DAT Quantitative Reasoning Practice Questions

If tan θ = 5/12 and sin θ > 0, then cos θ = ?

a. -5/12

b. 12/13

c. 13/12

d. -12/13

e. 0

b. 12/13

tanθ = opp/adj = 5/12

c = sqrt(5^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13

cosθ = adj/hyp = 12/13

If 60% of x equal to 30% of 20, then what is the value of (x + 5)^2?

a. 25.25

b. 26

c. 26.01

d. 2025

e. 225

e. 225

0.6x = (0.3) x 20 → x = 10

(x + 5)^2 → (10 + 5)^2 = (15)^2 = 225

In the xy-plane, the point (4,3) and (3,2) are on line A. Which of the following equations of lines is parallel to line A?

a. y = 3x

b. y = 10

c. y = x2

d. y = 2x

e. y = x

e. y = x

Slope of line A is:

m = (y2 - y1)/(x2 - x1) = (3 - 2)/(4 - 3) = 1

Parallel lines have the same slope and only choice (e.) has slope of 1.

When point A (10,3) is reflected over the y-axis to get the point B, what are the coordinates of point B?

a. (10,3)

b. (-10,-3)

c. (-10,3)

d. (10,-3)

e. (0,3)

c. (-10,3)

When points reflected over y-axis, the value of y in the coordinates doesn't change and the sign of the x changes. Therefore, the coordinate point B is (-10, 3).

If f(x) = 2x^3 + 5x^2 + 2x and g(x) = -2, what is the value of f(g(x))?

a. 36

b. 32

c. 24

d. 4

e. 0

e. 0

g(x) = -2, then f(g(x)) = f(-2)

f(-2) = 2(-2)^3 + 5(-2)^2 + 2(-2)

= -16 + 20 - 4 = 0

In the equation x = [8y + (r/r + 1)] / [(6/z)], when z is divided by 3, what is the effect on x?

a. x is divided by 2

b. x is divided by 3

c. x does not change

d. x is multiplied by 3

e. x is multiplied by 2

b. x is divided by 3

x = [8y + (r/r + 1)] / [(6/(z/3))]

x = [8y + (r/r + 1)] / [(3 x 6/(z)]

x/3 = [8y + (r/r + 1)] / [(3 x 6/(z)] x (1/3)

A boat sails 40 miles south and then 30 miles east. How far is the boat from its start point?

a. 45 miles

b. 50 miles

c. 60 miles

d. 70 miles

e. 80 miles

b. 50 miles

Use Pythagorean Theorem: a^2 + b^2 = c^2

40^2 + 30^2 = c^2

→ 1600 + 900 = c^2

→ 2500 = c^2 → c = 50

x is y% of what number?

a. 100x/y

b. 100y/x

c. x/100y

d. y/100x

e. xy/100

a. 100x/y

Let the number be A. Then:

x = y% * A

Solve for A.

x = y/100 * A

Multiply both sides by 100/y:

x * 100/y = y/100 * 100/y * A

A = 100x/y

If cotangent of an angle β is 1, then tangent of angle β is

a. -1

b. 0

c. 1

d. 2

e. 3

c. 1

Tangent = 1/cotangent = 1

What is the value of y in the following system of equations?

3x - 4y = -20

-x + 2y = 10

a. -1

b. -2

c. 1

d. 4

e. 5

e. 5

How long does a 420-mile trip take moving at 50 miles per hour (mph)?

a. 4 hours

b. 6 hours and 24 minutes

c. 8 hours and 24 minutes

d. 8 hours and 30 minutes

e. 10 hours and 30 minutes

c. 8 hours and 24 minutes

When 40% of 60 is added to 12% of 600, the resulting number is:

a. 24

b. 72

c. 96

d. 140

e. 180

c. 96

A ladder leans against a wall forming a 60o angle between the ground and the ladder. If the bottom of the ladder is 30 feet away from the wall, how long is the ladder?

