GRE Preparation Kit 1 - Section 5

[Samuel]

SECTION 5

Time –30 minutes

30 Questions

In the rectangular coordinate system, the circle with center P is tangent to both the x- and y-axes.

1. The x-coordinate of P The y- coordinate of P

2. 5
    3
    +
    3
    2
    1

3.  x 2 x 2
    The square is inscribed in the circle.

4. The length of a diagonal The length of a diameter of the square of the circle
     x<y<20

5. x + y 35
    In college M the average (arithmetic mean) number of students per course is 30 and the ratio of 
    the number of students to the number of faculty is 20 to 1.

6. The total number 600 of students in College M
     x > 0

7. 800
    590 x
    790
    600 x

8. x 80
    Integer n will be randomly selected from the integers 1 to 13, inclusive.

9. The probability that The probability that n will be even n will be odd
     p + q = 1
     0 < p < q

10. pq
     1
     1
     2x + 3y = 29
     3x + 4y = 41

11. x + y 12
     PQ = OQ = 5

12. The area of region OPQ 10

13. 5 + 52 20
      4
      n
      +
      8
      r
      =
      8
      s
      +
      6
      t
      n, r , s, and t are positive integers.

14. 2n + r 2s + t
      In the xy-coordinate system, the point (x, y) lies on the circle with equation x 2 + y 2 = 1

15. x + y 1.01

16. A health food store prepares a breakfast food that consists of oats, raisins, and nuts mixed in 
      the ratio 9:2:1, respectively, by weight. If the nuts in the mixture weigh 9.2 pounds, how many 
      pounds does the total mixture weigh?
      (A) 82.2
      (B) 92.2
      (C) 101. 2
      (D) 110.4
      (E) 165.6

17. 3 - 257(32)=
     (A) –30
     (B) –10
     (C) 23
     (D) 63
     (E) 77

18. For every positive integer n greater than 1, n! Is defined as the product of the first n positive
      integers, For example, 4! = (1) (2) (3) (4) = 24. What is the value of 10! 12! ?
     (A) 2
     (B) 66
     (C) 121
     (D) 132
     (E) 144

19. A market survey showed that 76 percent of the visitors at a certain resort came from Pacific or
      southwestern states. Of these,
      3
      2
      were from California, and 87 percent of the Californians were from southern California.     
      Approximately what percent of the visitors at the resort were from southern California?
     (A) 40%
     (B) 45%
     (C) 50%
     (D) 55%
     (E) 65%

20. If
      n
      54 1
      is an integer an n is an integer, then n could be each of the following EXCEPT
     (A) 4
     (B) 6
     (C) 13
     (D) 25
     (E) 26

Questions 21-22 refer to the following table.

21. What is the ration of the amount budgeted annually for food to the amount budgeted annually
      for savings?
      (A) 4 to 3
      (B) 4 to 7
      (C) 5 to 3
      (D) 7 to 3
      (E) 7 to 4

22. If a pie graph (such as the one above) were drawn to scale to represent the budges distribution
      into the five categories, what would be the measure of the central angle of the sector 
      representing savings?
     (A) 15º
     (B) 30º
     (C) 36º
     (D) 42º
     (E) 54º

Questions 23-25 refer to the following graphs.

23. The funds distributed in 1992 for youth development were approximately
      (A) $38,000
      (B) $170,000
      (C) $380,000
      (D) $450,000
      (E) $1,700,000

24. The increase in the amount of money distributed for family support from 1992 to 1993 was 
      closest to which of the following?
     (A) $0
     (B) $24,000
     (C) $40,000
     (D) $60,000
     (E) $94,000

25. If all of the emergency assistance funds in 1993 were distributed among 40 groups, which of the
     following is closest to the average (arithmetic mean) amount distributed per group?
     (A) $10,000
     (B) $11,000
     (C) $12,000
     (D) $13,000
     (E) $14,000

26. The curve above consists of three semicircles: AB, BC, and CD. The diameter of AB is 2, the 
      diameter of BC is twice the diameter of AB, and the diameter of CD is twice the diameter of 
      BC. What is the total length of the curve?
     (A) 2
     (B) 4
     (C) 6
     (D) 7
     (E) 8

27. What is the cost, in cents, of using a certain fax machine to send n pages of a report if the total
      cost for sending the first k pagers is r cents and the cost for sending each additional page is s
      cents? (Assume that n > k.)
     (A) r + s (n - k)
     (B) r + s (n + k)
     (C) rs(n + k)
     (D) kr + s(n - k)
     (E) kr + ns

28. A rectangular solid has a square base and altitude of 7. If the volume of the solid is 252, then 
      the perimeter of the square base is
     (A) 9
     (B) 24
     (C) 28
     (D) 36
     (E) 49

29. In a series of races, 10 toy cars are raced, 2 cars at a time. If each car must race each of the
      other cars exactly twice, how many races must be held?
     (A) 40
     (B) 90
     (C) 100
     (D) 180
     (E) 200

30. (210 - 29 )(28 - 27 ) =
     (A) 2
     (B) 2 2
     (C) 24
     (D) 28
     (E) 216