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

GMAT Practice Questions -5

1. If $x \ne 3$, then $\frac{3x^{2}+18x+27}{(x+3)^{2}}$
   
   
   1. $1$
   2. $3$
   3. $9$
   4. $27$
   5. $81$
   
   
2. If $\frac{x+5}{x-5}=y$, what is the value of $x$ in terms of $y$?
   
   
   1. $-5-y$
   2. $\frac{5}{y}$
   3. $\sqrt{y^{2}+5}$
   4. $\frac{-5y-5}{1-y}$
   5. $\frac{-5y+5}{1-y}$
   
   
3. $\frac{1-\frac{1}{3}}{2}$
   
   
   1. $3$
   2. $\frac{2}{3}$
   3. $\frac{3}{2}$
   4. $\frac{1}{3}$
   5. $\frac{1}{5}$
   
   
4. $\frac{\frac{1}{x}}{\frac{1}{y}-z}$
   
   
   1. $\frac{xy}{y-xyz}$
   2. $\frac{1}{xy-xyz}$
   3. $\frac{y}{xyz+x}$
   4. $\frac{y}{x-xyz}$
   5. $\frac{x-xyz}{y}$
   
   
5. The average of $x$, $\frac{1}{x}$ and $\frac{1}{x^{2}}$ is
   
   
   1. $\frac{1+x^{2}}{3x}$
   2. $\frac{1+x^{2}+x^{3}}{3x^{2}}$
   3. $\frac{1+x+x^{2}}{3x^{2}}$
   4. $\frac{1-x+x^{2}}{3x}$
   5. $\frac{1+x^{2}+x^{3}}{3}$
   
   
6. $\frac{1}{5}$ of $.01$ percent equals :
   
   
   1. $.00002$
   2. $.0002$
   3. $.002$
   4. $.02$
   5. $.2$
   
   
7. $\frac{2^{a+1}-2^{a-1}}{2^{a+1}+2^{a-1}}$
   
   
   1. $\frac{1}{4}$
   2. $\frac{3}{5}$
   3. $2$
   4. $\frac{1}{2}$
   5. $\frac{5}{3}$
   
   
8. If $x$ is $\frac{50}{51}$ of $\frac{51}{52}$ and $y=\frac{50}{51}$, then $\frac{x}{y}=$
   
   
   1. $\frac{50}{51}$
   2. $\frac{50}{52}$
   3. $\frac{51}{52}$
   4. $\frac{2550}{2500}$
   5. $\frac{2601}{2704}$
   
   
9. The decimal $.01$ is how many times greater than the decimal $(.0001)^{4}$
   
   
   1. $10^{6}$
   2. $10^{8}$
   3. $10^{10}$
   4. $10^{12}$
   5. $10^{14}$
   
   
10. Let $a=.79$, $b=\sqrt{.79}$ and $c=(.79)^{2}$, then which of the following is true?
    
    
    1. $a < b < c$
    
    
    2. $c < b < a$
    
    
    3. $a < b < c$
    
    
    4. $c < a < b$
    
    
    5. $b < a < c$
    
    
    

    Answer Key

    1	B
    2	D
    3	D
    4	D
    5	C
    6	A
    7	B
    8	C
    9	E
    10	D

GMAT Practice Questions -4

1. If $n$ is a positive integer and $(n+3)(n+5)$ is odd, then $(n+4)(n+6)$ must be a multiple of which one of the following?
   
   
   1. $3$
   2. $5$
   3. $7$
   4. $8$
   5. $16$
   
   
2. The number of prime numbers divisible par 2 plus the number of prime numbers divisible by 5 is
   
   
   1. $0$
   2. $1$
   3. $2$
   4. $3$
   5. $4$
   
   
3. If $13x+17=0$, then $-13|x|$ equals which one of the following?
   
   
   1. $-\frac{17}{13}$
   2. $\frac{17}{13}$
   3. $17$
   4. $13$
   5. $-17$
   
   
4. Which one of the following is divisible by both 2 and 3?
   
   
   1. $1007$
   2. $3096$
   3. $1616$
   4. $2306$
   5. $1791$
   
   
5. Which one of the following equals the product of exactly two prime numbers?
   
   
   1. $13.6$
   2. $11.9$
   3. $17.21$
   4. $19.51$
   5. $17.23$
   
   
6. If $m$, $n$, and $p$ are different prime numbers, then the least common multiple of the the three numbers must equal which one of the following?
   
   
   1. $mn(p+n)$
   2. $m+n+p$
   3. $m+np$
   4. $m+n-p$
   5. $pnm$
   
   
7. Each of the positive integer $a$ and $b$ ends with the digit 3. With which one of the following numbers does $a-b$ ends?
   
