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In the floor of a particular kitchen owned by an abstract artist, each

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In the floor of a particular kitchen owned by an abstract artist, each  [#permalink]

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New post 31 Oct 2015, 07:01
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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 leftmost row contain?

A. 52
B. 56
C. 60
D. 64
E. 68

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Re: In the floor of a particular kitchen owned by an abstract artist, each  [#permalink]

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New post 31 Oct 2015, 07:43
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shasadou 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 leftmost row contain?

A. 52
B. 56
C. 60
D. 64
E. 68


Add all the tiles From left row to right row : consider x tiles in left most row.
x+(x-2)+(x-4)..........+(x-16) = 504
X=64
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Re: In the floor of a particular kitchen owned by an abstract artist, each  [#permalink]

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New post 31 Oct 2015, 14:42
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Hi shasadou,

This question can be solved in a variety of ways: with algebra, by TESTing THE ANSWERS and by using a great Number Property shortcut involving consecutive integers.

We're given a few facts to work with:
1) There are 9 rows of tiles.
2) When going from 'left to right', each row contains TWO FEWER tiles than the one next to it.
3) There are a total of 504 tiles

We're asked how many tiles the left-most most row holds (meaning the one with the MOST tiles).

To start, 504 is divisible by 9, so we can figure out the AVERAGE number of tiles per row. That is 504/9 = 56. Since we're dealing with a set of 9 consecutive integers that differ by 2 each, we know that the '5th row' will have 56 tiles (the average). Then we just have to 'add 2s' until we get to the first row...

56 +2 +2 +2 +2 = 64.

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In the floor of a particular kitchen owned by an abstract artist, each  [#permalink]

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New post 01 Nov 2015, 05:43
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as given , each row to the right = subtract 2 additional tiles.
also the number of rows = 9

therefore total no of tiles to be subtracted =2+4+6+8+10+12+14+16=72
now , total tiles given =504

since units digit is different in each of the choice

9*(option choice) - 504 should give us 72 (or simply 2) in the units digit

the only option that gives that is 64
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Re: In the floor of a particular kitchen owned by an abstract artist, each  [#permalink]

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New post 05 Apr 2016, 11:14
shasadou 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 leftmost row contain?

A. 52
B. 56
C. 60
D. 64
E. 68


"each row of tiles to the right of the first row contains two fewer tiles than row directly to its left"
I actually don't understand the question and I really have trouble getting what was going on. Can anyone please help draw a picture of how the row are laying out in the question and help explain it to me?
thank you so much!
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Re: In the floor of a particular kitchen owned by an abstract artist, each  [#permalink]

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New post 06 Apr 2016, 10:37
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Hi ahuan077,

The use of the word "row" in this question is a bit strange, since rows go from 'left-to-right' and the 2nd row would be beneath the 1st row. As such, it would probably be easier if you think of this question in terms of "columns" - we start with the 1st column, then the 2nd column, then the 3rd column, etc.

We're told that each "column" has 2 fewer tiles than the one to its immediate left, so here's a simple example of what the columns could be if there was no other information to work with:

1st column = 10 tiles
2nd column = 8 tiles
3rd column = 6 tiles
4th column = 4 tiles
5th column = 2 tiles
6th column = 0 tiles

We're clearly dealing with LOTS more tiles though (504 tiles) and only 9 columns, but this IS a constant sequence of values, so there are a number of patterns that we can use to our advantage (my original post - a few posts up) explains them.

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Re: In the floor of a particular kitchen owned by an abstract artist, each  [#permalink]

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New post 06 Apr 2016, 13:24
Hi, Rich:

Thank you so much for your kind explanation, I really appreciate it.

Now I know what the question was talking about. Previously I understood as there are two separate columns to start with, one one the right side of the first row and one on the left side of the first row, and they each extend to nine rows(columns). That's why no matter how hard I tried, I simply could not come up with a sensible solution.

Many, many thanks!



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Re: In the floor of a particular kitchen owned by an abstract artist, each  [#permalink]

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New post 23 Oct 2018, 06:37
It's basically a decreasing AP series. (The use of the word row is really odd and confusing)

\(\frac{9}{2} * [2a + (9-1) * -2] = 504\)
a - 8 = 56
a = 64
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Re: In the floor of a particular kitchen owned by an abstract artist, each  [#permalink]

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New post 25 Oct 2018, 11:16
can anyone paraphrase this question using simple English ??? i have no clue what this question is about

thanks
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Re: In the floor of a particular kitchen owned by an abstract artist, each &nbs [#permalink] 25 Oct 2018, 11:16
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