List of top Quantitative Ability and Data Interpretation Questions on Identities

Which of the following statements are true?
A. If  \(x : y = 3 : 1\) then \(x ^3 − y ^3 = \frac{10}{11}\)
B. If \(x=y+12,x:y=3:2\) and \(z:y=1:3\),then \(z+x=44\)
C. If \(3x=8y\) and \(5y=9z\),then \(\frac{x}{z}=\frac{72}{15}\)
Choose the most appropriate answer from the options given below:

If \(5^a\) = \(9^b\) = 2025, then the value of \(\frac{ab}{a+b}\)= ____.

If \((x + y) = 3, xy = 2\), then what is the value of \(x ^3+ y^3 :\)