   
   1. $0$
   2. $1$
   3. $2$
   4. $3$
   5. $4$
   
   
8. If $p-10$ is divisible by 4, then which one of the following must be divisible by 4?
   
   
   1. $p$
   2. $p-2$
   3. $p-6$
   4. $p+3$
   5. $p+8$
   
   

GMAT Practice Questions -3

1. If $a+5a$ is 6 less than $b+5b$, then $a-b=$
   
   
   1. $6$
   2. $-1$
   3. $-\frac{1}{6}$
   4. $\frac{1}{6}$
   5. $-6$
   
   
2. If $w \ne 0$, $w=5x=\sqrt{5}y$, what is the value of $w-x$ in terms of $y$?
   
   
   1. $5y$
   2. $\frac{\sqrt{5}}{5}y$
   3. $\sqrt{5y}$
   4. $\frac{5}{4\sqrt{5}}y$
   5. $\frac{4\sqrt{5}}{5}y$
   
   
3. If $(a-1)(a+5)(a-7)=0$, and $a < 0$, then $a=$
   
   
   
   1. $-1$
   
   
   2. $-7$
   
   
   3. $-5$
   
   
   4. $-3$
   
   
   5. $-2$
   
   
4. A aytem of equations is as shown below
   $x-l=8$
   $x+m=7$
   $x-p=6$
   $x+q=5$
   What is the value of $l+m+p+q$?
   
   
   1. $-4$
   2. $-3$
   3. $-2$
   4. $-1$
   5. $0$
   
   
5. If $\frac{a^{2}-25}{20a}=\frac{a-5}{a+5}$, $a=5 \ne 0$, and $a \ne 0$, then $a=$
   
   
   1. $1$
   2. $3$
   3. $5$
   4. $20$
   5. $25$
   
   
6. If $a$, $b$, $c$,and $d$ are not equal to 0 or 1, and if $a^{x}=b$, $b^{y}=c$, $c^{z}=d$ and $d^{t}=a$, then $xyzt=$
   
   
   1. $0$
   2. $1$
   3. $abc$
   4. $abcd$
   5. $a^{b^{c^{d}}}$
   
   
7. If $(x-3y)(x+3y)=-9$ and $(3x-y)(3x+y)=-1$, then $\frac{x^{2}+y^{2}}{x^{2}-y^{2}}=$
   
   
   1. $-2$
   2. $-1$
   3. $0$
   4. $1$
   5. $2$
   
   
8. If $p-q=5$ and $pq=11$, then is the value of $\frac{1}{p^{2}}+\frac{1}{q^{2}}$?
   
   
   1. $\frac{25}{121}$
   2. $-\frac{47}{121}$
   3. $\frac{5}{11}$
   4. $-\frac{5}{11}$
   5. $\frac{47}{121}$

GMAT Practice Questions -2

1. If n is an integer, which of the following CANNOT be an integer?
   
   
   1. $\frac{n+2}{2}$
   2. $\sqrt{n+1}$
   3. $\frac{3}{n+2}$
   4. $\sqrt{n^{2}+5}$
   5. $\sqrt{\frac{1}{n^{2}+3}}$
   
   
2. If n is an integer, which one of the following is an odd integer?
   
   
   1. $n^{2}$
   2. $\frac{n+3}{2}$
   3. $-2n-8$
   4. $n^{2}-3$
   5. $\sqrt{n^{4}+1}$
   
   
3. If $x$, $y$, $z$ and $t$ are positive integers such that $x < y < z < t$ and $x+y+z+t=10$, then what is the value of $t$?
   
   
   
   1. $2$
   
   
   2. $3$
   
   
   3. $4$
   
   
   4. $5$
   
   
   5. $6$
   
   
4. The remainder when the positive integer $m$ is divided by $n$ is r. What is the remainder when $3m$ is divided by $3n$?
   
   
   1. $r$
   2. $3r$
   3. $3n$
   4. $m-3n$
   5. $3(m-nr)$
   
   
5. If $(x-5)(x+4)=(x-4)(x+5)$, then $x=$
   
   
   1. $-5$
   2. $-4$
   3. $0$
   4. $4$
   5. $5$
   
   
6. If $(3x-1)^{2}=121$, then which one of the following COULD equal x?
   
   
   1. $-4$
   2. $\frac{10}{3}$
   3. $\frac{13}{3}$
   4. $-\frac{10}{3}$
   5. $\frac{17}{3}$
   
   
7. (The average of 5 consecutive integers starting from 17)-(The average of 6 consecutive integers starting from 17)=
   
   
   1. $-\frac{1}{8}$
   2. $-\frac{1}{2}$
   3. $0$
   4. $\frac{1}{8}$
   5. $\frac{1}{2}$
   
