Free Full Length DAT Quantitative Reasoning Practice Test

Full Length DAT Quantitative Reasoning Practice Test

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DAT Quantitative Reasoning 
Practice Test 4

 

 

40 questions

Total time for this section: 45 Minutes

You may use a basic calculator on this test.

1-

If the interior angles of a quadrilateral are in the ratio 1:2:3:6, what is the measure of the largest angle?

(A) 72
(B) 180
(C) 30
(D) 90
(E) 60
2-

A bank is offering 2.7% simple interest on a savings account. If you deposit $18,000, how much interest will you earn in three years?

(A) $1,450
(B) $1,458
(C) $1,456
(D) $1,445
(E) $1,440
3-

If f(x)=6 x + 3 and g(x)=2 x2 + 2 x, then find (fg)(x).

(A) 6 x + 32 x2 + 2 x
(B) 6 x  32 x2 + 2 x
(C) 3 x  3x2 + 2 x
(D) 3 x + 3x2 + 2 x
(E) 3 x + 3x2  2 x
4-

If the area of a circle is 36 square meters, what is its diameter?

(A) 6 π6
(B) 6 ππ
(C) 6 ππ
(D) 6 π
(E) 6
5-

If the ratio of home fans to visiting fans in a crowd is 6:4 and all 30,000 seats in a stadium are filled, how many visiting fans are in attendance?

(A) 12,000
(B) 10,000
(C) 14,000
(D) 11,000
(E) 16,000
6-

In the standard (x,y) coordinate plane, which of the following lines contains the points (2, 6) and (5,18)?

(A) y=8 x + 22
(B) y=8 x + 10
(C) y=8 x  22
(D) y=8 x  10
(E) y=4 x  10
7-

In the figure below, line A is parallel to line B. What is the value of angle x?
DAT_Math

(A) 125 degree
(B) 135 degree
(C) 60 degree
(D) 120 degree
(E) 130 degree
8-

If sin A=64 in a right triangle and the angle A is an acute angle, then what is cos A?

(A) 206
(B) 204
(C) 64
(D) 46
(E) 206
9-

The length of a rectangle is 32 times its width. If the width is 18, what is the perimeter of this rectangle?

(A) 95
(B) 80
(C) 92
(D) 72
(E) 90
10- If 120% of a number is 60, then what is 80% of that number?
(A) 45
(B) 40
(C) 60
(D) 65
(E) 44
11-

Last week 32,000 fans attended a football match. This week four times as many bought tickets, but one Fourth of them cancelled their tickets. How many are attending this week?

