| Direction: Q. 36 to 40 |
| In our daily life we all see traffic lights. A traffic controller set the timmings of traffic lights in such a way that all light are not green at the same time or specially not in the rush hour. It may create problem in an hour because lights are for few minutes only. So, he take the timmings of nearby places in same area and calculate 1 cm of all traffic stops and he easily manage the traffic by increasing the duration set at different times. There are two traffic lights on a particular highway which shows green light at the interval of 90 seconds and 144 seconds respectively. |
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| Read the above paragraph carefully and answer the question that follows : |
A) 18
B) 20
C) 16
D) 22
Correct Answer: A
Solution :
| Sol. Using the factor tree for the prime factorisation of 90 and 144, we have | ||||||
| \[90=2\times {{3}^{2}}\times 5\] | ||||||
| and \[144={{2}^{4}}\times {{3}^{2}}\] | ||||||
| To find the HCF, we list the common prime factors and their least exponents in 90 and 144 as under: | ||||||
| ||||||
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,HCF={{2}^{1}}\times {{3}^{2}}=2\times 9=18\] | ||||||
| So, option [a] is correct. |
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