   
8. If $n^{3}+n^{2}-n-2=-1$, then which one of the following could be the value of $n$
   
   
   1. $0$
   2. $1$
   3. $2$
   4. $3$
   5. $4$
   
   
9. Solve the the system of equations given?
   $x+3y=8$
   $x+2y=5$
   
   
   1. $-1,4$
   2. $1,3$
   3. $2,3$
   4. $1,-3$
   5. $-1,3$
   
   
10. If $(a-b)(a+b)=7 \times 3$ then $a$ and $b$ equals respectively?
    
    
    1. $-5,-2$
    2. $5,3$
    3. $7,2$
    4. $9,2$
    5. $-3,-10$

GRE Practice Questions -2

1. $4x+3=-1$, then $x-1=$
   
   
   1. $2$
   2. $1$
   3. $0$
   4. $-1$
   5. $-2$
   
   
2. $\frac{7}{\frac{1}{6}+1}$
   
   
   1. $-6$
   2. $7$
   3. $\frac{1}{6}$
   4. $\frac{1}{6}$
   5. $6$
   
   
3. $32^{17}=2^{3a+4}$, then $a=$
   
   
   1. $3$
   2. $9$
   3. $27$
   4. $81$
   5. $243$
   
   
4. $a=5b$, $b^{2}=3c$ and $5c=d$, then $\frac{a^{2}}{d}=$
   
   
   1. $15$
   2. $\frac{3}{5}$
   3. $\frac{15}{3}$
   4. $9$
   5. $\frac{1}{5}$
   
   
5. $(x-3)(x+2)=(x+4)(x-5)$
   
   
   1. $7$
   2. $14$
   3. $-7$
   4. $3$
   5. There is no solution
   
   
6. $\frac{1}{2}$ of $0.02$ percent equals
   
   
   1. $1$
   2. $0.1$
   3. $0.01$
   4. $0.001$
   5. $0.0001$
   
   
7. If the average of $2x$, $3x$ and $5x$ is 3, then $x=$
   
   
   1. $\frac{10}{9}$
   2. $9$
   3. $10$
   4. $\frac{9}{10}$
   5. $-\frac{9}{10}$
   
   
8. $-2^{5}-(1-x^{2})^{2}$
   
   
   1. $-x^{4}+2x^{2}+31$
   2. $-x^{4}+2x^{2}-31$
   3. $-x^{4}+2x^{2}+33$
   4. $-x^{4}-2x^{2}+33$
   5. $-x^{4}+2x^{2}-33$
   
   
9. A truckmaker sells six models of cars, and each model comes with 7 options.
   How many different types of trucks does the truckmaker sell?
   
   
   1. $20$
   2. $25$
   3. $32$
   4. $42$
   5. $52$
   
   
10. If $a$, $b$, and $c$ are consecutive integers and $a < b < c$, which of the following must be true?
    
    
    
    1. $b^{3}$ is a prime number
    
    
    2. $\frac{a+c}{2}=b$
    
    
    3. $\frac{c-a}{2}=1$ is odd
    
    
    4. $\frac{ab}{3}$
    
    
    5. $c-a=b$
    
    

GMAT Practice Questions -1

1. If $C=\frac{7r}{3s}$ and $s \ne 0$, what is the value of C?
   
   
   1. $r=6s$
   2. $r=\frac{3}{7}$
   
   
2. If $7a=5b$ and $ab \ne 0$, what is the ratio of $\frac{a}{5}$ to $\frac{b}{7}$
   
   
   1. $\frac{49}{25}$
   2. $\frac{7}{5}$
   3. $\frac{5}{7}$
   4. $1$
   5. $\frac{25}{49}$
   
   
3. If the diameter of a circle is $18$, then the area of the circle is
   
   
   1. $9 \pi$
   2. $18 \pi$
   3. $36 \pi$
   4. $81 \pi$
   5. $324 \pi$
   
   
4. For any numbers $a$ and $b$, $a*b=ab(5-b)$. If $a$ and $a*b$ both represent positive numbers, which of the following could be a value of $b$?
   
