Quantitative ability[50 questions]Q.Let A and B be two solid spheres such that the surface area of B is 300% higher than the surface area of A. The volume of A is found to be k% lower than the volume of B. The value of k must be1. 85.52. 92.53. 90.54. 87.5 Soln. (4) — The surface area of a sphere is proportional to the square of the radius. Thus, BAS4S1(S. A. of B is 300% higher than A)BAr2r1The volume of a sphere is proportional to the cube of the radius. Thus, BAV8V1Or, VAis 7th8less than B i.e. 87.5%Q.A test has 50 questions. A student scores 1 mark for a correct answer, –1/3 for a wrong answer, and –1/6 for not attempting a question. If the net score of a student is 32, the number of questions answered wrongly by that student cannot be less than 1. 62. 12 3. 34. 9 Soln. (3) — Let the number of correct answers be ‘x’, number of wrong answers be ‘y’ and number of questions not attempted be ‘z’. Thus, x + y + z = 50 … (i) And yzx ––3236The second equation can be written as, 6x – 2y – z = 192 … (ii)Adding the two equations we get, 2427x – y = 242 or x =+ y7Since, x and y are both integers, y cannot be 1 or 2. The minimum value that y can have is 3. Q.The sum of 3rdand 15thelements of an arithmetic progression is equal to the sum of 6th, 11th and 13thelements of the same progression. Then which element of the series should necessarily be equal to zero?1. 1st2. 9th3. 12th4. None of the aboveSoln. (3) — If we consider the third term to be ‘x”The 15thterm will be (x + 12d)6thterm will be (x + 3d)11thterm will be (x + 8d) and 13thterm will be (x + 10d)Thus, as per the given condition, 2x + 12d = 3x + 21d. Or x + 9d = 0 x + 9d will be the 12thterm.Q.When the curves y = log10x and y = x–1are drawn in the x–y plane, how many times do they intersect for values x1?
xQ.At the end of year 1998, Shepard bought nine dozen goats. Henceforth, every year he added p% of the goats at the beginning of the year and sold q% of the goats at the end of the year where p>0 and q>0. If Shepard had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true?