The Advanced Numeracy Test Workbook - Mike Bryon [41]
Explanation The odds always remain the same, as the first sweet is replaced before the next is drawn, so 1/4 × 1/2 = 1/8.
Q43. Answer A.
Explanation 18 × 5 = 90/6 = 15.
Q44. Answer B.
Q45. Answer B.
Explanation 102.0 – 100.5 = 1.5/102.0 = 1.5%.
Q46. Answer D.
Explanation The probability of the yellow ball being drawn is one in three – which is 33% to the nearest percentage point.
Q47. Answer D.
Q48. Answer B.
Explanation The box has 6 sides: 4 sides that are 3 × 2 = 6 square metres and 2 sides that are 2 × 2 = 4 square metres = (4 × 6) + (2 × 4) = 24 + 8 = 32 square metres.
Q49. Answer C.
Q50. Answer D.
Explanation
At start: 100;
After 1 hour: 100 × 2 = 200;
After 2 hours: 200 × 2 = 400; 400 – 50 = 350;
After 3 hours: 350 × 2 = 700;
After 4 hours: 700 × 2 = 1,400; 1,400 – 50 = 1,350;
After 5 hours: 1,350 × 2 = 2,700.
Test 8: Data interpretation
Q1. Answer D.
Explanation In 1995 1: 50 or 2 in 100 would be expected to reach age 100 or older. By 2010 this figure has improved to 1:16 or 6.25 in 100. This is an improvement of 4.25 in 100 or 4,250 in 100,000.
Q2. Answer B.
Explanation The number of centenarians in 2007 = 9,296 (2008 figure) – 1,000, and 7 women for every man live to age 100 or older. This figure is valid for the last few years and the data set is dated as 2010, so this ratio of 7: 1 can be used for 2008) 8,296 ÷ 8 × 7 = 7,259 women – 1,037 men = 6,222.
Q3. Answer A.
Explanation Find 1,000 as a percentage of 8,296. 1% = 82.96, 9,296 ÷ 92.96 = 112.05% so the increase was just over 12%.
Q4. Answer C.
Explanation The data set is dated 2010 and the ONS data relating to pensioners is identified as published one month earlier. In 2010 for every child under the age of 16 there are therefore 1.005 pensioners and for every 100,000 children (100,000 × 1.005) there are 100,500 pensioners or 500 more pensioners.
Q5. Answer A.
Explanation People in their mid-80s in 1995 will be aged 100 or older in 2010. The number of centenarians in 2008 is given and the rate of annual increase is also stated. The number of centenarians in 2010 can therefore be calculated and the number of people in their mid-80s in 1995 worked out from that. In 2008 there were 9,296 centenarians, so in 2009 there were 9,296 × 105.4% = 9,798 centenarians. The figure for 2010 is 9,798 × 105.4% = 10,327. Multiply this figure by 50 (the number of people in their mid-80s in 1995 who could be expected to live to age 100 or older).
Q6. Answer D.
Explanation It is stated that customers in market B perceive the higher price of Morning Tea to imply higher quality. To lower the price therefore risks losing the perception of higher quality and losing sales. It is stated that the buy decision in market A is almost entirely down to price and that the product is sold at a modest premium over competitor brands, so it is reasonable to infer that to remove the premium would result in an increase in sales.
Q7. Answer C.
Explanation No year is stated in the question and the magnitude of the difference between the markets varies each year so the best answer is a mean difference over the years. Find this by totalling the values and dividing by the number of years: 479 (market A) ÷ 76 (market B) = 6.3.
Q8. Answer B.
Explanation The figures for sales in market A do not support the suggestion that competitor brands are winning Morning Tea’s market share and for this reason you should select suggested answer B.
Q9. Answer C.
Explanation In 2006 82,400 units were sold for a total value of $120,304 = $1.46 a unit. In 2005 80,000 units were sold for a total value of $120,000 = $1.5 a unit, so the difference is 4 cents.
Q10. Answer A.
Explanation The unit value in 2004 = $1.5 (2005 value) × 97% = $1.455. The units sold in 2004 = 58,300 × $1.455 = value of $84,826.5 (add value of market B + 30%) × 130% = $110,274.45.
Q11. Answer D.
Explanation there are 2,000 staff and at $150 a delegate all 2,000 staff must have gone on this module to arrive at the total cost of $300,000.