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In the floor of a particular kitchen

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In the floor of a particular kitchen

by conquistador » Thu Jun 25, 2015 9:34 pm
In the floor of a particular kitchen owned by an abstract artist, each row of tiles to the right of the first row contains two fewer tiles than the row directly to its left. If there are nine rows in all and a total of 504 tiles in the floor, how many tiles does the left-most row contain?

(A) 52
(B) 56
(C) 60
(D) 64
(E) 68

While the problem is quite simple, the row concept confused me a lot because row is horizontal in nature and I did not understand what did he mean by left row.
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by theCEO » Fri Jun 26, 2015 12:03 am
Mechmeera wrote:In the floor of a particular kitchen owned by an abstract artist, each row of tiles to the right of the first row contains two fewer tiles than the row directly to its left. If there are nine rows in all and a total of 504 tiles in the floor, how many tiles does the left-most row contain?

(A) 52
(B) 56
(C) 60
(D) 64
(E) 68

While the problem is quite simple, the row concept confused me a lot because row is horizontal in nature and I did not understand what did he mean by left row.
It depends on where you are standing you can have a different view!

For example the following represents 3 rows in a supermarket. If you were walking down the aisle2, from left to right, isle 1 will be to the left, isle 3 will be to the right.

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(1)
-------------
(2)
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(3)
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by theCEO » Fri Jun 26, 2015 12:17 am
The number of tiles in each row are as follow with X being the number in the first row
1 = X
2 = X-2
3 = X-4
4 = X-6
5 = X-8
6 = X-10
7 = X-12
8 = X-14
9 = X-16

If we sum the total amount of tiles, we get
9X-2-4-6-8-10-12-14-16
9X-2(1+2+3+4+5+6+7+8)

The sum of the first n consecutive numbers = (n*n+1)/2
Therefore the sum of the first 8 consecutive integers = (8*9)/2=36

9X-2(1+2+3+4+5+6+7+8) = 9x -2(36) = total number of tiles
9X - 72 = 504
9X = 504 + 72 = 576
X = 64
ANS = D
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by GMATGuruNY » Fri Jun 26, 2015 2:35 am
Mechmeera wrote:In the floor of a particular kitchen owned by an abstract artist, each row of tiles to the right of the first row contains two fewer tiles than the row directly to its left. If there are nine rows in all and a total of 504 tiles in the floor, how many tiles does the left-most row contain?

(A) 52
(B) 56
(C) 60
(D) 64
(E) 68
Since each row contains 2 fewer tiles than the row directly to its left, the 9 rows constitute an EVENLY SPACED SET.
For any evenly spaced set, average = median = sum/number.
Thus, the length of the center row = the median length of the 9 rows = (total number of tiles)/(total number of rows) = 504/9 = 56.
Since there are 4 rows to the left of the center row, and each successive row to the left increases by a length of 2 tiles, the length of the leftmost row = 56 + 4*2 = 64.

The correct answer is D.
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by nikhilgmat31 » Wed Jul 01, 2015 9:58 pm
64 D is the answer
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