GRE Practice Questions -3

1. If $m=\frac{\sqrt{5}-3}{\sqrt{2}+1}$, then for which one of the following equals $m-3$
   
   
   1. $\sqrt{10}-3\sqrt{2}-\sqrt{5}+3$
   2. $\sqrt{10}-3\sqrt{2}-\sqrt{5}$
   3. $\sqrt{10}-3\sqrt{2}+\sqrt{5} $
   4. $\sqrt{10}-3\sqrt{2}-\sqrt{5}-6 $
   5. $\sqrt{10}+3\sqrt{2}-\sqrt{3} $
   
   
2. If $y < 0$ and $x$ is 7 more than the square of $y$, which one of the following expresses $y$ in terms of $x$?
   
   
   1. $y=-\sqrt{x-7}$
   2. $y=\sqrt{x-7} $
   3. $y=\sqrt{x+7} $
   4. $y=\sqrt{x^{2}-7}$
   5. $y=-\sqrt{x^{2}-7}$
3. If $\sqrt[m]{125}=5^{3m}$ and $4^{m} > \frac{1}{2}$, then what is the value of $m$?
   
   
   1. $-1$
   2. $-\frac{1}{5}$
   3. $0 $
   4. $\frac{1}{5}$
   5. $1$

4. Column A	Column B
   $x^{2}(x^{5})^{2}$	$(x^{4})^{3}$

5. 
   

   Column A		Column B
   $17^{\frac{1}{x}-\frac{1}{y}}$	$0 < x < y$	$17^{x-y}$





Answer Key

1	A
2	B
3	E
4	C
5	A