3) If 'S' is a set of all integers that are multiples of 3 & multiples of 5, provided it should be of 2 digits, then find the range of S?A. 81 B. 77 C. 87 D. 89 E. 91 Solution:Multiples of 3 and Multiples of 5 ( condition : it should be of 2 digits)Multiples of 3 = { 12 , 15 , 18 , 21 ,........................., 99}Multiples of 5 = { 10, 15, 20, 25, .............................,95}Therefore, S = { 10,12,15,18,...........................99}Range = Maximum number – Minimum NumberRange of S = 99 – 10 = 89Answer : Option D (89) 4) Find the number of possible values of x & y in the expression (5+x)/(7+y), so that the resultant ratio is 5:7 where x and y lie between 12 and 29?Solution:(5+x)/(7+y) = 5/7x and y should lie between 12 and 29To Find :x and y5+x must be a multiple of 5 , the possible values will be (5+0), (5+5), (5+10), (5+15),(5+20),(5+25), (5+30),..................7+y must be a multiple of 7 , the possible values will be (7+0), (7+7), (7+14), (7+21),(7+28),(7+35), (7+42),..................(5+x)/(7+y) can be (5+0)/(7+0) , (5+5)/(7+7), (5+10)/(7+14), (5+15)/(7+21) , (5+20)/(7+28) , (5+25)/(7+35) , (5+30)/(7+42)All the above said are possible values that x and y can take, butthe condition given is x and y should lie between 12 and 29.So , eliminating options, which does not lie in this range, we get(5+15)/(7+21) and (5+20)/(7+28).Answer : x = 15 and y = 21 (or) x = 20 and y = 28Whichever option given in the question can be marked as the answer.5) If -2 < x < -1, thenCol A: 1/x3Col B: 1/xSolution: