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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

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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Source: Beat The GMAT — Problem Solving | Tue Feb 09, 2010 1:09 pm

Mom4MBA: Senior | Next Rank: 100 Posts; Posts: 90; Joined: Fri Jan 22, 2010 1:10 pmFollowed by: 4 members; Location: New Jersey; Thanked: 13 times; GMAT Score:640

by Mom4MBA » Tue Feb 09, 2010 1:28 pm

this will make a equilateral triangle with sides 12x4= 48 cms

Area of equilateral triangle = (âˆš3 aÂ²) / 4 = 576 âˆš3 cmsÂ²

Stay focused

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jeffedwards: Master | Next Rank: 500 Posts; Posts: 109; Joined: Mon Oct 12, 2009 4:58 amFollowed by: 1 member; Thanked: 12 times; GMAT Score:720

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 576âˆš3

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

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

Area (sqrt(3)/4)x48^2 = 576sqrt(3) cm^2

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

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

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.

It takes time and effort to explain, so if my comment helped you please press Thanks button

Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

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