(A) 96,000
(B) 128,000
(C) 32,000
(D) 98,000
(E) 90,000
12- The width of a box is one Fourth of its length. The height of the box is one Fourth of its width. If the length of the box is 32 cm, what is the volume of the box?
(A) 510 cm3
(B) 515 cm3
(C) 520 cm3
(D) 512 cm3
(E) 514 cm3
13- If tan⁡x=512, then sin ⁡x=
(A) 1213
(B) 135
(C) 1312
(D) 513
(E) 125
14- Convert 860,000 to scientific notation.
(A) 86 × 105
(B) 8.6 × 104
(C) 8.6 × 105
(D) 8.6 × 106
(E) 8.6 × 107
15- If (x  3)2 + 2 > 4 x  5, then x can equal which of the following?
(A) 1
(B) 6
(C) 8
(D) 3
(E) 4
16- What is the solution of the following inequality?
|x + 4|  7
(A) x  3  x  11
(B) Set of real numbers
(C) x  3  x  11
(D) x  3
(E) x  11
17- In the following figure, ABCD is a rectangle. If a=5, and b=3 a, find the area of the shaded region. (the shaded region is a trapezoid)
(A) 5
(B) 5 5
(C) 4 5
(D) 5
(E) 4
18- In two successive years, the population of a town is increased by 30% and 40%. What percent of the population is increased after two years?
(A) 182%
(B) 85%
(C) 82%
(D) 80%
(E) 88%
19- Which of the following is one solution of this equation?
x2  2 x  4=0
(A) 1  4
(B) 1 + 4
(C) 1  5
(D)  5
(E) 5
20- (x2)69 equal to?
(A) x69
(B) x129
(C) x29
(D) x126
(E) x96
21- three-kilograms apple and four -kilograms orange cost $30. If onekilogram apple costs $6 how much does one-kilogram orange cost?
(A) $9
(B) $8
(C) $6
(D) $4
(E) $3
22- In the following figure, what is the perimeter of ABC if the area of ADC is 30?
DAT_Math1
(A) 35
(B) 15
(C) 45
(D) 40
(E) 30
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23- Which of the following expressions is equal to x25  x225?
(A) 4 x5
(B) 2 x5
(C) 5 x2
(D) 6 x2
(E) 3 x2
24- If 5 x=y, then x=
(A) y5
(B) 25y
(C) 5y
(D) y25
(E)  y25
25- A card is drawn at random from a standard 72card deck, what is the probability that the card is of Hearts? (The deck includes 16 of each suit clubs, diamonds, hearts, and spades)
(A) 29
(B) 49
(C) 169
(D) 92
(E) 129
26- The average weight of 23 girls in a class is 50 kg and the average weight of 25 boys in the same class is 65 kg. What is the average weight of all the 45 students in that class?
(A) 57.82
(B) 57.83
(C) 57.81
(D) 57.80
(E) 57.84
27- A football team had $35,000 to spend on supplies. The team spent $18,000 on new balls. New sport shoes cost $135 each. Which of the following inequalities represent how many new shoes the team can purchase? 
(A) 135 x  18,000  35,000
(B) 135 x  18,000  35,000
(C) 135 x + 18,000  35,000
(D) 135 x + 18,000  35,000
(E) 135 x + 18,000  35,000
28- What is the value of the expression 4 (x + 3 y)  (3 + x)2 when x=4 and y=2?
(A) 89
(B) 9
(C)  9
(D)  89
(E) 49
29- The average of five consecutive numbers is 25. What is the smallest number?
(A) 25
(B) 27
(C) 32
(D) 30
(E) 26
30- If y=( 4 x3)2, which of the following expressions is equal to y?
(A) 16 x3
(B) 64 x3
(C)  16 x6
(D)  64 x6
(E) 16 x6
31- The surface area of a cylinder is 192 π cm2. If its height is 4 cm, what is the radius of the cylinder? 
(A)  8 cm
(B) 8 cm
(C) 12 cm
(D)  12 cm
(E) 96 cm
32- Mia purchased a sofa for $616.85. The sofa is regularly priced at $845. What was the percent discount Mia received on the sofa?
(A) 73%
(B) 75%
(C) 25%
(D) 27%
(E) 20%
33- What is the difference in area between a 6 cm by 3 cm rectangle and a circle with diameter of 8 cm? (π=3)
(A) 35
(B) 18
(C) 48
(D) 66
(E) 30
34- A cruise line ship left Port A and traveled 50 miles due west and then 120 miles due north. At this point, what is the shortest distance from the cruise to port A?
(A) 140 miles
(B) 130 miles
(C) 120 miles
(D) 110 miles
(E) 170 miles
35- What is the slope of a line that is perpendicular to the line?
9 x  3 y=24?
(A) 13
(B) 12
(C)  13
(D)  12
(E)  19
36- If f(x)=4 x3  5 and (x)=x6, what is the value of f(g(x))?
(A) x354 + 5
(B) x354  5
(C) x3216  5
(D) x3216 + 5
(E) x3216
37- The ratio of boys to girls in a school is 1:5. If there are 750 students in a school, how many boys are in the school. 
(A) 133
(B) 120
(C) 135
(D) 140
(E) 125
38- If the ratio of 7 a to 4 b is 18, what is the ratio of a to b?
(A) 116
(B) 115
(C) 114
(D) 113
(E) 112
39- If one angle of a right triangle measures 30, what is the sine of the other acute angle?
(A) 32
(B) 23
(C) 33
(D) 22
(E) 1
40- If x=8, what is the value of y in the following equation? 
4 y=4 x22  4
(A) 30
(B) 35
(C) 34
(D) 31
(E) 33
1- Choice B is correct

The correct answer is 180
The sum of all angles in a quadrilateral is 360 degrees. 
Let x be the smallest angle in the quadrilateral.
Then the angles are:
x,2 x,3 x,6 x
x + 2 x + 3 x + 6 x=36012 x=360x=30
The angles in the quadrilateral are: 30,60,90, and 180

2- Choice B is correct

The correct answer is $1,458
Use simple interest formula:
I=prt
(I= interest, p= principal, r= rate, t= time)
I=(18000) (0.027) (3)=1458

3- Choice A is correct

The correct answer is 6 x + 32 x2 + 2 x
(fg)(x)=f(x)g(x)=6 x + 32 x2 + 2 x

4- Choice C is correct

The correct answer is 6 ππ
Formula for the area of a circle is:
A =π r2
Using 36 for the area of the circle we have:
36=π r2
Let’s solve for the radius (r).
36π=r2r=36π=6π=6π × ππ=6 ππ

