Barkatis wrote:

In a single row of yellow, green and red colored tiles, every red tile is preceded immediately by a yellow tile and every yellow tile is preceded immediately by a green tile. What color is the 24th tile in the row?

(1) The 18th tile in the row is not yellow.

(2) The 19th tile in the row is not green.

I don't get why it's not C.

This is a tough question, I remember getting this in a MGMAT test and took me more than 3 minutes to think about it then. Let me break down my thought pattern :

What do we know ?Y,G,R tiles

Whenever there is R, Y preceeds it and whenever there is Y, G preceeds it.

So if there is a R somewhere, it will always have a GYR pattern

What do we need to find out ?Color of tile 24

Reasoning(1) Tile 18 is not yellow.

This means tile 18 is either green or it is red.

Now it is easy to claim to different patterns which do not violate the rules :

18 ..... 24

RGGGGGG

RGGGGYR

So clearly not enough

(2) Tile 19 is not green

This means tile 19 can be red or yellow.

Consider the following patterns :

19 .... 24

RGGGGG

RGGGYR

So again not enough

(1+2) Now we know 18 is either G or R and 19 is either R or Y

18 ..... 24

GYRGGGG

GYRGGYR

Again very easy to form two patterns with different colors at 24

What was the basic principle I used ?That the defining rules only specify restrictions looking right to left (preceeding tiles) for Y and R. So there is no restrictions on G either looking back or looking forward.

Answer is (E) _________________

Math write-ups

1) Algebra-101 2) Sequences 3) Set combinatorics 4) 3-D geometry

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