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succeeding in numerical reasoning tests 173 population: 4 290 thousand - we will need to add three zeroes here: 4 290 000 if we turn back to our simplified figures, our calculation would look like this: 100 million divided by 4 million we could use a calculator to obtain the result here, but let us recall what we said ear- lier - this is very close to one quarter of 100, which is 25. 25 is closest to option c and that is the correct answer. calculations with speed, time and distance questions involving the calculation of speed, time and distance can be expected at the exam. let's have a look first at the three elements and how they interact with each other. speed = distance / time from this, we can deduce the other two formulas. distance = speed x time time = distance / speed you can also remember them by thinking of real-life situations, e.g. driving for 3 hours at 100 km/h will take us a distance of 3 x 100 = 300 kms. a major pitfall with these questions can be converting between different units, as in the following example: let's assume that we drove 180 kilometers and it took us 2 hours and 15 minutes. what was our average speed? to answer this, it might be tempting to divide 180 kilometers by 2.15 hours. however 2 hours and 15 minutes is not 2.15 hours, because there are 60 minutes in an hour not 100. therefore, we need to find what part of an hour is represented by 15 minutes. this we can get as a simple ratio calculation, dividing 15 minutes / 60 minutes, which is 0.25 hours. here we don't need to further convert this into a percentage, we simply add it to the number of hours, giving us 2.25 hours. our calculation becomes 180 kilometers / 2.25 hours, resulting in 80 km/h estimation in a previous section, when calculating the per-capita apple production of croatia, we applied a sort of estimation to get to the correct answer. in that case, the estimation took the form of concentrating only on the number of digits in the correct answer. there are cases, however, where we need to be a little more precise than that let's go back to our table and ask a different question: bus companies in the united states, 2013 company profit number of passengers number of average (in million usd) (in millions) vehicles vehicle utilization (%) greyhound 46 289 4560 73
172 succeeding in numerical reasoning tests order of magnitude apple production in various european countries apple production (thousands oftonnes) population in 2000 (thousands) 1990 2000 2010 slovakia croatia bulgaria austria 4 895 4 290 8 930 10 354 31 103 120 546 25 98 90 490 35 112 134 560 note: 1 tonne=1000kg q. what was the production ofapples per person in croatia in 2000? q. a.0.23 kg b. 2.29 kg c.22.84 kg d. 228. 4 kg e. 2.28 tonnes an order of magnitude is a scale of amounts where each amount is in a fixed ratio to the amount preceding it. the most common ratio is 1:10, which means that the next amount in a scale can be calculated by multiplying the previous figure by 10. for example: 1, 10, 100, 1000, 10000 .and so on… if we look at the above answer options, we can see that that is exactly the situation we have here: 0.23, 2.29, 22.84, 228. 4, 2.28 tonnes, (which is 2280 kg) - with some small variations from exact multiples of ten which slightly disguise the relationship. ир. when we are faced with a set of numbers like the ones above, it gives us an important hint that the actual calculation of the figure may not really be necessary - all we need to figure out is the order of magnitude of the answer. let us consider the above sample test from the perspective of whether we can take advantage of this observation. we have the following information: • the amount of apples produced in croatia in 2000 in thousands of tonnes - 98 • • the population of croatia in thousands - 4290 since the answer options only differ in their order of magnitude, we can be quite flex- ible in rounding our numbers up or down to simplify our calculations. let us round 98 up to 100 and 4290 down to 4000. you can disregard the exact number of digits for a second. what is the relationship between the numbers 100 and 4000? if you think about that for a second, you will realize that 100 and 4000 are in a relationship to each other that is similar to that between 1 and 4 - that is, to one quarter. expressed in decimal terms, this is 0. 25. our answer options are close to this (this is especially appar- ent in option a - the difference of 0.23 versus 0.25 is caused by having rounded down the numbers). remember - we do not need to be particularly accurate in this case, all that we are looking for is the number of digits in the correct answer. now turn your atten- tion to those zeroes we disregarded so far. apple production: 98 thousand tonnes - we will add 6 zeroes here to make it kilo- grammes: 98 000 000 kg