Full-Length DAT Quantitative Reasoning Practice Test-Answers and Explanations

23- Choice D is correct
The weight of 14 meters of this rope is: \(14×732 \space g=10,248 \space g\)
\(1 \space kg = 1000 \space g\), therefore, \(10,248 \space g÷1000=10.248 \space kg\)

24- Choice E is correct
The slop of line A is: \(m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-(-6)}{4-2}=\frac{8}{2}=4\)
Parallel lines have the same slope and only choice E \((y=4x)\) has a slope of 4.

25- Choice E is correct
When points are reflected over the \(y\)-axis, the value of \(y\) in the coordinates doesn’t change and the sign of \(x\) changes. Therefore, the coordinates of point B are (4, 5).

26- Choice C is correct
The area of trapezoid is: \(\frac{(9+12)}{2}×x =42→21x=84→x=4\), \(y=\sqrt{3^2+4^2}=5\)
Perimeter is: \(4+9+5+3+9=30\)

27- Choice C is correct
Set of numbers that are not composite between 1 and 18: \(A = {1, 2, 3, 5, 7, 11, 13, 17}\)
Probability \(= \frac{number \space of \space desired \space outcomes}{number \space of \space total \space outcomes}=\frac{8}{18}=\frac{4}{9}\)

28- Choice B is correct
Check each option provided:
A. \(2 → \frac{4+6+8+12}{4}=\frac{30}{4}=7.5\)
B. \(4 → \frac{2+6+8+12}{4}=\frac{28}{4}=7\)
C. \(6 → \frac{2+4+8+12}{4}=\frac{26}{4}=6.5\)
D. \(8 → \frac{2+4+6+12}{4}=\frac{24}{4}=6\)
E. \(12 → \frac{2+4+6+8}{4}=\frac{20}{4}=5\)

29- Choice B is correct
\(0.5x=(0.2)×30→x=12→(x-4)^2=(12-4)^2=8^2=64\)

Best DAT Quantitative Reasoning Prep Resource for 2026

DAT Quantitative Reasoning Prep 2020-2021 The Most Comprehensive Review and Ultimate Guide to the DAT Quantitative Reasoning Test

Download

$29.99 Original price was: $29.99.$16.99Current price is: $16.99.

Rated 4.17 out of 5 based on 75 customer ratings

Satisfied 60 Students

30- Choice D is correct.
Let the number be \(x\). Then: \(12=4\%×x→12=0.04x\), Solve for \(x→x=\frac{12}{0.04}=300\)

The Ultimate Algebra Bundle From Pre-Algebra to Algebra II

Download

$109.99 Original price was: $109.99.$54.99Current price is: $54.99.

31- Choice C is correct
\(f(x)=2x^2-x,g(x)=x^2-6, (f-g)(x)=f(x)–g(x)=(2x^2-x)-(x^2-6 )=2x^2-x-x^2+6=x^2-x+6\)

32- Choice A is correct
\(f(x)=-x^3-4x^2+6x+7,g(x)=-1\), then: \(f(g(x))= f(-1)=-(-1)^3-4(-1)^2+6(-1)+7=-(-1)-4(1)-6+7=1-4-6+7=-2\)

33- Choice A is correct
Plug in \(\frac{z}{5}\) for \(z\) and simplify.
\(x=\frac{8y+\frac{r}{r+1}}{\frac{6}{\frac{z}{5}}}=\frac{8y+\frac{r}{r+1}}{\frac{5×6}{z}}=\frac{8y+\frac{r}{r+1}}{5×\frac{6}{z}}=\frac{1}{5}×\frac{8y+\frac{r}{r+1}}{\frac{6}{z}}=\frac{x}{5}\)

34- Choice B is correct
Use the information provided in the question to draw the shape.
Use Pythagorean Theorem: \(a^2+b^2=c^2\)
\(12^2+35^2=c^2 ⇒ 144+1225= c^2⇒1369=c^2⇒ c=37\)

35- Choice D is correct
\(y =ab^2-3a^2 b,a=2,b=-2\), Plug in the values of a and b in the equation: \(y=2(-2)^2-3(2)^2 (-2)=2(4)-3(4)(-2)=8+24=32\)

36- Choice A is correct
I. \(|a|<1→-1<a<1\)
Multiply all sides by \(b\). Since, \(b>0\) →\(-b<ba<b\) (it is true!)
II. Since, \(-1<a<1\), and \(a<0→-a>a^2>a\) (plug in \(−\frac{1}{2}\), and check!) (It’s false)
III. \(-1<a<1\), multiply all sdes by \(4\), then: \(-4<4a<4\)
Subtract \(5\) from all sides. Then: \(-4-5<4a-5<4-5→-9<4a-5<-1\) (It is false!)

37- Choice C is correct
\(One \space liter = 1000 \space cm^3→ 8 \space liters = 8000 \space cm^3⇒ 8000=16×5×h→h=\frac{8000}{80}=100 \space cm\)

38- Choice E is correct
\(\frac{3}{4}×120=90\)

39- Choice C is correct
\(tangent \space β= \frac{1}{cotangent \space β}=\frac{1}{1}=1\)

40- Choice E is correct
Surface Area of a cylinder \(= 2πr (r+h)\), The radius of the cylinder is \(4(8÷2)\) inches and its height is \(12\) inches. Therefore, the Surface Area of a cylinder \(=2π(4)(4+12)=128π\)

The Best Books to Ace the DAT Quantitative Reasoning Test

Prepare for the DAT Quantitative Reasoning Test in 7 Days A Quick Study Guide with Two Full-Length DAT Quantitative Reasoning Practice Tests

Download

$29.99 Original price was: $29.99.$16.99Current price is: $16.99.

Rated 4.41 out of 5 based on 282 customer ratings

Satisfied 268 Students