# FREE DAT Quantitative Reasoning Math Practice Test

Welcome to our FREE DAT Quantitative Reasoning Math practice test, with answer key and answer explanations. This practice test’s realistic format and high-quality practice questions can help you succeed on the DAT Quantitative Reasoning Math test. Not only does the test closely match what you will see on the real DAT Quantitative Reasoning, but it also comes with detailed answer explanations.

For this practice test, we’ve selected 20 real questions from past exams for your DAT Quantitative Reasoning Practice test. You will have the chance to try out the most common DAT Quantitative Reasoning Math questions. For every question, there is an in-depth explanation of how to solve the question and how to avoid mistakes next time.

Use our free DAT Quantitative Reasoning Math practice tests and study resources (updated for 2022) to ace the DAT Quantitative Reasoning Math test! Make sure to follow some of the related links at the bottom of this post to get a better idea of what kind of mathematics questions you need to practice.

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**10 Sample DAT Quantitative Reasoning Math Practice Questions**

1- If \(\sqrt{6x}=\sqrt{y}\), then \(x=\)?

A. \(6y\)

B. \( \sqrt{\frac{y}{6}}\)

C.\(\sqrt{6y}\)

D.\(y^2\)

E. \(\frac{y}{6}\)

2- The average weight of 18 girls in a class is 60 kg and the average weight of 32 boys in the same class is 62 kg. What is the average weight of all the 50 students in that class?

A. 60

B. 61.28

C. 61.68

D. 61.90

E. 62.20

3- If \(y=(-3x^3)^2\), which of the following expressions is equal to \(y\)?

A. \(-6x^5\)

B. \(-6x^6\)

C. \(6x^5\)

D. \(9x^5\)

E. \(9x^6\)

4- What is the value of the expression (5\(x-2y+2-x)^2\) when \(x=3\) and \(y=-2\)?

A. \(-4\)

B. 20

C. 36

D. 50

E. 80

5- Sophia purchased a sofa for $530.40. The sofa is regularly priced at $624. What was the percent discount Sophia received on the sofa?

A. \(12\%\)

B. \(15\%\)

C. \(20\%\)

D. \(25\%\)

E. \(40\%\)

6- If \(f(x) = 3x – 1\) and \(g(x) = x^2 – x\), then find \((\frac{f}{g})(x)\).

A. \(\frac{3x – 1}{x^2-x}\)

B. \(\frac{x – 1}{x^2-x}\)

C. \(\frac{3x + 1}{x^2-x}\)

D. \(\frac{x^2-x}{3x – 1}\)

E.\(\frac{x – 1}{x^2 – 1}\)

7- In the standard \((x,y)\) coordinate plane, which of the following lines contains the points

\((3, -5)\) and (8, 15)?

A. \(y=4x-17\)

B. \(y=\frac{1}{4} x+13\)

C. \(y=-4x+7\)

D. \(y=-\frac{1}{4} x+17\)

E. \(y=2x-11\)

8- A bank is offering \(3.5\%\) simple interest on a savings account. If you deposit $12,000, how much interest will you earn in two years?

A. $420

B. $840

C. $4,200

D. $8,400

E. $9,600

9- If the ratio of home fans to visiting fans in a crowd is 3:2 and all 25,000 seats in a stadium are filled, how many visiting fans are in attendance?

A. 100000

B. 100

C. 1000

D. 10

E.10000

10- If the interior angles of a quadrilateral are in the ratio 1:2:2:5, what is the measure of the largest angle?

A. \(36^\circ\)

B. \(72^\circ\)

C. \(108^\circ\)

D. \(144^\circ\)

E. \(180^\circ\)

11- If the area of a circle is 64 square meters, what is its diameter?

A. \(8π\)

B. \(8(\sqrt{π}) \)

C. \(\frac{8{\sqrt{π}}}{{\sqrt{π}}}\)

D. \(\frac{8}{π}\)

E. \(64π^2\)

12- The length of a rectangle is 5/4 times its width. If the width is 16, what is the perimeter of this rectangle?

