A cylindrical vessel is filled with water up to some height. When a sphere of diameter 8 cm is dropped into the cylinder the water level rises by half of the initial level. When a sphere of diameter 16 cm is dropped the water level rises by some other value. What percentage of this new height is the initial level of water? Answer: 20% Explanation: Let the radius of the … [Read more...] about Solid Geometry – Sphere and Cylinder Volumes
GRE Problem Solving
Solid Geometry Mensuration – Circles
Chord AC at a distance of 7 cm from the center of a circle subtends an angle of 120 degrees at the center. Find the area of major segment. Answer: 1232/3 + 49*root(3) Explanation: In triangle OCD, Angle (COD) = 60 degrees Angle (OCD) = 30 degrees Hence tan(OCD) = OD/CD CD = 7*root(3) Sin(OCD) = OD/OC OC = 14 Hence AC = 14*root(3) Area of triangle AOC = … [Read more...] about Solid Geometry Mensuration – Circles
Number Properties LCM HCF
If the HCF of two natural numbers whose sum is 216 is 12, how many such pairs exist? Answer: 3 pairs Explanation: Let the two number be 12a and 12b where a and b are relatively prime. Then 12a + 12b = 216 a + b = 18 Now, this boils down to finding out all possible ways of writing 18 as a sum of two natural numbers co-prime to each … [Read more...] about Number Properties LCM HCF
Word Problem – Rates Work and Time
If A and B together can complete a work in 4 days, B and C together in 6 days, C and A together in 5 days, then working individually, who will finish the work in the least time and in how many days? Answer: A, 120/17 days Explanation: Let the rates at which A, B and C work be a, b and c respectively. Therefore, a + b = ¼ b + c = 1/6 c + a = 1/5 Solving for a, b … [Read more...] about Word Problem – Rates Work and Time
Permutation Rearrangement
8 directors, the vice chairman and the chairman are to be seated around a circular table. If the chairman should sit between a director and the vice chairman, in how many ways can they be seated? Answer: 8! * 2 Explanation: Let us consider the vice chairman and the chairman together as one entity. Hence, 8 directors + this entity can be arranged circularly in (9-1)! ways. … [Read more...] about Permutation Rearrangement