# SAT II Math II : Other Mathematical Relationships

## Example Questions

### Example Question #1 : Other Mathematical Relationships       Explanation:

In modulo 9 arithmetic, a number is congruent to the remainder of its division by 9.

Since and , ,

making "5" the correct response.

### Example Question #2 : Other Mathematical Relationships varies directly as and inversely as If and , then .

To the nearest whole number, evaluate if and .

Insufficient information is given to answer the question.     Explanation: varies directly as and inversely as . This means that for some constant of variation , Alternatively, We can substitute the initial conditions for thevariables on the left side and the final conditions for those on the right side, then solve for :   ### Example Question #3 : Other Mathematical Relationships varies directly as both and the square of .

If and , then Evaluate if and .      Explanation: varies directly as both and the square of . This means that for some constant of variation , .

Alternatively stated, .

We can substitute the initial conditions for the variables on the left side and the final conditions for those on the right side, then solve for :   ### Example Question #4 : Other Mathematical Relationships  Evaluate .   The system has no solution.  Explanation:

Rewrite the two equations by setting and and substituting:    The result is a two-by-two linear system in terms of and :  This can be solved, among other ways, using Gaussian elimination on an augmented matrix: Perform row operations until the left two columns show identity matrix . One possible sequence:             and . In the former equation, substitute back for , and raise both sides to the power of 4:    