geometry

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rupsk: Master | Next Rank: 500 Posts; Posts: 123; Joined: Mon Feb 07, 2011 12:11 pmFollowed by: 1 member

by rupsk » Sun Sep 04, 2011 1:39 pm

If you were to construct a 7 Ãƒ- 7 checkered square (i.e., a 7 Ãƒ- 7 chess board), how many rectangles would there be in total? You need to include squares too because a square is a special kind of rectangle.

Possible Answers
Selected Possible Answer

A. 625

B. 918

C. 842

D. 676

E. 784

Another question

A block of wood in the form of a cuboid 4" Ãƒ- 10" Ãƒ- 13" has all its six faces painted pink. If the wooden block is cut into 520 cubes of 1" Ãƒ- 1" Ãƒ- 1", how many of these would have pink paint on them?

Possible Answers
Selected Possible Answer

A. 348

B. 352

C. 344

D. 340

E. 350

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Source: Beat The GMAT — Problem Solving | Sun Sep 04, 2011 1:39 pm

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Mon Sep 05, 2011 3:59 am

rupsk wrote:If you were to construct a 7 Ãƒ- 7 checkered square (i.e., a 7 Ãƒ- 7 chess board), how many rectangles would there be in total? You need to include squares too because a square is a special kind of rectangle.

Possible Answers
Selected Possible Answer

A. 625

B. 918

C. 842

D. 676

E. 784

The easiest way of doing this sum is using Combinations,
For a rectangle to be formed, we need 2 vertical lines and 2 horizontal lines.(This includes possibility of squares also)

A 7-by-7 chessboard has 8 vertical and 8 horizontal lines.
For a rectangle we need to pick 2 vertical and 2 horizontal lines from these 8 lines, so

we have, 8C2 * 8C2 = (8*7/2*1)*(8*7/2*1) = 16*49 = 784.

Another question

A block of wood in the form of a cuboid 4" Ãƒ- 10" Ãƒ- 13" has all its six faces painted pink. If the wooden block is cut into 520 cubes of 1" Ãƒ- 1" Ãƒ- 1", how many of these would have pink paint on them?

Possible Answers
Selected Possible Answer

A. 348

B. 352

C. 344

D. 340

E. 350

The fastest way of doing this is to determine the number of cubes which are not painted on any of its sides and then subtract that to the total cubes.

To find the number of cubes not painted on any side, imagine the cuboid beneath when all the small cubes painted pink are removed, the dimension of each of the sides would be reduced by 1cm on either side, so the cuboid formed will have dimension of (13-2) (10-2) and (4-2).
So, we have a cuboid of 11*8*2, when this is cut into cubes of 1cm, we have 176 cubes which are not shaded on any side.

So out of the 520 cubes, we now know 176 are not painted pink, so cubes painted pink = 520-176=344

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arnabis2good: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Tue Aug 21, 2007 7:41 pm; Thanked: 1 times

by arnabis2good » Mon Sep 05, 2011 4:34 am

What is the source for these questions? I have a doubt if these can appear in the real GMAT. Expert comments please.

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Sep 05, 2011 6:47 am

arnabis2good wrote:What is the source for these questions? I have a doubt if these can appear in the real GMAT. Expert comments please.

In my opinion, question 1 (# of rectangles) seems reasonable enough to be a GMAT question. I say this because it's easy enough to understand and there are multiple approaches one could take.

Question #2 is on the edge for me. The word "cuboid" certainly would not appear on the GMAT unless the it were explicitly defined in the question. That said, if we the question were reworded to remove any ambiguity, I'd say that it could be an official GMAT question.

My 2 cents

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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rupsk: Master | Next Rank: 500 Posts; Posts: 123; Joined: Mon Feb 07, 2011 12:11 pmFollowed by: 1 member

by rupsk » Mon Sep 05, 2011 6:53 am

thank you all.

What will be the formula when we have to identify no of squares in the first problem?

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Mon Sep 05, 2011 9:04 am

For number of squarer in a chessboard on (n*n)

Number of squares is given by : 1^2 + 2^2 + 3^2 + 4^2 + ..... n^2.

Theres an explanation for how you derive the formulae, but I guess its simple enough to just remember it.

rupsk wrote:thank you all.

What will be the formula when we have to identify no of squares in the first problem?

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rupsk: Master | Next Rank: 500 Posts; Posts: 123; Joined: Mon Feb 07, 2011 12:11 pmFollowed by: 1 member

by rupsk » Mon Sep 05, 2011 9:06 am

thanks

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