In a single row of yellow, green and red colored tiles

here's the OA
It's from a MGMAT Test

"It is tempting to view the information in the question as establishing a pattern as follows:
Green, Yellow, Red, Green, Yellow, Red, . . .
However, consider that the following non-pattern is also possible:
Green, Yellow, Red, Green, Green, Green, Green . . .
(1) INSUFFICIENT: This tells us that the 18th tile is Green or Red but this tells us nothing about the 24th tile. Statement (1) alone is NOT sufficient.
(2) INSUFFICIENT: This tells us that the 19th tile is Yellow or Red but this tells us nothing about the 24th tile. Statement (2) alone is NOT sufficient.
(1) AND (2) INSUFFICIENT: Together, the statements yield the following possibilities for the 18th and 19th tiles:
GY, GR, RY, or RR
However, only GY adheres to the rules given in the question. Thus, we know that tile 18 is green and tile 19 is yellow. However, this does not help us to determine the color of the next tile, much less tile 24 (the one asked in the question). For example, the next tile (tile 20) could be green or red. Thus, the statements taken together are still not sufficient.
The correct answer is E."


But if we know that 19 is Yellow , then the nxt one will be red right ? What am I missing ?

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)

the stimulus of the question yeilds this sequence : GYR as the only possibility.

now st1) a18 is not Y ie a18 = G/R => two possibilities =>we cant construct a definitie sequence => not suff

st2) a19 is not G ie a18 = Y/R => two possibilities =>we cant construct a definitie sequence => not suff

take both statements together
possibility 1 : a18, a19 = R G
possibility 2 : a18, a19 = G Y
=> two possibilities => no definite sequence can be constructed => not sufficient

Ans E

Hope my explanation helped.

If we have a red tile, it will be in this sequence only: GYR
If we have a yellow tile, it will be in this sequence: GY
There are no restrictions for Green tiles.

The data in the two statements seems to be very little since data is about 18th and 19th tiles while question asks about 24th tile. The required sequences are just 2/3 tiles long. Plus, the constraints are on the preceding tiles, not the following tiles. So in such situations, when the data seems sparse, I often check both conditions together to see whether even that is possible.
18th tile - G/R
19th tile - Y/R
But the 19th tile cannot be Red since we cannot have Yellow on the 18th tile. So 19th tile must be Yellow and 18th tile must be Green.
Now, all tiles from 20th to 24th could be any of the following:
GGGGG
GGGGY
GGYGY
GGGYR
RGGYR
etc
Hence (E).

It is a very vague question. Had it been given that tiles of the same color cannot be next to each other of something like that, then it would have been more interesting.

We don't know what precedes green tiles. It could be anything, which means that green can follow tiles of any color.

Also, it's worth mentioning that green can be followed by any color tile, not only yellow, because the rule about yellow tiles being preceded by green tiles doesn't preclude the possibility of other tiles also being preceded by green tiles.

In short, we could have a whole string of green tiles between the 18th and 24th tiles.

Consider stmt 1: 18th tile is not yellow. Therefore, it should be green/red (given: there are only 3 colors). If we have green color on 18th tile, then the order is:
18th - green (G)
19th - yellow (Y)
20th - red (R)
21th - G
22nd - Y
23rd - R
24th - G
Ans: Green
Similarly, if we consider 18th tile to be of red color, then we get 24th tile to be of red color.
Hence Stmt 1 is not sufficient
Now, consider Stmt 2. 19th tile should be Y/R color. If we take Y, then 24th tile is G and if we take R, then 24th tile is Y.
Hence, stmt 2 is not sufficient.
If we consider both stmts together, then 18th tile should be G and 19th should be Y which gives the answer as G.
Therefore, neither of the stmts alone is sufficient but both when used together are sufficient.

In questions such as these, some structured reasoning helps out. Write down little tit-bits of information to get a clear picture and avoid confusion.

