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Bunuel
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Figures 0, 1, 2, and 3 consist of 1, 5, 13, and 25 nonoverlapping unit 15 Mar 2019, 01:17
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85% (hard)

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42% (03:05) correct 58% (02:33) wrong based on 38 sessions

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TOUGH QUESTION:



Figures 0, 1, 2, and 3 consist of 1, 5, 13, and 25 nonoverlapping unit squares, respectively. If the pattern were continued, how many nonoverlapping unit squares would there be in figure 100?


(A) 10401
(B) 19801
(C) 20201
(D) 39801
(E) 40801


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C
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Samine
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Figures 0, 1, 2, and 3 consist of 1, 5, 13, and 25 nonoverlapping unit Updated on: 16 Mar 2019, 07:35
Originally posted by Samine on 15 Mar 2019, 08:14.
Last edited by Samine on 16 Mar 2019, 07:35, edited 2 times in total.
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Here is my solution:

From figure 0 to figure 100, we have 101 figures
The given sequence here is: 1, 5, 13, 25,.... the next number will be 41
=> new sequence (which is the difference between 2 numbers) is 4, 8, 12, 16,... This is an evenly spaced set, so the last number of this sequence is = 4 + (100-1)*4 = 400
This new sequence have average = (last number + first number) / 2 = (400 + 4) / 2 = 202
Because this is an evenly spaced set, Sum = average * total number of sequence = 202 * 100 = 20200

Notice the pattern here:
5 = 1+4
13 = 1+4+8
25 = 1+4+8+12
....
x (figure 100) = 1 + 20200 = 20201 => Option C

Correct me if I'm wrong!
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Figures 0, 1, 2, and 3 consist of 1, 5, 13, and 25 nonoverlapping unit 15 Mar 2019, 14:32
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Pattern formulae: first term + 2[(figure no)*(figure no+1)]

For figure no 100 and first term 1, no of squares: 1+2(100*101) = 1 + 2(10100) = 1+20200 = 20201

Ans C
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Figures 0, 1, 2, and 3 consist of 1, 5, 13, and 25 nonoverlapping unit 01 Apr 2019, 10:56
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There is pattern here:
Figure ........................................ No of unit squares
0 -------------------> 1------------------------> 1 square-----> 1
1 ------------------->1,3,1--------------------->5-------------> 2 square + 1 square
2 ------------------->1,3,5,3,1----------------->13------------>3 sq + 2 sq
3 ------------------->1,3,5,7,5,3,1------------->25------------>4 sq + 3 sq
;
;
;
;
Similarly,
100--------------------------------------------------------------->101 sq + 100 sq = 10201 + 10000 = 20201
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Figures 0, 1, 2, and 3 consist of 1, 5, 13, and 25 nonoverlapping unit 02 Apr 2019, 06:20
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Why can't this be the answer?

N=1, SQ=1
N=2, SQ=5
N=3, SQ=13 ((3*3)+(2*2))= 13
N=4, SQ=25 ((N*N) + (N-1)^2) , For eg ((4*4) + (3*3)) = 25


So For N-100

((100*100) + (99*99)) = 19,801
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Figures 0, 1, 2, and 3 consist of 1, 5, 13, and 25 nonoverlapping unit 02 Apr 2019, 06:43
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Well I had a different take on this -

Fig 1 - 5Sq ----> 1*(2+2)+1 = 5
Fig 2 - 13Sq ---> 2*(4+2)+1 = 13
Fig 3 - 25Sq ---> 3*(6+2)+1 = 25
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Fig 100 ----> 100 * (200+2)+1 = 20201
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AbhishekB19
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Figures 0, 1, 2, and 3 consist of 1, 5, 13, and 25 nonoverlapping unit 02 Apr 2019, 07:00
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teja18892
Why can't this be the answer?

N=1, SQ=1
N=2, SQ=5
N=3, SQ=13 ((3*3)+(2*2))= 13
N=4, SQ=25 ((N*N) + (N-1)^2) , For eg ((4*4) + (3*3)) = 25


So For N-100

((100*100) + (99*99)) = 19,801
Show more


---------------------
Because you have mistakenly quoted fig 0 as fig 1. The correct sequence will be : SQ(n)= {(N+1)^2} + (N^2).
For SQ(n) = 100
[(101)^2 + (100)^2] = 10201 + 10000 = 20201
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