5- Choice A is correct

The correct answer is 12,000
Number of visiting fans: 4 × 3000010=12,000

6- Choice C is correct

The correct answer is y=8 x  22
The equation of a line is: 
y=m x + b, where m is the slope and is the yintercept.
First find the slope:
m=y2  y1x2  x1=18  ( 6)5  2=243=8
Then, we have: y=8 x + b
Choose one point and plug in the values of x and y in the equation to solve for b.
Let’s choose the point (2, 6)
y=8 x + b 6=8 (2) + b 6=16 + bb= 22
The equation of the line is: y=8 x  22

7- Choice D is correct

The correct answer is 120 degree
The angle x and 35 are complementary angles.
Therefore:
x + 60=180
180  60=120

8- Choice B is correct

The correct answer is 204
sin A=64 
Since sin θ=oppositehypotenuse, we have the following right triangle. Then:
c=62  42=36  16=20
cos =204

9- Choice E is correct

The correct answer is 90
Length of the rectangle is: 32 × 18=27
perimeter of rectangle is: 2 × (27 + 18)=90

10- Choice B is correct

The correct answer is 40
First, find the number.
Let x be the number.
Write the equation and solve for x
120% of a number is 60, then:
1.2 × x=60x=60 ÷ 1.2=50
80% of 50 is:
0.9 × 50=40

11- Choice A is correct

The correct answer is 96,000
Three times of 32,000 is 128,000.
One sixth of them cancelled their tickets.
One sixth of 128,000 equals 32,000 (14 × 128000=32000)
96,000 (128000  32000=96000) fans are attending this week

12- Choice D is correct

The correct answer is 512 cm3
If the length of the box is 32, then the width of the box is one Fourth of it, 8, and the height of the box is 2 (one Fourth of the width). 
The volume of the box is:
V = (length) × (wdth) × (height) =(32) × (8) × (2)=512 cm3

13- Choice D is correct

The correct answer is 513
tan⁡=oppositeadjacet, and tan⁡x=512, therefore, the opposite side of the angle x is 5 and the adjacent side is 12.
Let’s draw the triangle.
Using Pythagorean theorem, we have:
a2 + b2=c252 + 122=c225 + 144=c2c=13
sin x=oppositehypotenuse=513

14- Choice C is correct

The correct answer is 8.6 × 105
860000=8.6 × 105

15- Choice A is correct

The correct answer is 1
Plug in the value of each option in the inequality.
A. 1   (1  3)2 + 2 > 4 (1)  56 > 1    Bingo!
B. 6   (6  3)2 + 2 > 4 (6)  511 > 19 No!
C. 8   (8  3)2 + 2 > 4 (8)  527 > 27 No!
D. 3   (3  3)2 + 2 > 4 (3)  52 > 7    No!
E. 4   (4  3)2 + 3 > 4 (4)  54 > 11   No!

16- Choice C is correct

The correct answer is x  3  x  11
x + 4  7x  7  4x  3
Or
x + 4   7x   7  4x   11
Then, solution is: x  3  x   11

17- Choice B is correct

The correct answer is 5 5
Based on triangle similarity theorem: aa + b=c4c=4 aa + b=4 54 5=1
area of shaded region is: (c + 42) (b)=52 × 2 5=5 5

18- Choice C is correct

The correct answer is 82%
the population is increased by 30% and 40%
15% increase changes the population to 130% of original population. 
For the second increase, multiply the result by 140%.
(1.30) × (1.40)=1.82=182%
82 percent of the population is increased after two years.

19- Choice C is correct

The correct answer is 1  5
x1,2= b±b2  4 a c2 a
a x2 + b x + c=0
2 x2  4 x  8=0 then: a=1, b= 2 and c= 4 
x=2 +  22  (4).(1).( 4)2.1=1  5
x=2   22  (4).(1).( 4)2.1=1 + 5

20- Choice B is correct

The correct answer is x129
(x2)69=x2 × 69=x126=

21- Choice E is correct

The correct answer is $3
Let x be the cost of one-kilogram orange, then:
4 x + (3 × 6)=30
4 x + 18=30
4 x=30  18
4 x=12x=124=$3

22- Choice D is correct

The correct answer is 40
Let x be the length of AB, then:
30=x × 22x=15
The length of AC =152 + 82=289=17
The perimeter of ABC =15 + 8 + 17=40

