Expert: Chanda Walker - 2/15/2009

Question

12. | 0.25 y + 1 | = 0.5
a.y = 1.1 or y = -1.1     c.y = 6 or y = 2
b.y = -6 or y = -2        d.y = 6 or y = -2

13. | 3 k - 2 | < 4
a.k > 1 or k < 2      b.k > -0.67 or k < 2
c.1 < k < 2           d.-0.67 < k < 2

14. | 0.25 y + 5 | > -0.75
a.-23 < y < -17         b.All real numbers
c.y < -5 or y > 4       d. -5 < y < 1

15. 7 - | 3 y - 2 | ≤  1
a.y ≤ 7 or y ≥ 8      b.y ≤ -1.33 or y  ≥ 2.67
c.y ≤ -4 or y ≥ 5     d.y ≤ -0.75 or y ≥ 0.375

16. | 4 + 2 y | ≥ -3
a.y ≤ -5 or y ≥ -0.5      b.All real numbers  
c.y ≤ -3.5 or y ≥ 1       d.-3.5 ≤ y ≤ -0.5

17.   | 1 - 0.3 x | ≥ -3
a.x ≥ 13.33 or x ≤ -6.67     b. All real numbers
c.x ≤ -2.2 or x ≤ 0.2        d.-1.66 ≤ x ≤ 8.33

18.| 1.2 - 0.4 x | < 2
a.-2 < x < 8        b.8 < x < -2
c.-8 > x > 2        d.x < -8 or x > 2

19. Find three consecutive even integers such that the sum of the first two is greater than 27 and the sum of the last two is less than 39.
a.10, 12, 14 and 6, 8, 10     b.4, 2, 6 and 4, 10, 6
c.22, 18, 14 and 12, 16, 14   d. 14, 16, 18 and 16, 18, 20

20. An oak tree is 6 times as old as a pine tree and an elm tree is 6 years younger than the oak tree.  In 3 years, the age of the elm will be 3 times the age of the pine.  How old is the oak tree now?
a.4 years old     b.24 years old
c.18 years old    d.6 years old

21. The ratio of the present ages of two museums is 3 to 5.  Twelve years ago, the sum of their ages was less than 56 years.  Find the possibilities for the present age of the younger museum.
a.Between 18 yr and 32 yr    b.Between 10 yr and 24 yr
c.Between 8 yr and 18 yr     d.Between 12 yr and 30 yr

22. Cities A and B are located on an east-west highway at a distance of 244 mi from each other.  A truck left City A at 8:00 A.M. driving 47 mi/h toward City B.  A car left City B at 10:00 A.M. traveling 53 mi/h toward City A.  At what time did the car pass the truck?
a.9:30 A.M.     b.10:30 A.M.
c.11:30 A.M.    d.12:30 P.M.

23. Find the solution set of the inequality:
| 2 y - 3 | < 11
a{y: -4 < y < 7}    b.{y: -2 < y < 8}
c.{y: 4 < y < 7}    d.{y: -10 < y < 2}

24. Find the solution set of the inequality:  
| 4 t + 6 | ≤ 14
a.{t: 2< t < 5}     b.{t: -5 ≤ t ≤ 2}
c.{t: -5 < t < 2}   d.{t: 2 ≤ t ≤ 5}

25. Find the solution set for the inequality:
14 > | 4 z - 2 |
a.{z: -3 < z < 4}    b.{z: 3< z < -4}
c.(z: -3 ≤ z ≤ 4}    d.{z: 1 ≤ z ≤ 6}

26. Find the solution set for the inequality:
| n - 2 | ≤ 5
a.{n: - 3 ≤ n ≤ 7}     b.{n: -2 ≤ n < 5}
c.{n: -3 ≤ n < 7}      d.{n: -1 ≤ n ≤ 4}