a. 30 feet

b. 40 feet

c. 50 feet

d. 60 feet

e. 120 feet

d. 60 feet

If 40% of a class are girls, and 25% of girls play tennis, what percentage of the class play tennis?

a. 10

b. 15

c. 20

d. 40

e. 80

a. 10

In five successive hours, a car travels 40 km, 45 km, 50 km, 35 km and 55 km. in the next 5 hours, it travels with an average speed of 50 km per hour. Find the total distance the car traveled in 10 hours.

a. 425 km

b. 450 km

c. 475 km

d. 500 km

e. 1000 km

c. 475 km

From last year, the price of gasoline has increased from $1.25 per gallon to $1.75 per gallon. The new price is what percent of the original price?

a. 72%

b. 120%

c. 140%

d. 160%

e. 180%

c. 140%

If 3x/16 = (x-1)/4, then x = ?

a. 1/4

b. 3/4

c. 3

d. 4

e. 9/4

d. 4

Find the distance between the point of intersection of the lines x - y = 2 and y = 4 and the point (6,3).

a. 1

b. 2

c. √2

d. 2√2

e. 3√2

a. 1

x - y = 2 and y = 4

x - 4 = 2 → point of intersection is (6,4)

distance = (x2-x1)2+(y2-y1)2

= (6-6)2+(3-4)2 = 0+1 = 1 = 1

Evaluate (2.004)^2

a. 4.16016

b. 4.016016

c. 4.001010

d. 4.000176

e. 4.001760

b. 4.016016

(2.004)2 = 4.016016

A wagon was loaded with 20 boxes each weighing 500 kg. If the maximum weight limit for the wagon is 20 tons, how much more weight can be loaded? (use 1 ton = 907 kg)

a. 81.40 kg

b. 814.0 kg

c. 8,140 kg

d. 81,400 kg

e. 8.140 kg

c. 8,140 kg

20 x 907 = 18,140 kg

500 x 20 = 10,000 kg

18,140 kg - 10,000 kg = 8,140 kg

A square is inscribed in a circle. The side of the square is 2 meters. What is the area of the circle not occupied by the square?

a. 2π - 4

b. 4π - 6

c. 4π - 8

d. 4π - 3

e. None of the above

a. 2π - 4

Two electrical poles are 12 feet apart. If one of the poles is 5 feet more in length than the other, what is the minimum length of the wire required for connecting them about their top?

a. 8 feet

b. 10 feet

c. 12 feet

d. 14 feet

e. 13 feet

e. 13 feet

The average salary of 3 people is $1,500. If one of them received a 100% raise, then the average salary becomes $2,000. What is the sum of the salary of the two people who did NOT get the raise?

a. $2,000

b. $3,000

c. $4,000

d. $5,000

e. $6,000

b. $3,000

Sum of salary of 3 people

= 3 x $1500 = $4500

1 person received a raise of 100%

Sum of new salaries

= 3 x $2000 = $6000

The increased salary of 1 person

= $1500

→ Salary of 2 people who did NOT get the raise = $4500 - $1500 = $3000

A pair of playing dice is thrown. What is the probability of getting a sum of 5?

a. 1/6

b. 1/36

c. 1/18

d. 1/9

e. 1/27

d. 1/9

A and B can do a job alone in 10 days and 12 days, respectively. A starts working along and 5 days later B joins to finish the work together. For how many days has B worked on the job?

a. 32/5

b. 24/5

c. 30/11

d. 24/11

e. 2

c. 30/11

A train of 300 meters long passes a lamp post in 12 seconds. How long will it take to cross a 450 meter bridge?

a. 15 seconds

b. 30 seconds

c. 45 seconds

d. 60 seconds

e. 75 seconds

b. 30 seconds

At present, the age ratio of A and B is 1:2. Ten years later the ratio is 2:3. What is the present age of B?

a. 5 years old

b. 10 years old

c. 20 years old

d. 30 years old

e. 40 years old

c. 20 years old

(1/6) + (3/8) - (5/12) =

a. 1/192

b. 5/24

c. 1/8

d. 23/24

e. -1/8

c. 1/8

A farmer has a rectangular garden with a perimeter of 72 feet. If one side is 4 feet longer than the other, then what is the area of the garden?

