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by shashank.ism » Tue Feb 09, 2010 1:09 pm
Balancing cards on one another where some are placed horizontally and others diagonally (slant fashion) is a popular trick of all magicians. 30 playing cards of length 12 cm and breadth 6 cm are used to build a pyramidal structure with 4 horizontal cards at the base. 8 cards are then put diagonally on these cards to give four peaks. 3 cards are then put on the 4 peaks. The process continues till the top is a peak made by 2 cards. Find the area covered by the front side of the pyramid.

288 sqrt(3) cm2
180 sqrt(3) cm2
360 sqrt(3) cm2
576 sqrt(3) cm2
None of these
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by Mom4MBA » Tue Feb 09, 2010 1:28 pm
this will make a equilateral triangle with sides 12x4= 48 cms

Area of equilateral triangle = (√3 a²) / 4 = 576 √3 cms²
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by jeffedwards » Tue Feb 09, 2010 5:31 pm
Nice I did the same thing...sort of.

I drew it out on a piece of paper (because that explanation was confusing) and noticed that when one card is laid flat with two on a diagonal that makes an equilateral triangle - 6 was thrown in there to confuse us.

If you continue this pattern, you get 7 triangles on the bottom then 5 then 3 then 1 (as you progress each level up). In other words you 16 total triangles.

Use the area formula for an equilateral triangle, with a side of 12cm, and times that by 16. That give you 576√3
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by shashank.ism » Wed Feb 10, 2010 12:01 pm
shashank.ism wrote:Balancing cards on one another where some are placed horizontally and others diagonally (slant fashion) is a popular trick of all magicians. 30 playing cards of length 12 cm and breadth 6 cm are used to build a pyramidal structure with 4 horizontal cards at the base. 8 cards are then put diagonally on these cards to give four peaks. 3 cards are then put on the 4 peaks. The process continues till the top is a peak made by 2 cards. Find the area covered by the front side of the pyramid.

288 sqrt(3) cm2
180 sqrt(3) cm2
360 sqrt(3) cm2
576 sqrt(3) cm2
None of these
Image

Area (sqrt(3)/4)x48^2 = 576sqrt(3) cm^2
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by harsh.champ » Wed Feb 10, 2010 10:45 pm
shashank.ism wrote:
shashank.ism wrote:Balancing cards on one another where some are placed horizontally and others diagonally (slant fashion) is a popular trick of all magicians. 30 playing cards of length 12 cm and breadth 6 cm are used to build a pyramidal structure with 4 horizontal cards at the base. 8 cards are then put diagonally on these cards to give four peaks. 3 cards are then put on the 4 peaks. The process continues till the top is a peak made by 2 cards. Find the area covered by the front side of the pyramid.

288 sqrt(3) cm2
180 sqrt(3) cm2
360 sqrt(3) cm2
576 sqrt(3) cm2
None of these
Image

Area (sqrt(3)/4)x48^2 = 576sqrt(3) cm^2
Thanks shashank for the figure.I was having a hard time figuring out how the total arrangement is.
Anyways,can this ques. come in the GMAT??
Means,in 2min. timeline ,Is it possible to solve such ques.??Because,it is also testing ur 3-D to 2-D visualization

Just a random doubt.
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