# Numerical Ability and Reasoning Test

a sample numerical ability and reasoning test including mathematical questions of matric (high school) standard:

**This test consists of two sections: Numerical Ability and Mathematical Reasoning.**

You have 60 minutes to complete the entire test.

There are 25 questions in total.

Answer all questions.

Each question carries one mark.

There is no negative marking for incorrect answers.

Do not use calculators or any other aids.

## Section 1: Numerical Ability

- If 3x + 5 = 20, what is the value of x?
- A car travels 150 kilometers in 3 hours. What is the average speed of the car?
- If a toy costs $25 and the price increases by 20%, what is the new price of the toy?
- What is the next number in the sequence: 2, 5, 10, 17, …?
- Simplify: (4 + 2) × (6 – 3).

## Section 2: Mathematical Reasoning

- If 2x + 3 = 11, what is the value of x?
- Solve for x: 5x – 7 = 23.
- A rectangle has a length of 8 cm and a width of 5 cm. What is the perimeter of the rectangle?
- What is the sum of the interior angles of a triangle?
- If the area of a square is 64 square units, what is the length of one side of the square?
- A bag contains 8 red marbles, 5 blue marbles, and 3 green marbles. If a marble is randomly selected, what is the probability of selecting a blue marble?
- If the circumference of a circle is 36π cm, what is the radius of the circle?
- If 4x + 7 = 19, what is the value of x?
- If a train travels at a speed of 80 km/h, how far will it travel in 4 hours?
- Simplify: (3x + 2)(4x – 5).

## some additional questions:

11. Solve for ( x ): ( 3(x + 4) = 27 ).

12. If a triangle has sides of lengths 5 cm, 12 cm, and 13 cm, is it a right triangle? (Yes/No)

13. Find the area of a circle with a radius of 6 cm. (Use ( pi = 3.14 ))

14. If ( frac{3}{4} ) of a number is 36, what is the number?

15. A box contains 24 chocolates. If you take out 6 chocolates, what percentage of chocolates are left in the box?

16. If ( 2^x = 16 ), what is the value of ( x )?

17. Solve for ( x ): ( frac{5x – 3}{2} = 7 ).

18. Find the perimeter of an equilateral triangle with each side measuring 9 cm.

19. Simplify: ( frac{3}{5} times frac{4}{7} ).

20. If ( f(x) = 2x^2 – 5x + 3 ), find ( f(3) ).

## End of Test

Once you’ve completed all questions, you can tally up your score by counting the number of correct answers out of 25. Good luck!

## solutions

### Numerical Ability

**1. If 3x + 5 = 20, what is the value of x?**

**2. A car travels 150 kilometers in 3 hours. What is the average speed of the car?**

**3. If a toy costs $25 and the price increases by 20%, what is the new price of the toy?**

**4. What is the next number in the sequence: 2, 5, 10, 17, …?**

**5. Simplify: (4 + 2) × (6 – 3).**

### Mathematical Reasoning

**1. If (2x + 3 = 11), what is the value of x?**

**2. Solve for (x): (5x – 7 = 23).**

**3. A rectangle has a length of 8 cm and a width of 5 cm. What is the perimeter of the rectangle?**

**4. What is the sum of the interior angles of a triangle?**

**5. If the area of a square is 64 square units, what is the length of one side of the square?**

**6. A bag contains 8 red marbles, 5 blue marbles, and 3 green marbles. If a marble is randomly selected, what is the probability of selecting a blue marble?**

**7. If the circumference of a circle is (36π) cm, what is the radius of the circle?**

**8. If (4x + 7 = 19), what is the value of (x)?**

**9. If a train travels at a speed of 80 km/h, how far will it travel in 4 hours?**

**10. Simplify: ((3x + 2)(4x – 5)).**

**Therefore, the solutions are:**

### let’s solve each problem:

**11. Solve for ( x ): ( 3(x + 4) = 27 ).**

**12. If a triangle has sides of lengths 5 cm, 12 cm, and 13 cm, is it a right triangle? (Yes/No)**

**13. Find the area of a circle with a radius of 6 cm. (Use ( pi = 3.14 ))**

**15. A box contains 24 chocolates. If you take out 6 chocolates, what percentage of chocolates are left in the box?**

**16. If ( 2^x = 16 ), what is the value of ( x )?**

**17. Solve for ( x ): ( frac{5x – 3}{2} = 7 ).**

**18. Find the perimeter of an equilateral triangle with each side measuring 9 cm.**

**19. Simplify: ( frac{3}{5} times frac{4}{7} ).**

**20. If ( f(x) = 2x^2 – 5x + 3 ), find ( f(3) ).**