a. 320 feet^2

b. 1476 feet^2

c. 1280 feet^2

d. 324 feet^2

e. 672 feet^2

a. 320 feet^2

Which is the smallest?

a. 11/63

b. 5/46

c. 1/5

d. 2/9

e. 7/36

b. 5/46

A young man works at a grocery store and is paid $10 an hour for up to 40 hours. Then if he works more than 40 hours he is paid $15 per hour for the time he works over 40 hours. If the young man works 44 hours and 17 minutes, how much will he be paid?

a. $444.25

b. $460.50

c. $464.25

d. $660.75

e. $463.75

c. $464.25

If x^2 + 6x + 9 = x + 3. What is the value for x that makes this statement true?

a. -2

b. -1

c. 3

d. 1

e. 2

a. -2

Dick is driving on I-75 at 65 miles per hour for 24 minutes then slows down to 55 miles per hour for 30 minutes due to construction. How many miles did Dick travel in 54 minutes?

a. 58.5

b. 53.5

c. 60

d. 55.5

e. 50.5

b. 53.5

What is 8% of 4% of 2?

a. 64

b. 0.64

c. 0.064

d. 6.4

e. 0.0064

e. 0.0064

If Chad has a 2-sided coin, what is the probability he will flip the coin on heads three times in a row?

a. 1/2

b. 1/4

c. 1/6

d. 1/8

e. 1/16

d. 1/8

Brandon shoots free throws at a ratio of 3:2 for made to misses, respectively. If he misses 150 shots then how many free throws did he make?

a. 450

b. 150

c. 300

d. 320

e. 225

e. 225

If the average of a and b is 5 and c = 10. What is the average of a, b, and c?

a. 10

b. 20/3

c. 5

d. 7.5

e. 6

b. 20/3

A few years back Kevin bought a new car for $30,000 but since then it has depreciated by half. Now Kevin is again buying a new car with his trade in worth 25% of the new car. What is the value of the new car?

a. $30,000

b. $15,000

c. $18,000

d. $45,000

e. $60,000

e. $60,000

If a + b > a - b, then which of the following must be true?

a. b ≤ 0

b. a - b > b - a

c. a > 0

d. a = 0

e. None of the above.

e. None of the above.

What is the square root of (.25 x 2.25)?

a. 2

b. 0.75

c. 0.5

d. 20

e. 75

b. 0.75

A rectangle with a perimeter of 68 inches has one side that is 4 inches longer than the other. What is the area of this rectangle?

a. 225 in2

b. 361 in2

c. 285 in2

d. 165 in2

e. 300 in2

c. 285 in2

1/2 +1/3 + 1/4 +1/5+ 1/6 =

a. 3/2

b. 82/60

c. 91/60

d. 5/2

e. 87/60

e. 87/60

What is the median number of the following group? {1, 2, 3, 5, 9}.

a. 1

b. 3

c. 5

d. 9

e. 7/3

b. 3

(x^2 -3) / (x-1) = 1 / (x-1)

What is the value for x that makes this statement true?

a. 3, -3

b. -4, 4

c. -6, 6

d. 0, 1

e. 2, -2

e. 2, -2

If 1 inch equals 2.5 centimeters them how many centimeters is 25 feet?

a. 10 cm

b. 100 cm

c. 1000 cm

d. 750 cm

e. 500 cm

d. 750 cm

Which value is the largest?

a. 2sin(0)

b. 2sin(π/6)

c. sin(π/4)

d. 2sin(π/2)

e. sin(π/3)

d. 2sin(π/2)

Brant is x feet tall. At what angle must the sun be at for his shadow to equal his height?

a. sin 1

b. cos 1

c. arcsin 1

d. arccos 1

e. arctan 1

e. arctan 1

0.4 is 30% of x. What is x = ?

