DS: Which is greatest?

Which is the greatest among x,y and z ?

1. x:y:z=3:4:5
2. xyz-y^2 is a positive integer

Solution:

1. x:y:z=3:4:5
This statement tell us about the magnitude of x, y and z but nothing about the sign. If all are positive numbers z is greatest, if all the negative z is smallest. INSUFFICIENT

2. xyz - y^2 is a positive integer
Do not oversimplify this! Y^2 is always positive. If we have (something) - positive = positive, then we know that something is positive and bigger in magnitude than what is subtracted. INSUFFICIENT

Combine the two, we know that z has the biggest magnitude and all the numbers are positive, thus Z is greatest.

The answer is (C).

Remember:

1. Do not forget to consider the impact of negative factor on the given equation.
2. In any relation like aX:bY:cZ, the value of variable (X, Y, Z) would be greater for which factor is greatest (a, b, c). This is only when all the factors are positive.

For example, X:3Y:5Z means Z is greatest in case X, Y and Z are positive in nature.