GRE Preparation Kit 2 - Section 1

[Samuel]

SECTION 1

1. 2(8-7) 2(7-8)
    x + y = 2

2. x y

3. 7
    3
   +
    7
    2
    1

4. x 5
   On Elm Street there are 6 houses on one side of the street and 4 houses on the other. Each pair
   of houses on Elm Street is connected by exactly one telephone line.

5. The total number of such 12 lines that connect houses on opposite sides of Elm Street

6. The area of triangular The area of triangular region OPQ region ORS

7. (0.01)(0.07)(70) 0.49
     x < y < z

8. 3
    x y z
    z
The three small rectangles have the same dimensions

9. RS
    PS
    2
    1
In a certain city, 20ºF was the average (arithmetic mean) of the low temperatures of xºF, 25ºF, and
37ºF on three consecutive days.

10. x 0
      m= 4x + 4y, x-y

11. x y
      m
      
     2
     8
     ABCD is a rectangle with diagonals AC and DB.

12  r + u + v r + u + v + w
     n is a positive integer.

13. n 100 100 n
     f(t) = kt for all t, where k is a constant, and
     f(3) =
     2
     1

14. k f(1)
     100x<y
     1,000x < 2y

15. 1,100x y

16. Mr. Gifford wishes to put 372 eggs into cartons that can hold 12 eggs each. If he has 50 empty 
      cartons and completely fills as many of them as possible with the 327 eggs, how many of the
      cartons will remain empty?
     (A) 12
     (B) 15
     (C) 19
     (D) 28
     (E) 31

17. Which of the following numbers is greatest?
     (A) -0.225
     (B) -0.0225
     (C) -0.323
     (D) -0.0325
     (E) -0.3205

18. If a certain automobile gets between 20 and 24 miles per gallon of gasoline, inclusive, what 
      would be the maximum amount of gasoline, in gallons, this automobile would consume on a trip
      of 360 miles?
     (A) 20.0
     (B) 18.0
     (C) 16.4
     (D) 16.0
     (E) 15.0

19. If y - x = 2 and y -z =3, which of the following best represents the relative positions of x, y, and
      z on the number line? (Note: The figures are drawn to scale.)

20. Two beads are to be independently and randomly selected, one from each of tw o bags. If
     7
     2
     of the beads in one bag and
     7
     3
     of the beads in the other bag are yellow, what is the probability that both beads selected will be
     yellow?
   (A) 3    2
   (B) 7    5
   (C) 7    6
   (D) 49   4
   (E) 49  6

Questions 21-23 refer to the graph below.

21. By what percent did the number of personal computers sold by Compaq increase from 1992 to
      1993?
     (A) 50%
     (B) 65%
     (C) 75%
     (D) 100%
     (E) 110%

22. In 1992, Packard Bell accounted for what percent of the computers sold by the four companies 
      listed?
     (A) 6%
     (B) 9%
     (C) 10%
     (D) 12%
     (E) 14%

23. If the ratio of the number of personal computers sold by IBM Compaq, and Tandy (not shown) 
      in 1993 was 6 to 4 to1, respectively, approximately how many personal computers were sold 
      by Tandy in 1993?
     (A) 350,000
     (B) 400,000
     (C) 450,000
     (D) 500,000
     (E) 550,000

Questions 24-25 refer to the following table.

24. For the categories given, which category accounts for approximately
     4
     1
     of the total number of graduates expected for each off the years shown?
    (A) High school diploma
    (B) Associate degree
    (C) Bachelor's degree
    (D) Master's degree
    (E) Doctoral degree

25. The number of associate degrees expected to be granted in 2001 is most nearly what percent 
      greater than the number of associate degrees expected to be granted in 1995?
     (A) 2%
     (B) 3%
     (C) 5%
     (D) 7%
     (E) 9%

26. If the area of the shaded region of the square above is 20, what is the perimeter of the square?
     (A) 4 5
     (B) 8 5
     (C) 16 5
     (D) 80
     (E) 400

27. If x =
      y
      1
      and y =
      1x
      1
     , them y =
     (A) 2
     (B) 2      1
     (C) -2    1
     (D) -1
     (E) -2

28. If 720 is the product of the consecutive integers beginning with 2 and ending with n, what is the
      value of n-1?
     (A) 5
     (B) 6
     (C) 8
     (D) 11
     (E) 23

29. When it was found that 150 more tickets for the school play were sold than the seating capacity
      of the auditorium. It was decided to have two performances. if the total number of tickets sold 
      was equal to the total number who attended and if the auditorium was 3
      2
      full for each of the two performances, what is the seating capacity of the auditorium?
     (A) 100
     (B) 200
     (C) 225
     (D) 300
     (E) 450

30. If n = pqr, where p, q, and r are three different positive prime numbers, how many different
      positive divisors does n have, including l and n?
     (A) 3
     (B) 5
     (C) 6
     (D) 7
     (E) 8