a. 12/10

b. 4/3

c. 40/3

d. 10/3

e. 8/5

b. 4/3

Jen is building a playground with a perimeter of 280 feet. If the length is 10 feet less than twice the width, then what is the area?

a. 7295 feet2

b. 17475 feet2

c. 11545 feet2

d. 654 feet2

e. 4500 feet2

e. 4500 feet2

(8 x 105) x (5 x 10-2) = ?

a. 4.0 x 10^3

b. 4.0 x 10^-10

c. 4.0 x 10^11

d. 4.0 x 10^-7

e. 4.0 x 10^4

e. 4.0 x 10^4

y = (x+5) / (x-9)represent this in the form of x =

a. (9y - 9)/(y + 5)

b. (9y + 5)/y

c. (9y + 5)/(y - 1)

d. (y + 5)/(y - 9)

e. 9y/(y - 1)

c. (9y + 5)/(y - 1)

√(x^2 - 9) / √(x-3) = 4

For what value of x is this statement true?

a. 3

b. 13

c. 23

d. 4

e. 14

b. 13

Danny caught a fish that weighed 5 pounds 8 ounces, Glen caught a fish that weighed 6 pounds 2 ounces, and Michael caught a fish that weighed 4 pounds 8 ounces. What is the average weight of these fish?

a. 5 lbs. 0 oz.

b. 5 lbs. 5 2/3 oz.

c. 5 lbs. 6 oz.

d. 5 lbs. 6 2/3 oz.

e. 5 lbs. 5 oz.

c. 5 lbs. 6 oz.

If a and b are prime numbers and a = x/b then which of the following could x = ?

a. 20

b. 24

c. 33

d. 36

e. 40

c. 33

Jacob is one fourth the age of his dad. In three and a half years he will be one third the age of his dad. How old is Jacob now?

a. 4

b. 5

c. 6

d. 7

e. 8

d. 7

At Adam's graduation there were 224 seniors graduating. If the ratio of girls to boys was 7 to 9 then how many girls were graduating with Adam?

a. 98

b. 177

c. 128

d. 130

e. 110

a. 98

If two x's and four o's are placed in a bag, then what is the probability that two draws from the bag at random, without replacement, will yield two x's?

a. 3/11

b. 2/15

c. 1/15

d. 1/10

e. 1/9

c. 1/15

Brian receives 6 magazines at the begining of each month. If he wants to read 2 magazines, then how many combinations of 2 could he select?

a. 12

b. 6

c. 15

d. 11

e. 36

c. 15

What is the distance between the two points (2, 6) and (-1, 3) on a graph?

a.. 3√2

b. 6

c. 9√2

d. 18

e. 4

a.. 3√2

3x + 2y is what percent of 6x2 + y, if x = 2 and y = 6?

a. 30%

b. 35%

c. 37%

d. 43%

e. 60%

e. 60%

What percent of 54/3 is 56/4 + 48/8 - 24/3 ?

a. 12

b. 18

c. 33.3

d. 66.6

e. 50

d. 66.6

A dog kennel has 220 dogs. The ratio of Labrador Retrievers to German Shepherds is 6 to 9. How many Labrador Retrievers are at this kennel?

a. 132

b. 147

c. 88

d. 15

e. 98

c. 88

Which is the smallest?

a. 17/23

b. 31/33

c. 9/11

d. 41/43

e. 34/39

a. 17/23

A bicyclist pedals at an average speed of 20 mph his first lap around a circle. His second lap was at an average speed of 30 mph. What was his average speed for the entire trip?

a. 25

b. 22

c. 24

d. 26

e. 30

c. 24

(27 X 756) - (30 X 756) = ?

a. 20,412

b. 22,680

c. -2,268

d. -22,680

e. 2,268

c. -2,268

A square's perimeter is 24 feet. What is the area?

a. 16 ft2

b. 26 ft2

c. 36 ft2

d. 10 ft2

e. 40 ft2

c. 36 ft2

( (.3)^2 (√.36) (10) ) / .6 =

a. 90

b. 9

c. 0.9

d. 0.09

e. 0.009

c. 0.9

If x = y/4 + z, and x = 14/13, and y = 35/70, what does z equal?