   
   1. $-7$
   2. $-1$
   3. $3$
   4. $6$
   5. $9$
   
   
5. $\sqrt{7^{2}+5^{2}-10}$
   
   
   1. $4\sqrt{2}$
   2. $6$
   3. $8$
   4. $10$
   5. $\sqrt{117}$
   
   
6. What is the perimeter of a square with area $\frac{7p}{4}$?
   
   
   1. $\frac{7p}{4}$
   2. $\frac{7p^{2}}{4}$
   3. $7p$
   4. $7p^{2}$
   5. $\frac{4p}{7}$
   
   
7. $\sqrt{169}+\sqrt{256}+\sqrt{361}=$
   
   
   1. $19$
   2. $29$
   3. $36$
   4. $46$
   5. $48$
   
   
8. If $45$ percent of $500$ is $50$ percent of x, then $x=$
   
   
   1. $350$
   2. $400$
   3. $450$
   4. $600$
   5. $1,200$
   
   
9. $(5^{3}-1)(5^{3}+1)(5^{6}+1)(5^{12}+1)$
   
   
   1. $(5^{24}-1)$
   2. $(5^{24}+1)$
   3. $(5^{48}-1)$
   4. $(5^{96}+1)$
   5. $5^{3}(5^{24}-1)$
   
   
10. How many minutes does it take to travel $160$ miles at $200$ miles per hour?
    
    
    1. $13$
    2. $16$
    3. $45$
    4. $48$
    5. $52$
    
    

GRE Practice Questions -1

1. If $5x+7=11$, then $5x-4=0$
   
   
   1. $11$
   2. $7$
   3. $5$
   4. $1$
   5. $0$
   
   
2. The smallest prime number greter than 50 is
   
   
   1. $51$
   2. $52$
   3. $53$
   4. $54$
   5. $55$
   
   
3. $\frac{6}{\frac{1}{5}+1}$
   
   
   1. $1$
   2. $\frac{1}{5}$
   3. $\frac{1}{6}$
   4. $5$
   5. $6$
   
   
4. $\sqrt{(120-39)(68+13)}$
   
   
   1. $2$
   2. $20$
   3. $40$
   4. $80$
   5. $81$
   
   
5. $(9^{y})^{3}$
   
   
   1. $9^{y+3}$
   2. $9^{6y}$
   3. $3^{3y^{2}}$
   4. $9^{y^{3}}$
   5. $3^{6y}$




6. $27^{13}=3^{a}$, then $a=$
   
   
   1. $39$
   2. $29$
   3. $19$
   4. $13$
   5. $9$




7. $x-y=h$, then $5x^{2}-10xy+5y^{2}=$
   
   
   1. $5h^{2}$
   2. $10h$
   3. $h^{2}$
   4. $5h$
   5. $10h^{2}$




8. $27x^{2}-12$
   
   
   1. $3(3x-2)(3x+2)$
   2. $3(9x-2)(9x+2)$
   3. $9(3x-2)(3x+2)$
   4. $3(3x-2)(9x+2)$
   5. $(9x-2)(9x+2)$
   
   
9. If the average of $3x$ and $9x$ is 6, then $x=$
   
   
   1. $20$
   2. $19$
   3. $9$
   4. $3$
   5. $1$
   
   
10. What percent of $5x$ is $10y$ if $x=2y$?
    
    
    1. $20 \%$
    2. $30 \%$
    3. $40 \%$
    4. $45 \%$
    5. $50 \%$

SAT Practice Questions - 7

1. If $3x+7=5x+1$
   
   
   1. $2.5$
   2. $3.5$
   3. $4$
   4. $3$
   5. $4.5$
   
   
2. What is the next term in the sequence: 6, 3, 10, 7, 14, 11, ...?
   
   
   1. $19$
   2. $15$
   3. $6$
   4. $17$
   5. $18$
   
   
3. The area of the basis of Cylinder A is 8 times the area of the basis of Cylinder B. What is the radius of Cylinder A in terms of the radius of Cylinder B?
   
   
   1. $r_{A}=\frac{r_{B}}{8}$
   2. $r_{A}=8r_{B}$
   3. $r_{A}=4r_{B}$
   4. $r_{A}=2\sqrt{2}r_{B}$
   5. $r_{A}=\frac{r_{B}}{4}$
   
   
4. If $x^{2}-2xy+y^{2}=121$, $x-y=$
   
   
   1. $10$
   2. $11$
   3. $12$
   4. $13$
   5. $14$
   
   
5. If c is equal to the sum b and twice of a, which of the following is the average of b and c?
   
   
   1. $a$
   2. $b$
   3. $c$
   4. $a+b$
   5. $b+c$
   
   
6. $f(x)=4x+8$, $f(c+3)=8$, $f(c)=$
   
   
   1. $-8$
   2. $0$
   3. $3$
   4. $8$
   5. $-3$
   
   
7. $5^{n}.125^{m}=78,125$, $n+3m=$
   
   
   1. $5$
   2. $6$
   3. $7$
   4. $8$
   5. $9$
   
   
8. $\frac{3b^{2}}{a^{3}}=27a^{2}$
   
   
   1. $3a^{3}$
   2. $9a^{3}$
   3. $\frac{1}{9a^{3}}$
   4. $\frac{1}{a^{3}}$
   5. $\frac{1}{3a^{3}}$
   