27. Solve the equation:
| 7.5 - 5 n | = 2.5
a.1, -2        b.2, 3
c.3, 1         d.2, 1

28. A rectangle is 3 times as wide as a square.  The rectangle's length is 15 ft shorter than 5 times the square's length.  Given that the sum of the two perimeters must be less than 150 ft, find the set of all possible lengths for the rectangle.
a.{l: l3 ft < l < 50 ft}     b.{l: 0 ft < l < 30 ft}
c.{l: 5 ft < l < 45 ft}      d.{l: 10 ft < l < 50 ft}

29. Mr. McTier invests $600 at 9% per year, and $800 at 12% per year.  During what time period will the $1,400 earn between $525 and $975, inclusive, in simple interest? a.2.5 yr ≤ t ≤ 6.5 yr          b.3.5 yr ≤ t ≤ 6.5 yr
c.1.0 yr ≤ t ≤ 4.0 yr          d.4.0 yr ≤ t ≤ 6.5 yr

30. A rectangle's length is 12 in. less than 3 times its width.  Find the set of all the possible widths given that the perimeter must be less than 48 in.
a.{w: 2 in. < w < 4 in.}    b.{w: 1 in. < w < 5 in.}
c.{w: 4 in. < w < 9 in.}    d.{w: 6 in. < w < 14 in.}  

Answer
There are too many problems for me to help with all of them.  I'll work some to show you how they are done.  If you still can't do them, please ask SPECIFIC questions and I'll try to help further.


12. | 0.25 y + 1 | = 0.5
a.y = 1.1 or y = -1.1     c.y = 6 or y = 2
b.y = -6 or y = -2        d.y = 6 or y = -2

0.25 y + 1 = -0.5
0.25y = -1.5
y = -6

OR

0.25 y + 1 = 0.5
0.25 y = -0.5
y = -2

The answer is B.


15. 7 - | 3 y - 2 | ≤  1
a.y ≤ 7 or y ≥ 8      b.y ≤ -1.33 or y  ≥ 2.67
c.y ≤ -4 or y ≥ 5     d.y ≤ -0.75 or y ≥ 0.375

7 - (3y -2) ≤ 1
7 - 1 ≤ 3y -2
6 + 2 ≤  3y
8/3 ≤ y
y  ≥ 2.67

7 + (3y - 2) ≤ 1
6 ≤ - 3y + 2
4 ≤ - 3y
4/3 ≤ -y
y ≤ -1.33

The answer is B.


19. Find three consecutive even integers such that the sum of the first two is greater than 27 and the sum of the last two is less than 39.
a.10, 12, 14 and 6, 8, 10     b.4, 2, 6 and 4, 10, 6
c.22, 18, 14 and 12, 16, 14   d. 14, 16, 18 and 16, 18, 20

consecutive even integers:
x, x+ 2, x+4

x + x + 2> 27
2x > 25
x > 12.5
x ≥  14  (remember we have to have EVEN INTEGERS

x + 2 + x + 4 < 39
2 x + 6 < 39
2x < 33
x < 16.5
x ≤ 16

So 14, 16, 18
and 16, 18, 20.

The answer is D.


23. Find the solution set of the inequality:
| 2 y - 3 | < 11
a{y: -4 < y < 7}    b.{y: -2 < y < 8}
c.{y: 4 < y < 7}    d.{y: -10 < y < 2}

2y - 3 < 11
2y < 14
y < 7

2y - 3 > -11
2y > - 8
y > -4

y:-4 < y< 7

The answer is A.

28. A rectangle is 3 times as wide as a square.  The rectangle's length is 15 ft shorter than 5 times the square's length.  Given that the sum of the two perimeters must be less than 150 ft, find the set of all possible lengths for the rectangle.
a.{l: l3 ft < l < 50 ft}     b.{l: 0 ft < l < 30 ft}
c.{l: 5 ft < l < 45 ft}      d.{l: 10 ft < l < 50 ft}

w = 3s
l = 5s - 15

2w + 2l + 4s < 150


2(3s) + 2*(5s - 15) + 4s < 150
6s + 10 s - 30 + 4s < 150
20s - 30 < 150
20s < 180
s < 9

The length therefore must be
l < 5*9 - 15
l < 45 - 15
l < 30

The answer is B.