Task #159

A bus takes 24 min to travel from White City to Hammersmith with no stops. Each time the bus stops to pick up and/or drop off passengers. it takes approximately 90 sec. This morning, the bus picked up passengers from 5 stops and dropped off passengers at 7 stops.

What is the minimum journey time from White City to Hammersmith this morning?

1.28min 2.34min 3.34.5min 4.36min 5.37.5min 6.42min

Answer: C. Remember that pick up and drop off stops may be the same stop, therefore the minimum number of stops the bus had to make was 7. This would take 7 x 1.5 = 10.5 minutes.Therefore the total journey time = 24 + 10.5 = 34.5 minutes.

Task #209

A shop puts its dresses on sale at 20% off the normal selling price. During the sale, the shop makes a 25% profit over the price at which they bought the dresses.

What is the percentage profit when the dresses are sold at full price?

1.36% 2.42.5% 3.56.25% 4.64% 5.77% 6.80%

Answer: A. As the question uses percentages, it does not matter what figure you use. To make calculations easier, use an initial price of £100. When on sale, the dress is 20% off, so using a normal price of £100, the dress would be £80. When the dresses are 20% off, the shop is making a 25% profit. Therefore: £80 = 1.25 x purchase price. Therefore, the purchase price is: . Thus, the normal profit is £100 - £64 = £36. I.e. when a dress sells for £100, the shop makes £36 or 36% profit.

Task #233

Jina is playing darts. A dartboard is composed of equal segments, numbers from 1 to 20. She takes three throws, and each of the darts lands in a numbered segment. None land in the center or in double or triple sections.

What is the probability that her total score with the three darts is odd?

1.1/4 2.1/3 3.1/2 4.3/5 5.2

Answer: C. For the total score to be odd, there must be either three odd or one odd and two even scores were obtained. Since the solitary odd score could be either the first, second or third throw there are four possible outcomes that result in an odd total score. Additionally, there are the same number of possibilities giving an even score (either all three even or two odd and one even scores obtained), and the chance of throwing odd or even with any given dart is equal. Therefore, there is an equal probability of three darts totaling an odd score as to an even score, and so the chance of an odd score is ½.

Task #237

A farmer is fertilizing his crops. The more fertilizers are used, the more the crops grow. Fertilizers cost 80p per kg. Fertilizing at a rate of 0.2kg/m2 increases the crop yield by 1.30$/m2. For each additional 100g of fertilizer above 200g, the extra yield is 30% lower than the linear projection of the stated rate.