SAT Diagnostic

Graham walked to school at an average speed of 3 miles an hour and jogged back along the same route at 5 miles an hour. If his total traveling time was 1 hour, what was the total number of miles in the round trip?

• 3

• $3\frac{1}{8}$

• $3\frac{3}{4}$

• 4

• 5

A 50-foot wire runs from the roof of a building to the top of a 10-foot pole 14 feet across the street. How much taller would the pole have to be if the street were 16 feet wider and the wire remained the same length?

• 2 feet

• 8 feet

• 14 feet

• 16 feet

• 18 feet

A dress is selling for $100 after a 20% discount. What was the original selling price?

• $200

• $125

• $120

• $80

• $75

For the equation $\frac{a^x}{a^y}=a^{10}\ and\ \left(a^y\right)^3=a^x,\ if\ a>1$ , what is the value of x? 

• 5

• 10

• 15

• 20

• 25

If $x>0$ , which of the following is equivalent to  $\sqrt{x^3}$  ?
I.  $x+x^{\frac{1}{2}}$  
II.  $\left(x^{0.5}\right)^3$  
III.  $\left(x^2\right)\left(x^{-\frac{1}{2}}\right)$  

• None

• I and II only

• I and III only

• II and III only

• I, II and III 

If $4x+2=4$  what is the value of  $4x-6$  ? 

• -6

• -4

• 0

• 4

• 8

if  $\sqrt{5}=x-2$   , what is the value of  $\left(x-2\right)^2$  ?

•  $\sqrt{5}$  

•  $\sqrt{7}$  

• 5

• 9

• 25

In the expression $x^2+kx+12$  , k is an integer and k<0. Which of the following is a possible value of k?

• -13

• -12

• -6

• 7

• It cannot be determined with the information given.

If $2x-3y=5$ , what is the value of  $4x^2-12xy+9y^2$  ?

•  $\sqrt{5}$  

• 5

• 12

• 25

• 100

if $4x\ +y=14$  and   $3x+2y=13$  , then   $x-y=?$  

• -1

• 1

• 2

• 3

•  $\frac{1}{2}$