I have tiled my square bathroom well with congruent square tiles. All the tiles are red, except those along the two diagonals, which are blue. If I used $121$ blue tiles, then the number of red tiles, I used is

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900

1800

3600

7200

answer is C.

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Detailed Solution

Here in the question we have stated that we have tiled the square bathroom well with matching square tiles. All tiles are red, except those along the two diagonals, which are blue. If I used 121 blue tiles, we need to find the number of red tiles used.
Here, congruent means that the tiles have the same area, same perimeter, same length and thickness.
We used blue tiles in the diagonal and the number of blue tiles is given in the question, which is 121 then we need to find out the number of red tiles that are in the bathroom.
Now let's assume that the dimension of a square tile

means n square slab in length and n square slab in width.
In the case of 1
We have an odd number of square tiles. So if we have n as odd then the number of diagonal square pies is given as

and we are given that there are 121 blue tiles on the diagonal so we can say that

⇒ 2 n − 1 = 121 ⇒ 2 n = 122 ⇒ n = 61

Therefore total number of tiles used

= n 2 = 612 = 3721

Number of red tiles will be

= total number of tiles used − number of blue tiles used

= 3721 − 121 = 3600

For case 2
If we have

n

as even that is even number of tiles then the number of diagonal tiles will be

2 n

.
So,

⇒ 2 n = 121 ⇒ n = 60.5

but we know that n cannot be in fraction or decimal points because it indicates the number of tiles, which must be an exact number, so we can say that n cannot be even.
Hence the number of red tiles is 3600.
So option 3 is correct.

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