   
9. Which of the following statements must be true about the x and y coordinates that satisfy the equation $ay-ax=0$, $a \ne 0$, $x \ne 0$ ,$y \ne 0$
   
   
   1. $x>y$
   2. $xy=1$
   3. $x=-y$
   4. $y>x$
   5. $x=y$
   
   
10. What is the length of the side of a cube whose volume is 125 cubic units?
    
    
    1. $4$
    2. $5$
    3. $6$
    4. $7$
    5. $4.5$

    Answer Key

    1	D
    2	E
    3	D
    4	B
    5	D
    6	D
    7	C
    8	E
    9	E
    10	B

SAT Practice Questions - 6

1. If $\frac{1}{2}$ of a number is 3, what is $\frac{1}{3}$ of the number?
   
   
   1. $1$
   2. $2$
   3. $3$
   4. $6$
   5. $8$
   
   
2. If $x=-1$, then $x^{5}+x^{4}+x^{3}+x^{2}-5=$
   
   
   1. $-10$
   2. $-6$
   3. $-5$
   4. $-3$
   5. $-1$
   
   
3. If $f(x)=2^{x}+7x$, then $f(4)=$
   
   
   1. $24$
   2. $36$
   3. $44$
   4. $54$
   5. $64$
   
   
4. If $x-3=y$, then $(y-x)^{3}=$
   
   
   1. $27$
   2. $54$
   3. $-54$
   4. $-27$
   5. $81$
   
   
5. If $a>b$, and $\frac{a}{b}>0$, which of the following is true?
   
   
   1. $a>0$
   2. $b>0$
   3. $ab>0$
   
   
   1. I only
   2. II only
   3. III only
   4. I and II only
   5. I and III only
   
   
6. Which of the following is equal to $(\frac{x^{-7}y^{-5}}{x^{-3}y^{3}})^{-2}$
   
   
   1. $x^{8}y^{16}$
   2. $\frac{x^{8}}{y^{16}}$
   3. $\frac{y^{16}}{x^{8}}$
   4. $x^{4}y^{8}$
   5. $x^{8}y^{8}$
   
   
   
7. What is the slope of the line passing through the points (-1,7) and (3,5)?
   
   
   1. $\frac{1}{2}$
   2. $-2$
   3. $-\frac{1}{2}$
   4. $1$
   5. $2$
   
   
8. The symbol $\otimes$ represents a binary operation defined as $a \otimes b=3^{a}+2^{b}$, what is the value of $(-2)\otimes (-3)$
   
   
   1. $-\frac{17}{72}$
   2. $\frac{72}{17}$
   3. $-72$
   4. $72$
   5. $\frac{17}{72}$
   
   
9. If $\sqrt{\frac{49}{x}}=\frac{7}{3}$
   
   
   1. $6$
   2. $9$
   3. $25$
   4. $49$
   5. $147$
   
   
10. A bike that originally sold for $150 \$$ was on sale for $120 \$$. What was the rate of discount?
    
    
    1. $15 \%$
    2. $21 \%$
    3. $20 \%$
    4. $25 \%$
    5. $30 \%$
    
    

    Answer Key

    1	B
    2	C
    3	C
    4	D
    5	C
    6	A
    7	C
    8	E
    9	B
    10	C

SAT Practice Questions - 5

1. If $0.10 < x < 0.12$, which of the following could be a value of $x$?
   
   
   1. $9 \%$
   2. $10 \%$
   3. $11 \%$
   4. $12 \%$
   5. $13 \%$
   
   
2. If $\frac{xyz}{t}=w$ and $x$ and $t$ are doubled, what happens to the value of w



1. The value of $w$ is two times smaller.
2. The value of $w$ is halved.
3. The value of $w$ is four times greater.
4. The value of $w$ is doubled
5. The value of $w$ remains the same.


3. What is the tenth term of the pattern below?
   $\frac{3}{2}$, $\frac{9}{4}$, $\frac{27}{8}$, $\frac{81}{16}$,...
   
   
   1. $\frac{3}{2^{10}}$
   2. $\frac{30}{20}$
   3. $(\frac{3}{2})^{10}$
   4. $\frac{3^{10}}{2}$
   5. $\frac{300}{200}$
   
   
4. If $a > 0$ and $b < 0$, which of the following is always negative?
   
   
   1. $-ab$
   2. $a+b$
   3. $|a|-|b|$
   4. $\frac{a}{b}$
   5. $b^{a}$
   
   
5. Which of the following number pairs is in the ratio $3:7$?
   
   
   1. $\frac{1}{3}$,$\frac{1}{7}$
   2. $\frac{1}{7}$,$\frac{1}{3}$
   3. $\frac{1}{7}$,$\frac{3}{7}$
   4. $7$,$\frac{1}{3}$
   5. $1$,$\frac{1}{7}$
   