a. -8/13

b. 99/104

c. 0

d. 125/104

e. 8/13

b. 99/104

John buys a paper everyday for 26 weeks. If he pays $0.50 daily for the paper, then how much would he have saved if he bought weekly subscriptions at $2.10?

a. $54.60

b. $36.40

c. $3.64

d. $34.50

e. $91.00

b. $36.40

What is 2% of 15% of 12?

a. 2.4

b. 0.36

c. 0.018

d. 0.036

e. 0.24

d. 0.036

Which of the following is equivalent to cos (π/3)?

a. sin(π/4)

b. cos(2π/3)

c. -sin(π/6)

d. sin(π/3)

e. -cos(2π/3)

e. -cos(2π/3)

If: x2 + 7x + 1 = -x - 15. Which of the following is a solution for x = ?

a. 0

b. -4

c. 7

d. 4

e. 1

b. -4

Each side of a square is increased by 5 inches which increases the area of the square by 65 square inches. What was the area of the original square?

a. 81 in2

b. 64 in2

c. 49 in2

d. 16 in2

e. 25 in2

d. 16 in2

If: 3x - 4 > -(x + 6), then a solution for "x" that would make the statement true is which of the following?

a. x < -2

b. x < -1

c. x > -1/2

d. x < -4

e. x < -8

c. x > -1/2

Hose A fills a trough in 12 minutes and hose B fills the same trough in 24 minutes. How long does it take to fill the trought with both hose A and B going at the same time?

a. 10

b. 8

c. 12

d. 16

e. 6

b. 8

If 25 mm is 1 in then how many feet is 0.48 meter?

a. 1

b. 1.6

c. 1.5

d. 1.3

e. 2

b. 1.6

If y = (3+4)/(x+6), then which of the following represents x?

a. x = (3-6y)/(y-4)

b. x = (6y-4)/(y-3)

c. x = (6-4y)/(3-y)

d. x = (3y-4)/(6-y)

e. x = (4-6y)/(y-3)

e. x = (4-6y)/(y-3)

What is the probability of rolling two 6 sided dice simultaneously and receiving a value of seven?

a. 1/7

b. 7/36

c. 1/6

d. 1/18

e. 1/3

c. 1/6

Mackenzie is 1/3 the age of her mother. In 8 years she will be 1/2 the age of her mother. How old is Mackenzie's mother now?

a. 8

b. 16

c. 12

d. 24

e. 32

d. 24

What is the value of √(.64/.0016)?

a. 200

b. 20

c. 2

d. 0.2

e. 0.02

b. 20

If the bottom of a vase is a circle with an area of 49π, then which of the following represents the circles circumference?

a. 49

b. 14π

c. 7π

d. 25π

e. 10π

b. 14π

[3, 5, 3, 7, 8, 5, 3]. In this group of numbers what is the mode?

a. 5

b. 7

c. 3

d. 6

e. 8

c. 3

On one buffet bar there are 7 different meats, and on another buffet bar there are 6 different vegetables. People are allowed to chose one item from each bar. How many combinations of one meat and one vegetable can be chosen?

a. 42

b. 49

c. 21

d. 36

e. 25

a. 42

(2/a) / (c/4) Evaluate this expression if a= 4/10 and c = 5/23

a. 100/23

b. 1/2

c. 2

d. 5

e. 92

e. 92

Which of the following equations of lines is parallel to y = 5x + 4?

a. y = (1/3)x + 4

b. y = (1/5)x + 4

c. y = (1/5)x - 4

d. y = 5x -1

e. y = 10x - 2

d. y = 5x -1

If: f(x) = 6x - x2, then what does f(3) = ?

a. 6

b. 9

c. 7

d. 8

e. 10

b. 9

If: -4a + 8 > 12, then which of the following must be true?

