circumcircle area would be same irrespective of what angle the ladder makes as the ladder is nothing but the diameter, which will remain the same everytime...
ans D...
however the OA added is B....
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Hello Chetan,
I come up with the same answer.

I was trying to find "What can give me the length of the ladder as it is fixed whatever its position. Each statement alone is sufficient.
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A ladder of fixed length is stacked against a wall. The wall is perpen 30 Mar 2015, 02:33
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According to me :
There are 2 circles in Q, the circumcircle when ladder makes angle 60, and circumcircle when Ladder makes angle 30 with the floor.
Since ladder ends up forming a right angled triangle, thus, we get that the ladder is the diameter of the circumcircle in both the cases. Thus to find the area of circumcircle, we reduce the problem to find the length of the Ladder. (Please let me know if Im wrong in deducing this.)
stat 1) => given : 30-60-90 triangle + wall's height => we can find ladder's length. SUFF.
stat 2) => given : 60-30-90 triangle(of the other circumcircle) ie ladder is diam + area => Length of ladder can be calculated. SUFF.
Thus D.

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