   
6. If $x=-\frac{1}{4}$, then $(-x)^{-3}+(\frac{1}{x})^{2}=$
   
   
   1. $-80$
   2. $-64$
   3. $16$
   4. $64$
   5. $80$
   
   
7. For which of the following values of $x$ is the relationship $x < x^{2} < x^{3}$ true?
   
   
   1. $-3$
   2. $-\frac{2}{3}$
   3. $0$
   4. $\frac{2}{3}$
   5. $3$
   
   
8. $x^{2}+2xy+y^{2}=169$, $-|-(x+y)|=$
   
   
9. How many distincts factors does 900 have?
   
   
   1. $2$
   2. $3$
   3. $4$
   4. $5$
   5. more than $5$
   
   
10. If $x=-\frac{1}{7}$, then which of the following is always positive for $n > 0$?
    
    
    1. $x^{n}$
    2. $n^{x}$
    3. $nx$
    4. $n-x$
    5. $\frac{x}{n}$
    
    
    

    Answer Key

    1	C
    2	E
    3	C
    4	D
    5	B
    6	E
    7	3
    8	-13
    9	A
    10	B

    
    

SAT Practice Questions - 4

1. For how many positive integers, $n$, is true that $n^{2} \leq 3n$
   
   
   1. $2$
   2. $3$
   3. $4$
   4. $5$
   5. more than 5
   
   
2. If $a^{4}=16$, then $3^{a}$
   
   
   1. $3$
   2. $9$
   3. $16$
   4. $27$
   5. $81$
   
   
3. $\sqrt{20}\sqrt{5}=$
   
   
   1. $2\sqrt{5}$
   2. $10$
   3. $4\sqrt{5}$
   4. $5\sqrt{10}$
   5. $10\sqrt{5}$
   
   
   
4. The sum of three positive consecutive even integers is x.
   What is the value of the middle of the three integers?
   
   
   1. $\frac{x}{3}-1$
   2. $\frac{x}{3}+2$
   3. $3x$
   4. $\frac{x-2}{3}$
   5. $\frac{x}{3}$
   
   
5. What is the average of $5^{10}$, $5^{20}$, $5^{30}$, $5^{40}$ and $5^{50}$?
   
   
   1. $5^{9}+5^{19}+5^{29}+5^{39}+5^{49}$
   2. $5^{30}$
   3. $5^{149}$
   4. $150$
   5. $5^{29}$
   
   
6. Which of the following is equal to $(5^{6} \times 5^{9})^{10}$?
   
   
   1. $25^{150}$
   2. $25^{540}$
   3. $5^{540}$
   4. $5^{150}$
   5. $5^{15}$
   
   
7. What is the value of $3^{\frac{1}{3}} \times 3^{\frac{2}{3}} \times 3^{\frac{3}{3}}$?
   
   
   1. $3$
   2. $9$
   3. $27$
   4. $30$
   5. $81$
   
   
8. How many integers satisfy the inequality $|x| < 2 \pi$.
   
   
   1. $0$
   
   
   
   2. $3$
   
   
   
   3. $4$
   
   
   
   4. $7$
   
   
   
   5. More than $7$
   
   
   
9. What is the average of $5^{a} \times 5^{b}=5^{300}$
   
   
   1. $50$
   2. $100$
   3. $150$
   4. $200$
   5. $250$
   
   
10. If $5^{a}5^{b}=\frac{5^{c}}{5^{d}}$, what is d in terms of $a$, $b$ and $c$?
    
    
    1. $\frac{c}{a+b}$
    2. $c+ab$
    3. $c-a-b$
    4. $c+a-b$
    5. $\frac{b}{ac}$

    Answer Key

    1	B
    2	B
    3	B
    4	E
    5	A
    6	D
    7	B
    8	E
    9	C
    10	C

SAT Practice Questions - 3 & Answer Key

1. Which of the following is equivalent to $5^{9}$
   
   
   1. $5^{4}+5^{4}+5^{1}$
   2. $5^{2} \times 5^{4} \times 5^{3}$
   3. $\frac{10^{9}}{2^{10}}$
   4. $(5^{4})^{5}$
   5. $\frac{5^{5}}{5^{4}}$
   
   
2. Which of the following is equivalent to $\sqrt{289}$
   
   
   1. $14$
   2. $15$
   3. $16$
   4. $17$
   5. $18$
   
   
3. Which of the following is a perfect square?
   
   
   1. $120$
   2. $121$
   3. $122$
   4. $123$
   5. $124$
   
   
4. Which of the following is equivalent to $3\sqrt{10}$
   
   
   1. $3\sqrt{5} \times \sqrt{5}$
   2. $\sqrt{90}$
   3. $3\sqrt{5} + 3\sqrt{2}$
   4. $3\sqrt{5}+3\sqrt{5}$
   5. $\frac{3\sqrt{2}}{\sqrt{5}}$
   