A. 36

B. 48

C. 72

D. 144

E.180

13- In the figure below, line A is parallel to line B. What is the value of angle \(x\)?

\( \img {https://appmanager.effortlessmath.com/public/images/questions/test131313131313131313.JPG

} \)

A. 35 degree

B. 45 degree

C. 90 degree

D. 100 degree

E. 145 degree

14- Last week 24,000 fans attended a football match. This week three times as many bought tickets, but one-sixth of them canceled their tickets. How many are attending this week?

A. 60,000

B. 72,000

C. 48,000

D. 54,000

E.84,000

15- If sin A =\(\frac{1}{3}\) in a right triangle and the angle A is an acute angle, then what is cos A?

A. \(\frac{{\sqrt{8}}}{3}\)

B. \(\frac{2}{3}\)

C. \(\frac{{\sqrt{3}}}{8}\)

D.\(\frac{{\sqrt{8}}}{9}\)

E. \(\frac{9}{8}\)

16- Convert 670,000 to scientific notation.

A. \( 6.70×1000\)

B. \( 6.70×10^{-5}\)

C. \( 6.7×100\)

D. \( 6.7×10^5\)

E. \(6.7×10^4\)

17- In two successive years, the population of a town is increased by 15% and \(20\%\). What percent of the population is increased after two years?

A. \(32\%\)

B. \(35\%\)

C. \(38\%\)

D. \(68\%\)

E. \(70\%\)

18- \((x^6)^{\frac{5}{8}} \)equal to?

A. \(x^{\frac{15}{4}}\)

B. \(x^{\frac{53}{8}}\)

C. \(x^{\frac{4}{15}}\)

D. \(x^{\frac{8}{53}}\)

E. \(x^{\frac{5}{48}}\)

19- If one angle of a right triangle measures \(60^\circ\), what is the sine of the other acute angle?

A. \(\frac{1}{2}\)

B. \(\frac{{\sqrt{2}}}{2}\)

C. \(\frac{{\sqrt{3}}}{2}\)

D. 1

E.\(\sqrt{3}\)

20- In the following figure, what is the perimeter of ∆ ABC if the area of ∆ ADC is 15?

\( \img {https://appmanager.effortlessmath.com/public/images/questions/test2000000000000000000000000000000000000000000000000000.JPG

} \)

A. 37.5

B. 21

C. 15

D. 24

E.The answer cannot be determined from the information given

**Best DAT Quantitative Reasoning Math Prep Resource for 2022**

## Answers:

1- **D**

Solve for \(x\).

\(\sqrt{6x}=\sqrt{y}\)

Square both sides of the equation:

\((\sqrt{6x})^2=(\sqrt{y})^2\)

\(6x=y\)

\( x=\frac{y}{6}\)

2- **B**

average \(=\frac{sum \space of \space terms}{number \space of \space terms}\)

The sum of the weight of all girls is: \(18 × 60 = 1080\) kg

The sum of the weight of all boys is: \(32 × 62 = 1984\) kg

The sum of the weight of all students is: 1080 + 1984 = 3064 kg

average \(=\frac{3064 }{50}= 61.28\)

3-** E**

\(y=(-3x^3)^2=(-3)^2 (x^3)^2=9x^6\)

4- **C**

Plug in the value of \(x\) and \(y\).

\(x=3\) and \(y=-2\)

\(5(x-2y)+(2-x)^2=5(3-2(-2))+(2-3)^2=5(3+4)+(-1)^2 = 35+1=36\)

5- **B**

The question is this: 530.40 is what percent of 624?

Use percent formula:

part \(=\frac{percent}{100} ×\) whole

\(530.40 =\frac{percent}{100} × 624 ⇒ 530.40 = \frac{percent ×624}{100} ⇒53040 = percent ×624 ⇒ \)

percent \(= \frac{53040}{624}= 85\)

530.40 is \(85\%\) of 624. Therefore, the discount is: \(100\% – 85\% = 15\%\)

6- **A**

\((\frac{f}{g})(x)=\frac{f(x)}{g(x)}=\frac{3x – 1}{x^2-x}\)

7- **A**

The equation of a line is \(y=mx+b\), where \(m\)is the slope and \(b\) is the \(y\)-intercept.

