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# In how many ways can a square be identified in a chess board (figure a

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CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
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In how many ways can a square be identified in a chess board (figure a  [#permalink]

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02 Mar 2019, 00:08
1
3
00:00

Difficulty:

85% (hard)

Question Stats:

36% (01:55) correct 64% (01:15) wrong based on 42 sessions

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In how many ways can a square be identified in a chess board (8x8 squares) (figure attached)?

A) 64
B) 65
C) 204
D) 205
E) 408

http://www.GMATinsight.com

Attachments

chess.jpg [ 44.46 KiB | Viewed 587 times ]

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Re: In how many ways can a square be identified in a chess board (figure a  [#permalink]

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02 Mar 2019, 03:58
2
GMATinsight wrote:
In how many ways can a square be identified in a chess board (8x8 squares) (figure attached)?

A) 64
B) 65
C) 204
D) 205
E) 408

http://www.GMATinsight.com

total no of squares which can be formed in a 8x8 chess board :
no of 1*1 squares ; 8*8 = 64,
2*2 squares= 7*7 , 3*3 squares = 6*6;36, 4*4 squares=5*5
5*5 squares = 4*4
6*6 squares = 3*3
7*7 squares =2*2
8*8 squares = 1*1
total
1^2+2^2+3^2+....+8^2
1+4+9+16+25+36+49+64
IMO C ; 204
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Joined: 12 Sep 2017
Posts: 301
Re: In how many ways can a square be identified in a chess board (figure a  [#permalink]

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07 Mar 2019, 16:57
1
Archit3110 wrote:
GMATinsight wrote:
In how many ways can a square be identified in a chess board (8x8 squares) (figure attached)?

A) 64
B) 65
C) 204
D) 205
E) 408

http://www.GMATinsight.com

total no of squares which can be formed in a 8x8 chess board :
no of 1*1 squares ; 8*8 = 64,
2*2 squares= 7*7 , 3*3 squares = 6*6;36, 4*4 squares=5*5
5*5 squares = 4*4
6*6 squares = 3*3
7*7 squares =2*2
8*8 squares = 1*1
total
1^2+2^2+3^2+....+8^2
1+4+9+16+25+36+49+64
IMO C ; 204

Hello Archit3110 !

Could you please explain to me how do you get to 2*2 = 7*7 and 3*3 = 6*6?

I'm having trouble to see those squares.

Kind regards!
Intern
Joined: 18 Jan 2019
Posts: 28
Re: In how many ways can a square be identified in a chess board (figure a  [#permalink]

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08 Mar 2019, 01:19
jfranciscocuencag wrote:
Archit3110 wrote:
GMATinsight wrote:
In how many ways can a square be identified in a chess board (8x8 squares) (figure attached)?

A) 64
B) 65
C) 204
D) 205
E) 408

http://www.GMATinsight.com

total no of squares which can be formed in a 8x8 chess board :
no of 1*1 squares ; 8*8 = 64,
2*2 squares= 7*7 , 3*3 squares = 6*6;36, 4*4 squares=5*5
5*5 squares = 4*4
6*6 squares = 3*3
7*7 squares =2*2
8*8 squares = 1*1
total
1^2+2^2+3^2+....+8^2
1+4+9+16+25+36+49+64
IMO C ; 204

Hello Archit3110 !

Could you please explain to me how do you get to 2*2 = 7*7 and 3*3 = 6*6?

I'm having trouble to see those squares.

Kind regards!

likewise, for me I see 16 squares that are 2x2 rather than 49,
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Posts: 5008
Location: India
Concentration: Sustainability, Marketing
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In how many ways can a square be identified in a chess board (figure a  [#permalink]

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Updated on: 08 Mar 2019, 02:13
1
Ish1996 & jfranciscocuencag

Solution attached

I solved question by visualising squares...

hope this helps

solution in two parts...

kind apologizes for my bad handwriting .. hope you are able to understand whats written..
Attachments

File comment: File 1

IMG_20190308_143223988.jpg [ 3.95 MiB | Viewed 325 times ]

Originally posted by Archit3110 on 08 Mar 2019, 02:06.
Last edited by Archit3110 on 08 Mar 2019, 02:13, edited 3 times in total.
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5008
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
In how many ways can a square be identified in a chess board (figure a  [#permalink]

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08 Mar 2019, 02:08
1
Ish1996 & jfranciscocuencag

part 2 ...
hope this helps...
Attachments

File comment: File 2

IMG_20190308_143228986.jpg [ 3.51 MiB | Viewed 317 times ]

In how many ways can a square be identified in a chess board (figure a   [#permalink] 08 Mar 2019, 02:08
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