   
5. Which of the following is equivalent to $10^{\frac{2}{5}}$
   
   
   1. $\sqrt[5]{5}$
   2. $\sqrt[5]{10}$
   3. $\sqrt[5]{20}$
   4. $\sqrt[5]{100}$
   5. $\sqrt[5]{1000}$
   
   
6. Which of the following fractions is equivalent to $\frac{3}{6} \times \frac{2}{5}$?
   
   
   1. $\frac{6}{30}$
   2. $\frac{5}{30}$
   3. $\frac{5}{11}$
   4. $\frac{15}{12}$
   5. $\frac{9}{30}$
   
   
7. Which of the following expressions is equivalent to $\frac{7}{6} \div \frac{5}{2}$?
   
   
   1. $\frac{7}{30}+\frac{2}{30}$
   2. $\frac{9}{6}+\frac{9}{5}$
   3. $\frac{7}{8}+\frac{5}{8}$
   4. $\frac{7}{6}+\frac{2}{5}$
   5. $\frac{1}{7}+\frac{2}{35}$
   
   
8. If $3^{x}=729$, what is $x^{3}$?
   
   
9. What is the value of $||4|-|-7||$
   
   
   1. $-11$
   2. $-3$
   3. $0$
   4. $3$
   5. $11$
   
   
10. What is the value of $(\sqrt{3}+\sqrt{5})^{2}-(\sqrt{8})^{2}$
    
    
    1. $2\sqrt{15}$
    2. $\sqrt{15}$
    3. $0$
    4. $15$
    5. $30$
    
    

    Answer Key

    1	B
    2	D
    3	B
    4	B
    5	D
    6	A
    7	E
    8	125
    9	D
    10	A

SAT Practice Questions - 2

1. Solve $15x-32=18-10x$
   
   
   1. $-14$
   2. $10$
   3. $14$
   4. $2$
   5. $50$
   
   
2. Solve $\frac{x}{8}=\frac{x-2}{4}$
   
   
   1. $12$
   2. $4$
   3. $6$
   4. $-\frac{1}{2}$
   5. $-6$
   
   
3. Which of the following are the factors of $t^{2}+8t+16$
   
   
   1. $(t-4)(t-4)$
   2. $(t-8)(t-2)$
   3. $(t+8)(t+2)$
   4. $(t+1)(t+16)$
   5. $(t+4)(t+4)$
   
   
4. Solve for a in term of b, if $6a+12b=24$
   
   
   1. $24-12b$
   2. $2-\frac{1}{2}b$
   3. $4-2b$
   4. $24-18b$
   5. $2b-4$
   
   
5. If $ax+2b=5c-dx$, what does x equal in terms of a, b, c, and d?
   
   
   1. $5c-d-2b-a$
   2. $a-d$
   3. $(5c-2b)(a-d)$
   4. $\frac{5c-d-2b}{a}$
   5. $\frac{5c-2b}{a-d}$
   
   
6. If $(z-9)(z+3)=0$, what are the two possible values of z?
   
   
   1. $z=-9$ abd $z=3$
   2. $z=9$ abd $z=0$
   3. $z=0$ abd $z=-3$
   4. $z=9$ abd $z=-3$
   5. $z=-12$ abd $z=12$
   
   
7. If $z^{2}-6z=16$, which of the following could be a value of $z^{2}+6z$?
   
   
   1. $-8$
   2. $112$
   3. $110$
   4. $18$
   5. $108$
   
   
8. If $3\sqrt{ a}-10=2$, what is the value of a?
   
   
   1. $16$
   2. $4$
   3. $32$
   4. $64$
   5. $12$
   
   
9. Given $\frac{(x+6)(x^{2}-2x-3)}{x^{2}+3x-18}=10$, find the value of x.
   
   
   1. $18$
   2. $4$
   3. $12$
   4. $9$
   5. $12$
   
   
10. Solve the equation $\frac{5x}{8}-\frac{3x}{5}=2$.
    
    
    1. $40$
    2. $80$
    3. $160$
    4. $-80$
    5. $20$
    
    

    Answer Key

    1	D
    2	B
    3	E
    4	C
    5	E
    6	D
    7	B
    8	A
    9	D
    10	B

CLEP Precalculus Practice Questions -1

1. Evaluate the expression: $1000(2^{-1.5})$
   
   
   1. $2828,427$
   2. $2000.00$
   3. $353.55$
   4. $3000$
   5. $350.50$
   
   
2. Evaluate the expression: $\log_{49}7$
   
   
   1. $\frac{1}{4}$
   2. $\frac{1}{2}$
   3. $\frac{2}{5}$
   4. $\frac{1}{49}$
   5. $7$
   
