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

Analytical problem 2

The Fairfield Foreign Film Festival plans to show six films—one each from Belgium, Canada, Denmark, England, France, and Germany. The festival will open on a Thursday and close three days later on a Sunday. Each film will be shown once during the four days of the festival.

The order in which the films will be shown must adhere to the following conditions:

1. At least one film will be shown each day.
2. No more than three films will be shown on any two consecutive days.
3. The Belgian film must be shown on Saturday.
4. The Canadian film must be shown on the same day as another film.
5. The French film must be shown on a day before the German film is shown.
6. The Danish film must be shown on a day after the English film is shown.

Question I
If only one film is shown on Thursday, it could be the entry from which of the following countries?
(A) Belgium
(B) Canada
(C) Denmark
(D) France
(E) Germany

Question II
If the Belgian and French films are shown on the same day, which of the following must be true?
(A) The film from Denmark will be shown on
Thursday.
(B) The film from Denmark will be shown on
Friday.
(C) The film from Germany will be shown on
Thursday.
(D) The film from Canada will be shown on
Sunday.
(E) The film from England will be shown on
Sunday.

Question III
If the director of the festival decides to show two films on Thursday and two on Sunday, how many films would be eligible to be shown on Friday?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

Question IV
If the English and German films are shown on the same day, which of the following must be true?
(A) The film from England will be shown on
Thursday.
(B) The film from France will be shown on Friday.
(C) The film from Canada will be shown on
Saturday.
(D) The film from Germany will be shown on
Saturday.
(E) The film from Canada will be shown on
Sunday.

Question V
If the film from England is shown on Saturday, which of the following films cannot be shown on the same day as any other film?
(A) The film from Belgium.
(B) The film from Canada.
(C) The film from England.
(D) The film from France.
(E) The film from Germany.

Solution for GRE Math Problem 9:

"ratio of the number of insects in a given population having characteristic X to the number of insects in the population not having characteristic X is 5:3" means that of population has characteristics X, and of the population has not characteristics X.

To find, what proportion of the total insect population are male insects having the characteristic X, we must multiply the fraction of X-insects in the whole population by the fraction of males in X-insects.

Answer: D