# DAT Practice Test (Quantitative Reasoning)

#### What is the value of (x+5)² if % of x equals % of 20?

Correct answer: 225

0.6𝑥=(0.3)×20→𝑥=10→(𝑥+5)²=(15)²=225

#### Calculate the distance between the point of intersection of the lines x — y = 2 and y = 4 and the point (6,3).

Correct answer: 1

x - y = 2 and y = 4

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

distance = √(0 + 1) = √1 = 1

#### Solve the equation:

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

Correct answer: 1/8

To be able to solve this type of question you should have an understanding of addition/subtraction of fractions. The most important step in this process is finding a common denominator(number that is a common multiple of one or more numbers). Step one - In this question, 6, 8, and 12 are the denominators, and a common denominator of all three is 24. Step two - Now using this common denominator equivalent fractions are found. For example, the first fraction becomes 4/24, because 6 times 4 is 24. Step three - Now by substituting in the equivalent fractions, the numerators can be added or subtracted accordingly. ALWAYS PAY ATTENTION TO "+" OR "-".

#### The points (4,3) and (3,2) are on line A in the xy-plane. Line A is parallel to which of the following equations of lines?

Correct answer: 𝑦=𝑥

The slop of line A is:𝑚=𝑦2−𝑦1/𝑥2−𝑥1=3−2/4−3=1

Parallel lines have the same slope and only choice 𝐸(𝑦=𝑥) has slope of 1.

#### Solve (2.004)²

Correct answer: 4.016016

(2.004)²

= 2² + 2 x 2 x 0.004 + 0.000016

= 4 + 0.016 + 0.000016

= 4.016016

#### A 72-foot-long rectangular garden belongs to a farmer. What is the area of the garden if one side is 4 feet longer than the other?

Correct answer: 320 ft2

Knowledge of area, perimeter, and solving equations. Step one: It is always important to collect the data from a question and know what the question wants you to find. In this case, the question wants you to find the area: (L x W), and they give the perimeter: (2L + 2W = 72ft). Also we know that one side is 4 feet longer than the other(L = W + 4). Step two: Using the previous information, we simply substitute the value for length into the equation for the perimeter, and solve for Width (W). Step three: Length (L) is easily found knowing Width (W). Step four: Because the formula for area of a rectangle is length times width, the area is easily found by solving L x W.

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

Correct answer: (−10,3)

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

#### Twenty boxes, each weighing 500 kg, were placed into a wagon. How much extra weight can be loaded if the wagon's maximum weight limit is 20 tons? (A ton is equal to 907 kg)

Correct answer: 8,140 kg

20 x 907 = 18,140 kg

500 x 20 = 10,000 kg

Can take load of 8140 kg

#### Which one is the smallest?

Correct answer: 5/46

Knowledge and quickness of fractions and long division. To answer these type of questions, your first step should be to approximate the fractions as below. For this question the answer becomes obvious after the first step, because 1/9 is less than 1/6 or 1/5. It is not always the case that these questions will work out this easily. Usually you will be able to narrow the answer choices to two or three and then perform long division from there, as is demonstrated (step two). Normally it does not require that you divide the answer out more than two numbers to the right of the decimal. The red circled value is three places to the right for demonstration.

#### What is the perimeter of a trapezoid with a surface area of 100?

Correct answer: 35

The area of trapezoid is:

(8+12/2)×𝑥=100→10𝑥=100→𝑥=10

𝑦=√(32+42)=5

𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑖𝑠:12+10+8+5=35

#### The square has a 2 meter side. In m², what is the hashed area?

Correct answer: 2π - 4

*If the side of the square is 2m, then the area of the square is 4 square meters.

*The diagonal of the square = √(2^2 + 2^2) = √(8) = 2√(2)

*The radius of the circle = (1/2)(diagonal of square) = √(2)

Area of hashed = area of circle - area of square

= 2π - 4

#### A young man works in a supermarket and earns $10.00 per hour for up to 40 hours. Then, if he works more than 40 hours, he will be paid $15.00 per hour for the extra time. How much will the young man be paid if he works 44 hours and 17 minutes?

Correct answer: $464.25

Evaluating word problems involving money. For this type of problem it is important to first recognize what the question is asking and what values are given.(Step one) This step doesn't have to be written each time but it is helpful. Now that all the important values are known the problem can be solved.(Step two) Following the steps shown, the young man is paid $400 for the first 40 hours, $60 for the 4 hours over 40, and $4.25 for the 17 minutes. This last value had to be found by determining the pay per minute, which is $15 divided by 60 minutes, or $0.25/min. Then the pay for 17 minutes is 17 quarters, or $4.25. Finally in (step three) add all the values for the total of $464.25.

#### What is the value of f(g(x)) if f(x)=2𝑥³+5𝑥²+2𝑥 and g(x)= -2?

Correct answer: 0

𝑔(𝑥)=−2,𝑡ℎ𝑒𝑛𝑓(𝑔(𝑥))=𝑓(−2)=2(−2)³+5(−2)²+2(−2)=−16+20−4=0

#### The distance between two electrical poles is 12 feet. What is the minimum length of wire required to connect them about their top if one of the poles is 5 feet longer than the other?