   
3. Place into standard form: $(5+i)-(7-7i)$
   
   
   1. $-2+8i$
   2. $2+8i$
   3. $12+8i$
   4. $-2+6i$
   5. $2-8i$
   
   
4. Find the domaine of the function: $f(x)=\sqrt{-6x+12}$
   
   
   1. $x \geq 2$
   2. $x \geq 3$
   3. $x \leq -2$
   4. $x \leq -1$
   5. $x \leq 2$
   
   
5. What is the value of: $3\ln e^{6}$
   
   
   1. $6$
   2. $18$
   3. $9$
   4. $12$
   5. $3$
   
   
6. What is the value of: $\csc (150 deg)$
   
   
   1. $0$
   2. $1$
   3. $-1$
   4. $-2$
   5. $2$
   
   
7. Solve the equation: $x^{2}-10x+50=0$
   
   
   1. $5+5i$ or $5-5i$
   2. $2+5i$ or $2-5i$
   3. $4+5i$ or $4-5i$
   4. $1+5i$ or $1-5i$
   5. $5+i$ or $5-i$
   
   
8. What is the value of $x$: $\log_{10}x=-3$
   
   
   1. $0.01$
   2. $0.001$
   3. $0.1$
   4. $1$
   5. $10$
   
   
9. Factor the expression: $x^{2}-3ix-2$
   
   
   1. $(x+i)(x+2i)$
   2. $(x+i)(x-2i)$
   3. $(x-i)(x-2i)$
   4. $(-x-i)(x-2i)$
   5. $(x-1)(x-2)$
   
   
10. Identify the horizontal and vertical asymptotes for: $\frac{5x^{2}}{x^{2}-9}$
    
    
    1. $y=5$, $x=-3$, $x=3$
    2. $y=-5$, $x=-3$
    3. $y=5$, $x=3$
    4. $y=5$, $x=-3$
    5. $y=-5$, $x=3$, $x=-3$
       
       

Answer Key

1	C
2	B
3	A
4	E
5	B
6	E
7	A
8	B
9	C
10	A

CLEP College Algebra Practice Questions -- Functions and their properties

1. If $f(x)=-x^{3}+2x+1$ what is $f(-3x)$
   
   
   1. $27x^{3}-6x+1$
   2. $-27x^{3}-6x+1$
   3. $-27x^{3}+6x+1$
   4. $27x^{3}-6x-1$
   5. $-3x^{3}-6x+1$
   
   
2. If $f(x)=9x+3$ then $f^{-1}(x)=$
   
   
   1. $\frac{1}{9}x-\frac{1}{3}$
   2. $\frac{1}{3}+\frac{1}{9}$
   3. $9x-3$
   4. $\frac{1}{3}x+1$
   5. $x-\frac{1}{9}$
   
   
3. If $f(x,y)=\frac{x \log x}{y \log y}$ then $f(8,2)=$
   
   
   1. $4$
   2. $24$
   3. $\frac{3}{2}$
   4. $\log 2$
   5. $12$
   
   
4. $\log_{5}(\frac{1}{125})$
   
   
   1. $\frac{1}{3}$
   2. $-\frac{1}{3}$
   3. $5$
   4. $3$
   5. $-3$
   
   
5. The function $f$ is defined by $f(x)=\frac{1}{1-x}$. For what values of $x$ is $f(f(x))$ undefined?
   
   
   1. $\{0\}$
   2. $\{1\}$
   3. $\{-1,2\}$
   4. $\{0,1\}$
   5. $\{-1,0\}$
   
   
   
   
6. If $f(x)=\frac{7x-5}{2}$, find the solution set for $f(x)>3x$
   
   
   1. $\{x/ x>5 \}$
   2. $\{x/ x<5 \}$
   3. $\{ x/ x>3 \}$
   4. $\{ x/ x \leq -3 \}$
   5. None of the above
   
   
7. If $f(x)=3x+7$ and $g(x)=2x-1$, what is $f(g(1))$?



8. Find the equation for the line passing through $(4,2)$ and $(-1,3)$
   
   
   1. $5y-x=14$
   2. $5y+x=-14$
   3. $-5y+x=14$
   4. $y+5x=14$
   5. $5y+x=14$
   
   
9. Solve $2^{7x}=4^{2x-1}$
   
   
   1. $\frac{2}{3}$
   2. $\frac{3}{2}$
   3. $-\frac{2}{3}$
   4. $3$
   5. $\frac{2}{3}$
   
   
10. Find $\log_{3} 81$
    

Answer Key

1	A
2	A
3	E
4	E
5	D
6	A
7	10
8	E
9	C
10	4