The Advanced Numeracy Test Workbook - Mike Bryon [37]
Q49. Answer B.
Explanation The basic sin, cos, tan ratios can only be used with right-angled triangles. We will only be able to answer this if we now use the cosine rule, which states:
a2 = b2 + c2 – 2bc cos A;
a2 = 16 + 25 – 2 × 20 × cos A;
a2 = 41 – 40 × .5;
a2 = 21;
a = 4.58 (answer to two decimal points).
Q50. Answer C.
Explanation The cosine of 100 is a negative. Again use the cosine rule: a2 = b2 + c2 – 2bc cos A:
a2 = 49 + 81 – 2 × (7 × 9) × –0.173;
a2 = 49 + 81 – 126 × –0.173;
a2 = 49 + 81 – –21.798;
a2 = 151.798 (two negatives = a positive);
a = 12.32 (to two decimal places);
Perimeter = 9 + 7 + 12.32 = 28.32.
Test 5: A further test of quantitative operations
Q1. Answer C.
Explanation 3 divided by 8 × 100 = 37.5.
Q2. Answer A.
Explanation Convert the ratios to fractions (1/9, 3/9, 5/9) and then to percentages.
Q3. Answer B.
Explanation 5 divided by 16 × 100 = 31.2.
Q4. Answer D.
Explanation 4 divided into 7 × 100 = 57.1 (to one decimal point).
Q5. Answer A.
Explanation = 4.79. Prime numbers to 4.79 = 2, 3, neither of which divides exactly into 23, so 23 is a prime number.
Q6. Answer C.
Q7. Answer C.
Q8. Answer A.
Q9. Answer A.
Explanation = 4.35. Prime numbers to 4.35 = 2, 3, neither of which divides exactly, so 19 is a prime number.
Q10. Answer A.
Explanation 50/150 = 1/3 × 100 = 33 (expressed as nearest whole percentage point).
Q11. Answer C.
Q12. Answer B.
Explanation 938 divided by 7 × 6 = 804.
Q13. Answer D.
Q14. Answer B.
Explanation 2 and 3 for example both divide into 222, so 222 is not a prime number.
Q15. Answer B.
Explanation 5/16, 5/16, 6/16; then into percentages, eg 5 divided into 16 × 100.
Q16. Answer C.
Explanation 20 = 1/300 × the number, so 20 = 1/3 of 1% of 6,000.
Q17. Answer B.
Explanation £10,000 – 20% = £8,000 – 30% = £5,600 – 40% = £3,360.
Q18. Answer D.
Explanation × 100
Q19. Answer A.
Explanation Square root of 337 is 18.35. Prime numbers to value of 18.35 = 2, 3, 5, 7, 11, 13, 17. None divide exactly into 337, so 337 is a prime number.
Q20. Answer B.
Explanation 84% (100 – 16); 1% = = 32.5; 84 × 32.5 = 2,730.
Q21. Answer B.
Q22. Answer C.
Explanation To solve such problems, impose a convenient amount as turnover (with percentages, 100 is the ideal arbitrary amount). Charge reduced by 10% so turnover 100 – 10 = 90. Sales increase by 30% = 130% of 90 = 117. So turnover increases by 17%.
Q23. Answer A.
Explanation The mode is the most frequently occurring value.
Q24. Answer B.
Explanation The median value is the middle value and is identified by arranging the data into numerical order.
Q25. Answer C.
Explanation The lower quartile is found using the equation Q1 = ¼ (n + 1)th value.
Q26. Answer B.
Explanation Q3 is found by ¾ (n + 1)th value, and the interquartile range is found if you minus Q1 from Q3 = 89 – 27 = 62.
Q27. Answer D.
Explanation The average of any range of consecutive integers must be the average of the smallest and largest numbers from the range. So 282 + 419 = 701/2 = 350.5.
Q28. Answer B.
Explanation = 6.92. Prime numbers in the range are 2, 3, 5; 2 and 3 divide exactly into 48, so 48 is not a prime number.
Q29. Answer B.
Explanation Substitute a convenient figure: 100 + (3% of 100) = 103; 103 + (3% of 103) = 106.09.
Q30. Answer D.
Explanation Find the average to find the sum. Calculate the number of items and the average to find the sum. There are 45 numbers (including 16):
60 – 16 + 1 = 45. The average is = 38.
Sum = average number of items = 38 × 45 = 1,710.
Q31. Answers A and C.
Explanation Try some examples to test it: 3 × 6 = 18, 6 × 6 = 36, 9 × 6 = 54, etc.
Q32. Answer A.
Explanation = = 750.
Q33. Answer C.
Explanation = 46.5.
Q34. Answer B.
Explanation Try some examples: 3 × 4 = 12, 3 × 5 = 15; 1 + 2 = 3, 1 + 5 = 6. Both