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805+ Level|   Geometry|      
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Bunuel
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Four cubes with edge lengths 1, 2, 3, and 4 are stacked as shown. What 23 Apr 2019, 13:20
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95% (hard)

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39% (03:13) correct 61% (02:50) wrong based on 44 sessions

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Four cubes with edge lengths 1, 2, 3, and 4 are stacked as shown. What is the length of the portion of XY contained in the cube with edge length 3?


(A) \(\frac{3\sqrt{33}}{5}\)

(B) \(2\sqrt{3}\)

(C) \(\frac{2\sqrt{33}}{3}\)

(D) 4

(E) \(3\sqrt{2}\)


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e41120e351bda42fada2fe2803e19a131bc30b96.png
e41120e351bda42fada2fe2803e19a131bc30b96.png [ 9.58 KiB | Viewed 2974 times ]
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A
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Archit3110
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Four cubes with edge lengths 1, 2, 3, and 4 are stacked as shown. What 27 Apr 2019, 01:40
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Bunuel

Four cubes with edge lengths 1, 2, 3, and 4 are stacked as shown. What is the length of the portion of XY contained in the cube with edge length 3?


(A) \(\frac{3\sqrt{33}}{5}\)

(B) \(2\sqrt{3}\)

(C) \(\frac{2\sqrt{33}}{3}\)

(D) 4

(E) \(3\sqrt{2}\)


Show Spoiler
Attachment:
e41120e351bda42fada2fe2803e19a131bc30b96.png

use phythagorous and determine value of xy ; √10^2+4^2 + 4^2 ; 2√33
for portion of diagonal under cube 3 ; x/3 which will be same ratio for xy diagonal ; 2√33 /10 so x/3 = \(\frac{3\sqrt{33}}{5}\)

IMO A
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Four cubes with edge lengths 1, 2, 3, and 4 are stacked as shown. What 02 Jun 2019, 03:11
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hi. i am able to calculate the total length of the diagonal which comes to be 2*sq.root(33). Can someone now explain to me how to proceed further from here?
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Four cubes with edge lengths 1, 2, 3, and 4 are stacked as shown. What 02 Jun 2019, 04:11
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Archit3110
Bunuel

Four cubes with edge lengths 1, 2, 3, and 4 are stacked as shown. What is the length of the portion of XY contained in the cube with edge length 3?


(A) \(\frac{3\sqrt{33}}{5}\)

(B) \(2\sqrt{3}\)

(C) \(\frac{2\sqrt{33}}{3}\)

(D) 4

(E) \(3\sqrt{2}\)


Show Spoiler
Attachment:
e41120e351bda42fada2fe2803e19a131bc30b96.png

use phythagorous and determine value of xy ; √10^2+4^2 + 4^2 ; 2√33
for portion of diagonal under cube 3 ; x/3 which will be same ratio for xy diagonal ; 2√33 /10 so x/3 = \(\frac{3\sqrt{33}}{5}\)

IMO A

Cannot understand what you did after getting the value for xy. Can you please elaborate it ?
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Four cubes with edge lengths 1, 2, 3, and 4 are stacked as shown. What 02 Jun 2019, 04:20
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rishabhshreyas14
abhishek31
XY can be determined√10^2+4^2 + 4^2 ; 2√33
we need to determine the length portion XY under cube of length 3
so if we observe we have a BIG ∆ where X & Y are two points and the height is 10 ; 1+2+3+4
and other ∆ is within cube where height is 3
similar ∆ ; x/3 =2√33/10
solve for x = 3√33/5

hope this helps


rishabhshreyas14
Archit3110
Bunuel

Four cubes with edge lengths 1, 2, 3, and 4 are stacked as shown. What is the length of the portion of XY contained in the cube with edge length 3?


(A) \(\frac{3\sqrt{33}}{5}\)

(B) \(2\sqrt{3}\)

(C) \(\frac{2\sqrt{33}}{3}\)

(D) 4

(E) \(3\sqrt{2}\)


Show Spoiler
Attachment:
e41120e351bda42fada2fe2803e19a131bc30b96.png

use phythagorous and determine value of xy ; √10^2+4^2 + 4^2 ; 2√33
for portion of diagonal under cube 3 ; x/3 which will be same ratio for xy diagonal ; 2√33 /10 so x/3 = \(\frac{3\sqrt{33}}{5}\)

IMO A

Cannot understand what you did after getting the value for xy. Can you please elaborate it ?
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Four cubes with edge lengths 1, 2, 3, and 4 are stacked as shown. What 03 Jun 2019, 02:55
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Archit3110
Bunuel

Four cubes with edge lengths 1, 2, 3, and 4 are stacked as shown. What is the length of the portion of XY contained in the cube with edge length 3?


(A) \(\frac{3\sqrt{33}}{5}\)

(B) \(2\sqrt{3}\)

(C) \(\frac{2\sqrt{33}}{3}\)

(D) 4

(E) \(3\sqrt{2}\)



Show Spoiler
Attachment:
e41120e351bda42fada2fe2803e19a131bc30b96.png

use phythagorous and determine value of xy ; √10^2+4^2 + 4^2 ; 2√33
for portion of diagonal under cube 3 ; x/3 which will be same ratio for xy diagonal ; 2√33 /10 so x/3 = \(\frac{3\sqrt{33}}{5}\)

IMO A

Can you elaborate your solution, as what needs to be found is still unclear for me ? I mean I haven't understood the question
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Four cubes with edge lengths 1, 2, 3, and 4 are stacked as shown. What 08 Jun 2019, 03:06
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I calculated the length of XY but how to calculate length under 3rd cube?
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Four cubes with edge lengths 1, 2, 3, and 4 are stacked as shown. What 08 Jun 2019, 03:52
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neha283
I calculated the length of XY but how to calculate length under 3rd cube?


How did you do that ? Can you show.

Posted from my mobile device
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Four cubes with edge lengths 1, 2, 3, and 4 are stacked as shown. What 08 Jun 2019, 04:01
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I calculated the length of XY but how to calculate length under 3rd cube?


How did you do that ? Can you show.

Posted from my mobile device

Hi
please see below link for solution
https://artofproblemsolving.com/wiki/in ... Problem_19
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Four cubes with edge lengths 1, 2, 3, and 4 are stacked as shown. What 08 Jun 2019, 07:52
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rishabhshreyas14
Archit3110
Bunuel

Four cubes with edge lengths 1, 2, 3, and 4 are stacked as shown. What is the length of the portion of XY contained in the cube with edge length 3?


(A) \(\frac{3\sqrt{33}}{5}\)

(B) \(2\sqrt{3}\)

(C) \(\frac{2\sqrt{33}}{3}\)

(D) 4

(E) \(3\sqrt{2}\)


Show Spoiler
Attachment:
e41120e351bda42fada2fe2803e19a131bc30b96.png

use phythagorous and determine value of xy ; √10^2+4^2 + 4^2 ; 2√33
for portion of diagonal under cube 3 ; x/3 which will be same ratio for xy diagonal ; 2√33 /10 so x/3 = \(\frac{3\sqrt{33}}{5}\)

IMO A


Spent over 4 minutes to solve this question.
Just wondering - for those who managed to get 700+, did you manage to solve this question under 2 minutes?

I'm starting to worry if questions like this appear many times in quant section then I will definitely run out of time.
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Four cubes with edge lengths 1, 2, 3, and 4 are stacked as shown. What 23 Apr 2022, 21:50
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