Preparing for the DAT quantitative reasoning test? The best way to prepare for your DAT Quantitative Reasoning test is to work through as many DAT Quantitative Reasoning practice questions as possible. Here are the top 10 DAT Quantitative Reasoning practice questions to help you review the most important DAT Math concepts. These DAT Quantitative Reasoning practice questions are designed to cover mathematics concepts and topics that are found on the actual test. The questions have been fully updated to reflect the latest 2021 DAT guidelines. Answers and full explanations are provided at the end of the post.

Start your DAT Quantitative Reasoning test prep journey right now with these sample DAT Quantitative Reasoning questions.

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## DAT Quantitative Reasoning Math Practice Questions

1- A number is chosen at random from 1 to 25. Find the probability of not selecting a composite number.

A. \(\frac{1}{25}\)

B. 25

C. \(\frac{9}{25}\)

D. 1

E. 0

2- Removing which of the following numbers will change the average of the numbers to 6?

\(1, 4, 5, 8, 11, 12\)

A. 1

B. 4

C. 5

D. 11

E. 12

3- A rope weighs 600 grams per meter of length. What is the weight in kilograms of 12.2 meters of this rope? (1 kilograms = 1000 grams)

A. 0.0732

B. 0.732

C. 7.32

D. 7,320

E. 73,200

4- If \(y = 4ab + 3b^3\), what is y when \(a = 2\) and \(b = 3\)?

A. 24

B. 31

C. 36

D. 51

E. 105

5- If \(f(x) = 5 + x\) and \(g(x) = – x^2 – 1 – 2x\), then find \((g – f)(x)\)?

A. \(x^2 – 3x – 6\)

B. \(x^2 – 3x + 6\)

C. \(–x^2 – 3x + 6\)

D. \(–x^2 – 3x – 6\)

E. \(–x^2 + 3x – 6\)

6- The marked price of a computer is D dollar. Its price decreased by \(20\%\) in January and later increased by \(10\%\) in February. What is the final price of the computer in D dollar?

A. 0.80 D

B. 0.88 D

C. 0.90 D

D. 1.20 D

E. 1.40 D

7- The number 40.5 is 1,000 times greater than which of the following numbers?

A. 0.405

B. 0.0405

C. 0.0450

D. 0.00405

E. 0.000405

8- How many tiles of 8 cm\(^2\) is needed to cover a floor of dimension 6 cm by 24 cm?

A. 6

B. 12

C. 18

D. 24

E. 36

9- What is the area of a square whose diagonal is 8 cm?

A. 16 cm\(^2\)

B. 32 cm\(^2\)

C. 36 cm\(^2\)

D. 64 cm\(^2\)

E. 128 cm\(^2\)

10- What is the value of \(x\) in the following figure?

A. 150

B. 145

C. 125

D. 105

E. 95

## Best DAT Quantitative Reasoning Math Prep Resource for 2021

## Answers:

1- **C**

Set of number that are not composite between 1 and 25: A\(= \{2, 3, 5, 7, 11, 13, 17, 19, 23\}\)

Probability \(=\frac{number \ of \ desired \ outcomes}{number \ of \space total \ outcomes}=\frac{9}{25}\)

2- **D**

Check each option provided:

A. \(\frac{4+5+8+11+12}{5}=\frac{40}{5}=8\)

B. \(\frac{1+5+8+11+12}{5}=\frac{37}{5}=7.4\)

C. \(\frac{1+4+8+11+12}{5}=\frac{36}{5}=7.2\)

D. \(\frac{1+4+5+8+12}{5}=\frac{30}{5}=6\)

E. \(\frac{1+4+5+8+11}{5}=\frac{29}{5}=5.8\)

3- **C**

The weight of 12.2 meters of this rope is: \(12.2 × 600\) g \(= 7320\) g

1 kg = 1000 g, therefore, 7320 g \(÷ 1000 = 7.32\) kg

4- **E**

\(y = 4ab + 3b^3\)

Plug in the values of a and b in the equation: \(a = 2\) and \(b = 3\)

\(y = 4 (2) (3) + 3 (3)3 = 24 + 3(27) = 24 + 81 = 105\)

5- **D**

\( (g – f)(x) = g(x) – f(x) = (– x^2 – 1 – 2x) – (5 + x) – x^2 – 1 – 2x – 5 – x = – x^2 – 3x – 6\)

6- **B**

To find the discount, multiply the number by (\(100\% –\) rate of discount).

Therefore, for the first discount we get: (D) (\(100\% – 20\%\)) = (D) (0.80) = 0.80 D

For increase of \(10\ %\): (0.85 D) (\(100\% + 10\%\)) = (0.85 D) (1.10) = 0.88 D = \(88\%\) of D

7- **B**

1000 times the number is 40.5. Let \(x\) be the number, then:

\(1000x=40.5\)

\(x= \frac{40.5}{1000}=0.0405\)

8- **C**

The area of the floor is: 6 cm \(× 24\) cm = 144 cm

The number is tiles needed \(= 144 ÷ 8 = 18\)

9- **B**

The diagonal of the square is 8. Let \(x\) be the side.

Use Pythagorean Theorem: \(a^2 + b^2 = c^2\)

\(x^2 + x^2 = 82 ⇒ 2x^2 = 82 ⇒ 2x^2 = 64 ⇒x^2 = 32 ⇒x= \sqrt{32}\)

The area of the square is:

\(\sqrt{32} × \sqrt{32} = 32\)

10- **B**

\(x=20+125=145\)

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