# Ghana Prisons Service Aptitude Test Questions & Answers on Numeracy & Logical Reasoning

**Ghana Prisons Service Aptitude Test Questions & Answers on Numeracy & Logical Reasoning:** Ghana Prisons Service Numeracy & Logical Reasoning Questions & Answers For Prisons Service:

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1. Find the principal which amounts to ¢5,500 at simple interest in 5 years at 2% per annum.

A. ¢4,900

B. ¢5,000

C. ¢4,700

D. ¢4,800

**ANS: B**

2. Evaluate [(0.14)² × 0.275] ÷ 7(0.02), correct to 3 decimal places.

A. 0.039

B. 0.358

C. 0.033

D. 0.308

**ANS: A**

3. In a class, 24 students read Physics, 21 read Mathematics and 9 read both Physics and Mathematics. If each student reads at least one of the two subjects, find the number of students in the class.

A. 27

B. 36

C. 45

D. 54

**ANS: B**

4. Write 57774, correct to three significant figures.

A. 57800

B. 57700

C. 5780

D. 578

**ANS: A**

5. What is the least value of m if 2³×3³×7×m is a perfect square?

A. 7

B. 21

C. 42

D. 63

**ANS: C**

6. Factorize completely the expression

(h + 2k)² + 4k² – h².

A. 8k²

B. 2k(h + 2k)

C. 2k(2h + 3k)

D. 4k(h + 2k)

**ANS:** D

7. Evaluate in base two 11011 – 101

A. 10010

B. 10100

C. 10110

D. 10101

**ANS: C**

8. The length of a side of an equilateral triangle 🔼 is 10 cm. Find the height of the triangle 🔼.

A. 11.18 cm

B. 10.00 cm

C. 8.66 cm

D. 5.00 cm

**ANS: C**

9. Solve the equation 12 + 6/x = 9

A. 3

B. 2

C. -2

D. -3

**ANS: C**

10. If w = -3, x = 14, y = 17 and z = -2, evaluate [(x – y)³ + z²] ÷ w³

A. 23/27

B. 31/27

C. -23/27

D. -31/27

**ANS: C**

11. A function g is defined by g:x = (2x – 1)/x. For what value of x is g undefined?

A. 1

B. 0.5

C. 0

D. -0.5

**ANS: C**

12. In an examination, the sum of the marks obtained by Kofi and Ama was 81 and the difference was 17. If Kofi had a larger Mark, find Ama’s mark.

A. 32

B. 37

C. 47

D. 49

**ANS: A**

13. Find the gradient of the line joining the points P(-2,6) and Q(3,-2).

A. 8/5

B. 1/4

C. -5/8

D. -8/5

**ANS: D**

14. What is the time, in minutes, taken to cover 8.1 km at an average speed of 5 m/s?

A. 4.5

B. 16.2

C. 22.3

D. 27.0

**ANS: D**

15. Which of the following satisfies 3x + 1 = 4 (mod 9)?

A. 2

B. 3

C. 4

D. 5

**ANS: C**

16. If 8^x = 2√2, find the value of x.

A. 3/2

B. 1

C. 0.5

D. -1/2

**ANS: C**

17. If 3log(2 + x) = log27, find x.

A. -1

B. 1

C. 0.5

D. 6

**ANS: B**

18. Simplify √450 – √200

A. 2√5

B. 5√2

C. 5√5

D. 10√2

**ANS: B**

19. Quame borrowed ¢300,000.00 from a GCB BANK. He repaid the loan in six equal instalments of ¢55,000.00. How much interest did he pay?

A. ¢3,000.00

B. ¢30,000.00

C. ¢33,000.00

D. ¢50,000.00

**ANS: B.**

20. A man deposited $80,000.00 in a bank at a 12% compound interest per annum. How much did the man have in the bank at the second year?

A. $89,600.00

B. $90,752.00

C. $99,200.00

D. $100,352.00

**ANS: D**

21. The insurance premium on a 23-seater bus is ¢3,279,600.00 plus 5% of the insured value. What is the insurance premium on a 23-seater bus insured for ¢150,000,000.00?

A. ¢4,220,400.00

B. ¢7,500,000.00

C. ¢7,663,980.00

D. ¢10,779,600.00

**ANS: D.**

22. The length, l, of a simple pendulum varies directly as the square of its period, T. A pendulum of length 99.4 cm has a period of 2 seconds. Find, correct to two decimal places, the length of a pendulum of period 2.5 seconds.

A. 63 62 cm

B. 79.52 cm

C. 124.25 cm

D. 155.31 cm

**ANS: D**

23. Find the length of the vector (4, -2)

A. 2

B. 2√3

C. 2√5

D. 20

**ANS: C**

24. The bearing of Q from P is 040° and the bearing of R from P is 130°. If |PQ| = r and |PR| = 2r, find |QR|.

A. √3r

B. √5r

C. r√3

D. r√5

**ANS: C**

25. When the point (4, 5) is rotated through an angle in the anticlockwise direction about the origin, its image is (-5, 4). What is the angle of rotation?

A. 90°

B. 180°

C. 270°

D. 300°

**ANS: A**

26. If x + 6/x = 5, find the value of x² + 36/x².

A. 13

B. 19

C. 25

D. 37

**ANS: A**

27. The minute hand of a wall clock is 10.5 cm long. How far does its tip travel in 24 hours? [ Take π = 22/7 ]

A. 0.66 m

B. 1.32 m

C. 7.92 m

D. 15.84 m

28. A water tank is a cube of side 2 m the depth of water in it is 60 cm. What is the volume of water in the tank?

A. 2.4 m³

B. 4 m

C. 8 m³

D. 24 m³

**ANS: A**

29. Given that A = 60° and B = 30°, evaluate (sin B + 2 cos A) ÷ cos B, leaving your answer in surd form.

A. 3√3

B. 1 + 2√3

C. √3

D. 1 – √3

**ANS: C**

30. There are 40 identical marbles in a b

You sent There are 40 identical marbles in a box. 18 of the marbles are blue, 14 red and 8 green. What is the probability that a marble selected at

random is either blue or green?

A. 1/5

B. 9/20

C. 11/20

D. 13/20

**ANS: D**

31. The mean of the numbers 15, 21, 17, 26, 18, 29 is 21. Calculate the

the standard deviation of the numbers.

A. 0

B. 5

C. 6

D. 25

**ANS: B**

Alright friends these are the Sample of Ghana Prisons Service Aptitude Test Questions & Answers on Numeracy & Logical Reasoning.

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