First find the slope:

\(m=\frac{y_2-y_1}{x_2-x_1}=\frac{15-(-5)}{8-3}= \frac{20}{5}=4\)

Then, we have: \(y=4x+b\)

Choose one point and plug in the values of \(x\) and \(y\) in the equation to solve for b.

Let’s choose the point \((3, -5)\)

\(y=4x+b→-5=4(3)+b→-5=12+b→b=-17\)

The equation of the line is: \(y=4x-17\)

8- **B**

Use simple interest formula:

\(I=prt\)

(I = interest, p = principal, r = rate, t = time)

\(I=(12000)(0.035)(2)=840\)

9- **E**

The number of visiting fans:

\(\frac{2×25000}{5}=10,000\)

10- **E**

The sum of all angles in a quadrilateral is 360 degrees.

Let x be the smallest angle in the quadrilateral. Then the angles are:

\(x,2x,2x,5x\)

\(x+2x+2x+5x=360→10x=360→x=36\)

The angles in the quadrilateral are: \(36^\circ, 72^\circ, 72^\circ\), and \(180^\circ\)

11- **C**

The formula for the area of a circle is:

\(A=πr^2\)

Using 64 for the area of the circle we have:

\(64=πr^2\)

Let’s solve for the radius (r).

\(\frac{64}{π}=r^2→r=\sqrt{\frac{64}{π}}= \frac{8}{\sqrt{π}}=\frac{8}{\sqrt{π}}×\frac{\sqrt{π}}{\sqrt{π}}= \frac{8\sqrt{π}}{\sqrt{π}}\)

12- **C**

Length of the rectangle is: \(\frac{5}{4})×16=20\)

perimeter of rectangle is: \(2×(20+16)=72\)

13- **E**

The angle \(x\) and 35 are complementary angles. Therefore:

\(x+35=180\)

\(180^\circ-35^\circ=145^\circ\)

14- **A**

Three times of 24,000 is 72,000. One sixth of them cancelled their tickets.

One sixth of 72,000 equals \(12,000 (\frac{1}{6} × 72000 = 12000)\).

\(60,000 (72000 – 12000 = 60000)\) fans are attending this week

15- **A**

sin A\(=\frac{1}{3}\)

Since sin \(θ=\frac{opposite}{hypotenuse}\)

we have the following right triangle. Then:

\(c=\sqrt{(3^2-1^2 )}=\sqrt{(9-1)}=\sqrt{8}\)

cos A\(=\frac{\sqrt{8}}{3}\)

16- **D**

\(670000=6.7×10^5\)

17- **C**

the population is increased by \(15\%\) and \(20\%. 15\%\) increase changes the population to \(115\%\) of original population.

For the second increase, multiply the result by \(120\%\).

\((1.15) × (1.20) = 1.38 = 138\%\)

38 percent of the population is increased after two years.

18- **A**

\((x^6)^{\frac{5}{8}} \)

\(= x^{6 × \frac{5}{8}}= x^{\frac{30}{8}}=x^{\frac{15}{4}}\)

19- **A**

The relationship among all sides of the right triangle \(30^\circ-60^\circ- 90^\circ\) is provided in the following triangle:

\( \img {https://appmanager.effortlessmath.com/public/images/questions/test22222.22222.2.2.2.2.2.2.2.2.2.2.2.2.2.JPG

} \)

Sine of \(30^\circ\) equals to: \(\frac{opposite}{hypotenuse}=\frac{x}{2x}=\frac{1}{2}\)

20- **D**

Let \(x\) be the length of AB, then:

\(15=\frac{x×5}{2}→x=6\)

The length of AC =(\sqrt{(6^2+8^2 )}=\sqrt{100}=10)

The perimeter of ∆ABC=(6+8+10=24)

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