DAT Quantitative Reasoning Math FREE Sample Practice Questions

B. \(57 \space π \space in^2\)

C. \(66 \space π \space in^2\)

D. \(288 \space π \space in^2\)

E. \(400 \space π \space in^2\)

5- A chemical solution contains \(4\%\) alcohol. If there is 24 ml of alcohol, what is the volume of the solution?

A. 240 ml

B. 480 ml

C. 600 ml

D. 1200 ml

E. 2400 ml

6- Which of the following points lies on the line \(2x + 4y = 10\)?

A. \((2, 1)\)

B. \((–1, 3)\)

C. \((–2, 2)\)

D. \((2, 2)\)

E. \((2, 8)\)

7- In the following figure, ABCD is a rectangle, and E and F are points on AD and DC, respectively. The area of \(∆\)BED is 16, and the area of \(∆\)BDF is 18. What is the perimeter of the rectangle?

A. 20

B. 22

C. 32

D. 40

E. 44

8- What is the solution of the following inequality?
\(|x-10|≤3\)

A. \( x≥13 ∪ x≤7\)

B.\( 7≤x≤13\)

C. \( x≥13 \)

D. \( x≤7\)

E. Set of real numbers

9- A bag contains 18 balls: two green, five black, eight blue, a brown, a red, and one white. If 17 balls are removed from the bag at random, what is the probability that a brown ball has been removed?

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A. \(\frac{1}{9}\)

B. \(\frac{1}{6}\)

C. \(\frac{16}{17}\)

D. \(\frac{17}{18}\)

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

10- If a tree casts a 24–foot shadow at the same time that a 3 feet yardstick casts a 2–foot shadow, what is the height of the tree?

A. 24 ft

B. 28 ft

C. 36 ft

D. 48 ft

E. 52 ft

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Answers:

2- B
\(\frac{2}{3}×90=60\)

3- C
I. \(|a|<1→-10→-ba^2>a\) (plug in\( -1/2\), and check!) (It’s false)
III. \(-1<a<1\),multiply all sides by 2,then: \(-2<2a<2\)
Subtract 3 from all sides. Then:
\(-2-3<2a-3<2-3→-5<2a-3<-1 (It \space is \space true!)\)

4- C
Surface Area of a cylinder \(= 2πr (r + h)\),
The radius of the cylinder is \(3 (6 ÷ 2)\) inches and its height is 8 inches. Therefore,
Surface Area of a cylinder \(= 2π (3) (3 + 8) = 66 π\)

5- C
\(4\%\) of the volume of the solution is alcohol. Let \(x\) be the volume of the solution.
Then: \(4\%\) of \(x = 24\) ml ⇒ \(0.04 x = 24 ⇒ x = 24 ÷ 0.04 = 600\)

6- B
Plug in each pair of numbers in the equation:
A. \((2, 1): 2 (2) + 4 (1) = 8\) Nope!
B. \((–1, 3): 2 (–1) + 4 (3) = 10\) Bingo!
C. \((–2, 2): 2 (–2) + 4 (2) = 4\) Nope!
D. \((2, 2): 2 (2) + 4 (2) = 12\) Nope!
E. \((2, 8): 2 (2) + 4 (8) = 36\) Nope!

7- D
The area of \(∆\)BED is 16, then:
\(\frac{4×AB}{2}=16→4×\)AB\(=32\)→AB\(=8\)
The area of \(∆\)BDF is 18, then:
\(\frac{3×BC}{2} =18→3×\)BC\(=36\)→BC\(=12\)
The perimeter of the rectangle is \(= 2×(8+12)=40\)

8- B
\(|x-10|≤3→-3≤x-10≤3→-3+10≤x-10+10≤3+10→7≤x≤13\)

9- D
If 17 balls are removed from the bag at random, there will be one ball in the bag. The probability of choosing a brown ball is 1 out of 18. Therefore, the probability of not choosing a brown ball is 17 out of 18 and the probability of having not a brown ball after removing 17 balls is the same.

10- C
Write a proportion and solve for \(x\).
\(\frac{3}{2}=\frac{x}{24} ⇒ 2x=3 ×24 ⇒ x=36\) ft

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