Correct answer: 13 feet

BC = 20 ft, AB = 5ft

AC is the wire reqd.

AC = √(12 x 12+5 x 5) = 13

#### If (x+3) = x2 + 6x + 9. What is the value of x that allows this statement to be true?

Correct answer: -2

Solving Algebraic Equations. To solve this problem you must be familiar with the FOIL method, or in this case the reverse of it.(Step one) demonstrates this, if you are still confused, type "FOIL method" in on any internet search engine. This problem requires the reverse of what is demonstrated. In (Step two), it must be recognized that (x + 3)2 = x2 + 6x + 9. From here, solve this algebraic equation for x giving answer d.

#### A boat travels 40 miles to the south, then 30 miles to the east. What is the boat's distance from its starting point?

Correct answer: 50 miles

Use the information provided in the question to draw the shape.

Use Pythagorean Theorem: 𝑎²+𝑏²=𝑐²

402+302=𝑐2⇒1600+900=𝑐2⇒2500=𝑐2⇒𝑐=50

#### The average wage for a group of three people is $1,500. If one of them is given a 100% raise, the average wage rises to $2,000. What is the total pay of the two employees who did not receive a raise?

Correct answer: $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 = $1,500

Salary of 2 people who did not get the hike =
$4,500-$1,500=$3,000

#### Due to construction, Richard drives on I-75 at 65 miles per hour for 24 minutes, then drops to 55 miles per hour for 30 minutes. In 54 minutes, how far did Richard travel?

Correct answer: 53.5

Knowledge of word problems involving speed and distances. In (Step one) record the important data that is found in the question. Now that we know what the question is looking for, and we have all the values we can solve the problem. (Step two) Determine the distance traveled at each speed. This is done by converting miles per hour to miles per minute. (Step three) shows a quick way to solve the equation by dividing 12 out of the top equation, and 30 out of the lower equation. This gives the total distance Dick traveled at each speed, and then addition of these two yields the total distance traveled - a.

#### When the cotangent of an angle β is 1, the tangent of the angle β is:

Correct answer: 1

𝑡𝑎𝑛𝑔𝑒𝑛𝑡β=1/𝑐𝑜𝑡𝑎𝑛𝑔𝑒𝑛𝑡β=1

#### A set of two playing dice is tossed. What is the chance of having a 5 sum?

Correct answer: 1/9

We can get three:

1+4, 2+3, 3+2 and 4+1 = 4 possibilities

Total possibilities = 6 x 6 = 36

Prob. = 4/36 = 1/9

#### What does 8% of 4% of 2 equal?

Correct answer: 0.0064

These are the questions that you are able to make up ground if you are behind on time. (Step one) Write out the equation for what the question asks. This is step can be skipped on some questions but not here. Once you do this, solve and you're done. Don't forget to move your decimal two places to the left for percentages - as seen below.

#### A and B can complete a job in ten and twelve days, respectively. A begins working alone, and B joins him five days later to complete the task together. B has been on the job for how many days?

Correct answer: 30/11

“A” completes 5/10 = 1/2 part of the job in 5 days

“A” and “B” working together can (1/10 +1/12) part of the job in 1 day

12 + 10 /120= 22/120

let number of days “B” works be x

(22/120)*x = 1/2

x = 120/44 =30/11 days

#### What is the probability that Marvin will flip a two-sided coin three times in a row on heads?

Correct answer: 1/8

Key concept: knowledge of odds, and probability. Probability = # successes/# possibilities. Odds = # successes/failures. (Step one) Understanding the question write down what you know. (Step two) Understand that each event is separate, therefore on each flip there is a 1/2 chance of flipping heads. So on the first attempt the probability is 1/2. The probability of the second flip being heads is 1/2, and the probability of heads on the third flip is 1/2. The probability of flipping the coin on heads consecutively three times in a row is 1/2(first flip) x 1/2(second flip) x 1/2(third flip). So the probability is 1/8.

#### In 12 seconds, a 300-meter train goes through a lamp post. What is the time it takes to cross a 450-meter bridge?

Correct answer: 30 seconds

Speed of train = 300 m/12 sec = 25 m/s

Time taken to cross bridge = 300+450

So: = 750 divided by 25 m/s = 30 seconds

#### Anton shoots freethrows at a 3:2 ratio for made to missed attempts. How many free throws did he make if he missed 150 shots?

Correct answer: 225

Key concept: knowledge of ratios, and word problems. (Step one) Understand that a ratio of 3:2 is 3 made shots and 2 missed shots, or as a fraction he makes 3/5 of his shots and misses 2/5 of his shots. (Step two) Now using this information we can create an equation with the information we know. Because he misses 2/5 of all his shots, and he missed 150 shots we created this equation solving for total shots taken. (Step three) Now using total shots taken and the fraction for shots made we can find the number of shots made.