this conjecture by finding the even number in the range from 4 to 100 which can be expressed as the sum of two prime numbers in the largest number of ways. 2. The diagram shows an equilateral triangle, a square and a regular pentagon which all share a common vertex. What is the value of θ? A 98 B 102 C 106 D 110 E 112 Solution: B The interior angles of an equilateral triangle, a square and a regular pentagon are 60, 90and 108, respectively. Hence 102258360)1089060(360=−=++−=θ. 3. The price of my favourite soft drink has gone up in leaps and bounds over the past ten years. In four of those years it has leapt up by 5p each year, whilst in the other six years it has bounded up by 2p each year. The drink cost 70p in 2002. How much does it cost now? A £0.77 B £0.90 C £0.92 D £1.02 E £1.05 Solution: D The cost has risen by 5p four times, and by 2p six times. So the total price rise in pence has been 32)2654(=×+×. Therefore the price now is02.1£p102p)3270(==+.4. According to one astronomer, there are one hundred thousand million galaxies in the universe, each containing one hundred thousand million stars. How many stars is that altogether? A 1310B 2210C 10010D 12010E12110Solution: B One hundred thousand is 510and one million is610. So one hundred thousand million is11656510101010==×+. Therefore the total number of stars is221111111110101010==×+.
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