a. a > -1

b. a > 1

c. a = 0

d. a < -1

e. a = 1

d. a < -1

On a coordinate graph what is the distance between (3, 4) and (0, 8)?

a. 5

b. √89

c. 7

d. 2√5

e. 8√3

a. 5

What are four consecutive odd numbers that when added together equal 64?

a. {7, 9, 11, 13}

b. {9, 11, 13, 15}

c. {11, 13, 15, 17}

d. {13, 15, 17, 19}

e. {15, 17, 19, 21}

d. {13, 15, 17, 19}

Dayne has a gallon of orange juice. For breakfast he drinks 13 fluid ounces of the gallon. How many fluid ounces of the gallon remain?

a. 96

b. 115

c. 99

d. 84

e. 117

b. 115

Which of the following is equivalent to (sec x)(sin x)?

a. sin x

b. cos x

c. tan x

d. csc x

e. cot x

c. tan x

What is the value of x if: 8y = 2x + 4 and 3y + 8 = x?

a. 10

b. 10

c. 24

d. 36

e. 38

e. 38

What is the radius of a circle with the given area = (x2 + 4x + 4)π ?

a. x + 2

b. 2

c. 4

d. x + 4

e. 8

a. x + 2

If 1/5 of those in a high school are freshman, and 40% of the freshmen are women, and 3/5 of those in the other grades are women, how many men are enrolled in the high school, given that there are 600 students altogether?

a. 240

b. 264

c. 300

d. 336

e. 360

b. 264

(2/5)(freshmen) + (3/5)(non-freshmen)

= (2/5)(1/5) + (3/5)(4/5)

= 2/25 + 12/25

= 14/25 female in the whole student body.

1 - 14/25 = 11/25 male in the whole student body.

(11/25)(600) = 264 total men.

A roulette wheel consists of 38 slots. 36 of these are numbered 1 through 36 and colored red or black so that there are nine red even-numbered slots, nine black odd-numbered slots, etc. These slots occur with equal probability. The two slots marked 0 or 00 are each three times as likely to occur as any one of the other 36. What is the probability that a red even number, a red 23, or a 00 will occur on one roll of the wheel?

a. 2/7

b. 5/18

c. 13/38

d. 13/42

e. 3/10

d. 13/42

First determine the likelihood of each slot's occurrence: [36x + 2(3x) = 1 → x = 1/42]. Likelihood of red even number: [9/42]. The likelihood of red 23: [1/42]. The likelihood of 00 is: [3x → 3/42]. Probability of all: 9/42 + 1/42 + 3/42 = 13/42.

In the first 12 games of the season, the forward on a soccer team scored 20 goals. How many goals must he average in each of the 6 remaining games of the season in order to average 2.0 goals per game overall?

a. 1 ½

b. 2 ⅓

c. 2 ½

d. 2 ⅔

e. 20

d. 2 ⅔

(2)(18) = 36 goals in the season. 36 - 20 = 16 goals left to score in 6 games. (16/6) = 2.66 or 2 ⅔ goals average per game.

Susan has $10 with which to buy apples. Apples are priced at 6 for $0.89, or $0.20 each. How much change will Susan receive if she buys as many as she can?

a. $1.10

b. $0.89

c. $0.21

d. $0.10

e. $0.01

e. $0.01

(11)($0.89) = $9.79 + $0.20

= $9.99. $10 - $9.99

= $0.01 change.

If both x and y are both even numbers, which of the following expressions will always represent an odd number?

a. x + y

b. x^y

c. y^x

d. xy

e. xy + 1

e. xy + 1

An even number multiplied by an even number is always even. The sum of two even numbers is always even.

What is the value of 𝑦y in the following system of equation?

2𝑥 + 𝑦 = 7

4𝑥 − 2𝑦 = 18

a. −1

b. −2

c. 1

d. 2

e. 4

a. −1

The number 6.45 is 100 times greater than which of the following numbers?

a. 64.5

b. 0.645

c. 0.0645

d. 0.00645

e. 0.000645

c. 0.0645