23- Choice B is correct

The correct answer is 2 x5
Simplify the expression.
x25  x225=5 x225  x225=4 x225=425 x2=
425 × x2=25 × x=2 x5

24- Choice D is correct

The correct answer is y25
Solve for x.
5 x=y
Square both sides of the equation:
(5 x)2=(y)2
25 x=y
x=y25

25- Choice A is correct

The correct answer is 29
The probability of choosing a Hearts is 1672=29

26- Choice C is correct

The correct answer is 57.81
average =sum of termsnumber of terms
The sum of the weight of all girls is: 23 × 50=1150 kg
The sum of the weight of all boys is: 25 × 65=1625 kg
The sum of the weight of all students is: 1150 + 1625=2775 kg
average =277548=57.81

27- Choice D is correct

The correct answer is 135 x + 18,000  35,000
Let x be the number of shoes the team can purchase. Therefore, the team can purchase 120 x.
The team had $35,000 and spent $18000.
Now the team can spend on new shoes $17000 at most. 
Now, write the inequality:
135 x + 18,000  35,000

28- Choice C is correct

The correct answer is  9
Plug in the value of x and, 
x=4 and y=2
4 (x + 3 y)  (3 + x)2=
4 (4 + 3 (2))  (3 + 4)2=
4 (4 + 6)  (7)2=40  49= 9

29- Choice A is correct

The correct answer is 25
Let x be the smallest number.
Then, these are the numbers:
x,x + 1,x + 2,x + 3,x + 4
average =sum of termsnumber of terms
27=x + (x + 1) + (x + 2) + (x + 3) + (x + 4)5
27=5 x + 105
135=5 x + 10
125=5 xx=25

30- Choice E is correct

The correct answer is 16 x6
y=( 4 x3)2=( 4)2 (x3)2=16 x6

31- Choice B is correct

The correct answer is 8 cm
Formula for the Surface area of a cylinder is:
SA =2 π r2 + 2 π h192 π=2 π r2 + 2 π r (4)r2 + 4 r  96=0
Factorize and solve for r.
(r + 12) (r  8)=0r=8 or = 12 (unacceptable)

32- Choice D is correct

The correct answer is 27%
The question is this: 616.85 is what percent of 845?
Use percent formula:
part =percent100 × whole 
616.85=percent100 × 845
616.85=percent × 845100
61685= percent × 845 
percent =61685845=73
616.85 is 73% of 845.
Therefore, the discount is: 100%  73%=27%

33- Choice E is correct

The correct answer is 30
The area of rectangle is: 6 × 3=18 cm2
The area of circle is: π r2=π × (82)2=3 × 16=48 cm2
Difference of areas is: 48  18=30

34- Choice B is correct

The correct answer is 130 miles
Use the information provided in the question to draw the shape.
Use Pythagorean Theorem: a2 + b2=c2
502 + 1202=c2
2500 + 14400=c2
16900=c2c=130

35- Choice C is correct

The correct answer is  13
The equation of a line in slope intercept form is: y=m x + b
Solve for y.
9 x  3 y=24
 3 y=24  9 x
y=(24  9 x) ÷ ( 3)
y=3 x  8
The slope is 3.
The slope of the line perpendicular to this line is:
m1 × m2= 1
3 × m2= 1
m2= 13

36- Choice B is correct

The correct answer is x354  5
f(g(x))=4 × (x6)3  5=4 x3216  5=x354  5

37- Choice E is correct

The correct answer is 125
The ratio of boy to girls is 1:5.
Therefore, there are 1 boys out of 6 students.
To find the answer, first divide the total number of students by 6, then multiply the result by 1
750 ÷ 6=125125 × 1=125

38- Choice C is correct

The correct answer is 114
Write the ratio of 7 a to 4 b.
7 a4 b=18
Use cross multiplication and then simplify.
7 a × 8=4 b × 156 a=4 ba=4 b56=b14
Now, find the ratio of a to b.
ab=b14bb14 ÷ b=b14 × 1b=b14 b=114

39- Choice A is correct

The correct answer is 32
The relationship among all sides of right triangle 30  60  90 is provided in the following triangle: 
Sine of 60 equals to:
oppositehypotenuse=x32 x=32

40- Choice D is correct

The correct answer is 31
Plug in the value of x in the equation and solve for y.
4 y=4 x22  4
4 y=4 (8)22  4
4 y=4 (64)2  4
4 y=128  4=124
4 y=124y=31

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