Analytical Problem 4

John purchased a toy for his young daughter. The toy included nine colorful plastic pieces in the shape of the numbers from 1 to 9. In examining these pieces he made the following observations:

• One piece is purple and two pieces each are red, green, yellow, and blue.
• The two red pieces are consecutive numbers.
• The number 4 is green.
• The two blue pieces are not consecutive numbers.
• Both the 1 and the 9 are yellow.
• The purple piece is not a number immediately greater than or less than either green piece.

Question I. If one of the red pieces is the number 3, what number is the other red piece?
(A) 2   (B) 4   (C) 5   (D) 6   (E) 7

Question II. If the number 5 is green, each of the following could be true EXCEPT

(A) The purple piece and one of the yellow piece are consecutive numbers.

(B) The number 6 is purple.

(C)  The two blue pieces and the purple piece are three consecutive numbers.

(D) The number 2 is red.

(E) The number 8 is red.

Question III. If the number 6 is green, which of the following could be true?

(A) The number 2 is blue.

(B) The number 3 is purple.

(C) The number 5 is red.

(D)The number 5 is purple.

(E) The number 7 is blue.

Question IV.Which of the following, if true, would enable you to determine the color of every number?

(A) The 2 is blue.

(B) The 3 is blue.

(C) The 5 is red.

(D)The 7 is blue.

(E) The 7 is green.

Solution for GRE Math Problem 51:
If we take the second researcher's time as 100%, the first one's time will be 75%. Therefore, the ratio is 75:100=3:4. So, we should divide 35 into the ratio of 3:4. We'll get 15 and 20, their difference is 20-15=5<7
Answer:B

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