GRE sample question.

In a game, exactly six inverted cups stand side by side in a straight line, and each has exactly one ball hidden under it. The cups are numbered consecutively 1 through 6. Each of the balls is painted a single solid color. The colors of the balls are green, magenta, orange, purpose, red and yellow. The balls have been hidden under the cups in a manner that conforms to the following conditions:

The purple ball must be hidden under a lower-numbered cup than the orange ball.
The red ball must be hidden under a cup immediately adjacent to the cup under which the magenta ball is hidden.
The green ball must be hidden under cup 5.



1.Which of the following could be the colors of the balls under the cups, in order from 1 through 6?

(A) Green, yellow, magenta, red, purple, orange
(B) Magenta, green, purple, red, orange ,yellow
(C) Magenta, red, purple, yellow, green, orange
(D) Orange, yellow, red, magenta, green, purple
(E) Red, purple, magenta, yellow, green, orange

Ans : C
Explanation:  
Inverted cups are numbered 1 through 6 consecutively. Six balls of different colors are hidden under them. The colors are G, M, O, P, R, Y using the first alphabet of each color. We use the letter B for ball. For example PB stands for purple colored ball.
The given conditions are
(i) PB < OB ('<' indicates that this purple ball is hidden in a lower numbered cup than orange ball)
(ii) RB, MB are adjacent .
(iii) GB = 5 (this means that the green ball is hidden under cup No. 5)
No restrictions given for yellow colored ball.

(A) Wrong. Green Ball is not under Cup 5.
(B) Wrong. Green Ball is not under Cup 5.
(C) Correct: All three above conditions satisfied.
(D) Wrong : Purple Ball is not before orange Ball.
(E) Wrong : RB and MB are not adjacent.



2.If the magenta ball is under cup 4, the red ball must be under cup

(A) 1 (B) 2 (C) 3 (D) 5 (E) 6

Ans : C
Explanation: 
Inverted cups are numbered 1 through 6 consecutively. Six balls of different colors
are hidden under them. The colors are G, M, O, P, R, Y using the first alphabet of
each color. We use the letter B for ball. For example PB stands for purple colored
ball.
The given conditions are
(i) PB < OB
('<' indicates that this purple ball is hidden in a lower numbered cup than orange ball)
(ii) RB, MB are adjacent .
(iii) GB = 5
(this means that the green ball is hidden under cup No. 5)
No restrictions given for yellow colored ball.
Here MB = 4. Since GB = 5, RB which is to be adjacent to MB must occupy place 3.
So, C is the correct answer.



3. A ball of which of the following colors could be under cup 6?

(A) Green (B) Magenta (C) Purple (D) Red (E) Yellow

Ans : E
Explanation:
Inverted cups are numbered 1 through 6 consecutively. Six balls of different colors
are hidden under them. The colors are G, M, O, P, R, Y using the first alphabet of each color. We use the letter B for ball. For example PB stands for purple colored ball.
The given conditions are
(i) PB < OB
('<' indicates that this purple ball is hidden in a lower numbered cup than orange ball)
(ii) RB, MB are adjacent .
(iii) GB = 5
(this means that the green ball is hidden under cup No. 5)
No restrictions given for yellow colored ball.
(A) Wrong: GB is 5 and cannot be 6.
(B) Wrong: RB cannot be 5 and so MB, RB cannot be adjacent.
(C) Wrong: If PB = 6, there is no place for OB and so PB < OB fails.
(D) Wrong: If RB = 6, then MB cannot be 5 as GB = 6. So the condition RB, MB adjacent fails.
(E) Correct: No restriction for yellow Ball.
So, the answer is E. 



4. If the purple ball is under cup 4, the orange ball must be under cup

(A) 1 (B) 2 (C) 3 (D) 5 (E) 6

Ans : E
Explanation: 
Inverted cups are numbered 1 through 6 consecutively. Six balls of different colors
are hidden under them. The colors are G, M, O, P, R, Y using the first alphabet of
each color. We use the letter B for ball. For example PB stands for purple colored
ball.
The given conditions are
(i) PB < OB
('<' indicates that this purple ball is hidden in a lower numbered cup than orange ball)
(ii) RB, MB are adjacent .
(iii) GB = 5
(this means that the green ball is hidden under cup No. 5)
No restrictions given for yellow colored ball.
PB = 4
(A), (B), (C) are wrong as orange Ball should be after 4.
(D) is wrong because Green Ball should be at 5.
(E) is correct.
So the correct answer is E.



5. Which of the following must be true?
(A) The green ball is under a lower-numbered cup than the yellow ball.
(B) The orange ball is under a lower-numbered cup than the green ball.
(C) The purple ball is under a lower-numbered cup than the green ball.
(D) The purple ball is under a lower-numbered cup than the red ball.
(E) The red ball is under a lower-numbered cup than the yellow ball.
Ans : C
Explanation: 
Inverted cups are numbered 1 through 6 consecutively. Six balls of different colors
are hidden under them. The colors are G, M, O, P, R, Y using the first alphabet of
each color. We use the letter B for ball. For example PB stands for purple colored
ball.
The given conditions are
(i) PB < OB
('<' indicates that this purple ball is hidden in a lower numbered cup than orange ball)
(ii) RB, MB are adjacent .
(iii) GB = 5
(this means that the green ball is hidden under cup No. 5)
No restrictions given for yellow colored ball.
(A) Wrong: It can happen as number 6 slot is vacant. But it is not a must.
(B) Wrong: Orange Ball can be event at Number 6.
(C) Correct: Purple Ball cannot be at Number 6 as it should be before Orange Ball as per the initial condition.
Since GB=5, PB must be less than Green Ball number.
(D) and (E) are also not a must.
So the correct answer is C.