Say, if see a Red tile, I will see YR together.
Similarly, if I see a Yellow, I will see GY together.
Updating - if I see Red, I will see GYR

So take a moment to think what the row could look like before jumping on to the statements:

GGGGGGGGGGGGGGGGGGGGGGGGYR
or
GYGYGYGGYGYGGGGGGGGGYRGGGG
or
GYRGGGGGYGGGGGYGGGGGGGYRGGG
etc

That is, there are no constraints on G. Before a Y, I will see a G and Before an R, I will see GY.

Now look at the statements:

(1) The 18th tile in the row is not yellow.
So 18th tile is G or R. There are no constraints on what will come AFTER G or R so we cannot decide the color of 24th tile.
18th to 24th tiles could look like this: GGGGGGG or GYGYGYR etc

(2) The 19th tile in the row is not green.
So 19th tile is Y or R. Again, there are no constraints on what will come AFTER Y or R so we cannot decide the color of 24th tile.
18th to 24th tiles could look like this: GYGGGGG or GYGYGYR etc

Taking both together, if 19th tile is R, 18th tile must be Y but it cannot be according to statement 1 so 19th tile must be Y and 18th tile must be G. But still, do we have any constraints on the 24th tile? We can have any tile after the 19th Y tile - R or G.
18th to 24th tiles could look like this: GYGGGGG or GYGYGYR etc

Answer (E)

Hi All,

This question is more complex than a typical "sequence" question that you'll see on Test Day. The information at the beginning of the prompt is "causal" but only deals with tiles that PRECEDE other tiles; we have to deduce what tiles can FOLLOW other tiles. We know what comes immediately before a red (a yellow) and we know what comes immediately before a yellow (a green), but we're not told what comes before a green.

Up-Front Deductions:
A Green can be followed by another Green or a Yellow (but not a Red)
A Yellow can be followed by a Green or a Red (but not a Yellow)
A Red can be followed by a Green (but not a Yellow or Red)

We're asked for the 24th Tile....

Fact 1: 18th = NOT Yellow

This Fact tells us that the 18th = Green OR Red

IF....
18th = Red
We would have G, G, G, G, G to infinity, so the 24th Tile = GREEN

IF
18th = Green
We COULD have G, G, G, G, G, Y, so the 24th Tile = YELLOW
Fact 1 is INSUFFICIENT

Fact 2: 19th is NOT Green

This Fact tells us that the 19th = Yellow OR Red

IF
19th = Red
We would have G, G, G, G, G, so the 24th Tile = GREEN

IF 19th = Yellow
We could have R, G, G, G, Y so the 24th Tile = YELLOW
Fact 2 is INSUFFICIENT

Combined, we know...
18th = Green OR Red
19th = Yellow OR Red

Since Red can only be followed by GREEN, the 18th Term CAN'T be Red!

So, 18th = Green and 19th = Yellow
we could have G, G, G, G, G, so the 24th = GREEN
we could have G, G, G, G, Y, so the 24th = YELLOW
Combined, INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich

MANHATTAN PREP OFFICIAL EXPLANATION:

It is tempting to view the information in the question as establishing a pattern as follows:

Green, Yellow, Red, Green, Yellow, Red, . . .

However, consider that the following non-pattern is also possible:

Green, Yellow, Red, Green, Green, Green, Green . . .

(1) INSUFFICIENT: This tells us that the 18th tile is Green or Red but this tells us nothing about the 24th tile. Statement (1) alone is NOT sufficient.

(2) INSUFFICIENT: This tells us that the 19th tile is Yellow or Red but this tells us nothing about the 24th tile. Statement (2) alone is NOT sufficient.

(1) AND (2) INSUFFICIENT: Together, the statements yield the following possibilities for the 18th and 19th tiles:

GY, GR, RY, or RR

However, only GY adheres to the rules given in the question. Thus, we know that tile 18 is green and tile 19 is yellow. However, this does not help us to determine the color of the next tile, much less tile 24 (the one asked in the question). For example, the next tile (tile 20) could be green or red. Thus, the statements taken together are still not sufficient.

The correct answer is E.

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