Chapter 14 Practice Test 4 With Answers - Mcgraw-Hill'S Psat/nmsqt Page 41
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45CHAPTER 14 / PRACTICE PSAT 4
513
7 gallons (7/10 Â 10 ¼ 7) of lemon gelatin and 3
x þ (x þ 2) þ (x þ 4) ¼ 66
23. E
gallons (3/10 Â 10 ¼ 3) of lime gelatin. Therefore in
Combine like terms:
3x þ 6 ¼ 66
20 gallons of a mixture, there are 13 gallons of
Subtract 6:
3x ¼ 60
lemon gelatin, or 13/20.
x ¼ 20
Divide by 3:
(Chapter 8 Lesson 4: Ratios and Proportions)
The three integers are x, x þ 2, and x þ 4. They are
therefore 20, 22, and 24.
If you answered 23, you forgot they needed to be
28. B
even.
l
(Chapter 9 Lesson 1: Solving Equations)
B
C
2w
A
2.5w
24. B
2w
2.5w
POLITICAL PARTY MEMBERSHIP
Total
Men
Women
D
320
600
Democrat
m
197
Republican
At points of tangency, right angles are formed, so we
38
105
Independent
have two identical right triangles in the figure. If you
555
645
1,200
Total
draw the hypotenuse from point A to point C, you
break the angles into angles measuring 2.5w and 2w.
There are 1808 in a triangle, so 2.5w þ 2w þ 90 ¼ 180
There are 1,200 total people, of which 645 are
Combine like terms:
4.5w þ 90 ¼ 180
women. Therefore, 1,200 2 645 ¼ 555 are men. Of
Subtract 90:
4.5w ¼ 90
these men, 38 are independent and 320 are Demo-
Divide by 4.5:
w ¼ 20
crats. Therefore 555 2 38 2 320 ¼ 197 are Republi-
(Chapter 11 Lesson 8: Circles)
cans.
(Chapter 11 Lesson 2: Triangles)
(Chapter 10 Lesson 8: Data Analysis)
1
XY ¼
XY ¼ 2,
29. 8
Since
(YZ),
if
then
3
25. B
Begin by looking at the far-right column.
YZ ¼ 3(2) ¼ 6.
X þ Y ¼ 9. The middle column tells us the same infor-
2
6
mation, and the far-left column tells us that
W
X
Y
Z
3 þ 2 ¼ Y.
Therefore Y ¼ 5 and X ¼ 9 2 5 ¼ 4.
If WX is half of WY, then XY must also be equal to
(Chapter
10
Lesson
3:
Numerical
Reasoning
one-half of WY. Therefore WX ¼ XY ¼ 2.
Problems)
2
2
6
W
X
Y
Z
Try a few positive odd integers for x and see
26. C
if there is a pattern:
As a result, XZ ¼ 8.
(Chapter
10
Lesson
3:
Numerical
Reasoning
2
1
2
x ¼ 1 (4
)
¼ 4
¼ 16
Problems)
2
3
2
x ¼ 3 (4
)
¼ 64
¼ 4,096
2
5
2
x ¼ 5 (4
)
¼ 1,024
¼ 10,48,576
30. 6
r and s must be positive integers. Use trial
They all end in 6.
and error to plug in numbers and find out how
(Chapter 10 Lesson 7: Sequences)
many pairs will work given the rules of the question.
4r þ 5s , 30
r ¼ 1
27. C
Let’s say you have 10 gallons of each type of
4(1) þ 5s , 30
gelatin. In 10 gallons of citrus gelatin there are 4
Subtract 4:
5s , 26
gallons (2/5 Â 10 ¼ 4) of orange-flavored gelatin
s could be 2, 3, 4, or 5
and 6 gallons (3/5 Â 10 ¼ 6) of lemon-flavored
r ¼ 2
4(2) þ 5s , 30
gelatin. In 10 gallons of sour gelatin there are
Subtract 8:
5s , 22
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