Quantitative Aptitude - Arithmetic Ability Questions

Two spheres of equal radius are taken out by cutting from a solid cube of side (12 + 4√3) cm. What is the maximum volume (in cm3) of each sphere?

90% of X = 40% of Y and Y = a% of X. What is the value of a?

The ratio of three numbers is 2 : 3 : 5. If the sum of the three numbers is 275, then what is the largest among the three numbers?

If (1/x) + (1/y) + (1/z) = 0 and x + y + z = 9, then what is the value of x3 + y3 + z3 – 3xyz?

There are two buckets, smaller bucket can hold only 3/5th of the water as compared to the larger bucket. If 6,000 buckets of larger capacity are needed to fill a pond. Then how many smaller capacity buckets are needed to fill the same pond?

Consider  the  multiplication  999  ×  abc  =  def132  in  decimal  notation, where  a,  b,  c,  d,  e  and  f  are digits. What are the values of a, b, c, d, e and f respectively?

What is the LCM (least common multiple) of 57 and 93?

If Cosec θ = 17/8, then Cot θ = ?