Tuesday, August 30, 2011

PCAT Quantitative Practice Questions -8

1. Evaluate the expression: $1000(2^{-1.5})$

1. $2828,427$
2. $2000.00$
3. $353.55$
4. $3000$

2. Evaluate the expression: $\log_{49}7$

1. $\frac{1}{4}$
2. $\frac{1}{2}$
3. $\frac{2}{5}$
4. $\frac{1}{49}$

3. Place into standard form: $(5+i)-(7-7i)$

1. $-2+8i$
2. $2+8i$
3. $12+8i$
4. $-2+6i$

4. Find the domaine of the function: $f(x)=\sqrt{-6x+12}$

1. $x \geq 3$
2. $x \leq -2$
3. $x \leq -1$
4. $x \leq 2$

5. What is the value of: $3\ln e^{6}$

1. $6$
2. $18$
3. $9$
4. $12$

6. What is the value of: $\csc (150 deg)$

1. $1$
2. $-1$
3. $-2$
4. $2$

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 $1-5i$

8. What is the value of $x$: $\log_{10}x=-3$

1. $0.01$
2. $0.001$
3. $0.1$
4. $1$

9. Factor the expression: $x^{2}-3ix-2$

1. $(x+i)(x+2i)$
2. $(x+i)(x-2i)$
3. $(x-i)(x-2i)$
4. $(-x-i)(x-2i)$

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. $y=5$, $x=-3$
11.  1 C 2 B 3 A 4 D 5 B 6 D 7 A 8 B 9 C 10 A

PCAT Quantitative Practice Questions -7

1. For how many positive integers, $n$, is true that $n^{2} \leq 3n$

1. $2$
2. $3$
3. $4$
4. $5$

2. If $a^{4}=16$, then $3^{a}$

1. $3$
2. $9$
3. $16$
4. $27$

3. $\sqrt{20}\sqrt{5}=$

1. $2\sqrt{5}$
2. $10$
3. $4\sqrt{5}$
4. $5\sqrt{10}$

4. The sum of three positive consecutive even integers is x.
What is the value of the middle of the three integers?

1. $\frac{x}{3}+2$
2. $3x$
3. $\frac{x-2}{3}$
4. $\frac{x}{3}$

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. $150$

6. Which of the following is equal to $(5^{6} \times 5^{9})^{10}$?

1. $25^{150}$
2. $25^{540}$
3. $5^{540}$
4. $5^{150}$

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. $30$

8. How many integers satisfy the inequality $|x| < 2 \pi$.

1. $3$

2. $4$

3. $7$

4. More than $7$

9. What is the average of $5^{a} \times 5^{b}=5^{300}$

1. $50$
2. $100$
3. $150$
4. $200$

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. $c+a-b$
 1 B 2 B 3 B 4 D 5 A 6 D 7 B 8 D 9 C 10 C

PCAT Quantitative Practice Questions -6

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. $(5^{4})^{5}$

2. Which of the following is equivalent to $\sqrt{289}$

1. $14$
2. $15$
3. $16$
4. $17$

3. Which of the following is a perfect square?

1. $120$
2. $121$
3. $122$
4. $123$

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. Which of the following is equivalent to $10^{\frac{2}{5}}$

1. $\sqrt[5]{5}$
2. $\sqrt[5]{10}$
3. $\sqrt[5]{20}$
4. $\sqrt[5]{100}$

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. $\frac{15}{12}$

7. Which of the following expressions is equivalent to $\frac{7}{6} \div \frac{5}{2}$?

1. $\frac{9}{6}+\frac{9}{5}$
2. $\frac{7}{8}+\frac{5}{8}$
3. $\frac{7}{6}+\frac{2}{5}$
4. $\frac{1}{7}+\frac{2}{35}$

8. If $3^{x}=729$, what is $x^{3}$?

9. What is the value of $||4|-|-7||$

1. $-11$
2. $-3$
3. $0$
4. $3$

10. What is the value of $(\sqrt{3}+\sqrt{5})^{2}-(\sqrt{8})^{2}$

1. $2\sqrt{15}$
2. $\sqrt{15}$
3. $0$
4. $15$

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

PCAT Quantitative Practice Questions -5

1. Solve $15x-32=18-10x$

1. $-14$
2. $10$
3. $14$
4. $2$

2. Solve $\frac{x}{8}=\frac{x-2}{4}$

1. $12$
2. $4$
3. $6$
4. $-\frac{1}{2}$

3. Which of the following are the factors of $t^{2}+8t+16$

1. $(t-8)(t-2)$
2. $(t+8)(t+2)$
3. $(t+1)(t+16)$
4. $(t+4)(t+4)$

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. If $ax+2b=5c-dx$, what does x equal in terms of a, b, c, and d?

1. $a-d$
2. $(5c-2b)(a-d)$
3. $\frac{5c-d-2b}{a}$
4. $\frac{5c-2b}{a-d}$

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 $z=-3$

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. $18$

8. If $3\sqrt{ a}-10=2$, what is the value of a?

1. $16$
2. $4$
3. $32$
4. $64$

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. $9$

10. Solve the equation $\frac{5x}{8}-\frac{3x}{5}=2$.

1. $40$
2. $80$
3. $160$
4. $-80$

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

PCAT Quantitative Practice Questions -4

1. $2(5x-5)+5(2x+2)=$
1. $0$
2. $20x$
3. $20x-10$
4. $20x+10$

2. If $x=a+2$, and $y=-8-a$ then $x+y=$

1. $10$
2. $2a-6$
3. $-10$
4. $-6$

3. If $x \ne -5$, then $\frac{x^{2}+3x-10}{x+5}-(x-2)=$

4. If $(a-\frac{1}{a})^{2}=8$, then $a^{2}+\frac{1}{a^{2}}=$

1. $8$
2. $6$
3. $10$
4. $12$

5. $(x+y)^{2}=16$, and $x^{2}+y^{2}=6$ then $xy=$

1. $5$
2. $10$
3. $6$
4. $4$

6. $(x+y)=2$, and $x^{2}-y^{2}=6$ then $x-y=$

1. $12$
2. $4$
3. $6$
4. $\frac{1}{3}$

7. $\frac{15y+3}{3}-5y=$

1. $1$
2. $0$
3. $10y+1$
4. $3$

8. if $b^{2}-a^{2}=9$ then $5(a-b)(a+b)=$

1. $\frac{9}{5}$
2. $4$
3. $50$
4. $-45$

9. When $c \ne 3$, then $\frac{c^{2}-9}{c-3}=$

1. $c-3$
2. $1$
3. $c+3$
4. $3-c$

10. If $b>0$, and $b^{2}-1=10 \times 12$, then $b=$

1. $1$
2. $12$
3. $10$
4. $11$

 1 B 2 D 3 0 4 C 5 A 6 D 7 A 8 D 9 C 10 D

PCAT Quantitative Practice Questions -3

1. If $3x+7=5x+1$

1. $2.5$
2. $3.5$
3. $4$
4. $3$

2. What is the next term in the sequence: 6, 3, 10, 7, 14, 11, ...?

1. $15$
2. $6$
3. $17$
4. $18$

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. $r_{A}=2\sqrt{2}r_{B}$

4. If $x^{2}-2xy+y^{2}=121$, $x-y=$

1. $10$
2. $11$
3. $12$
4. $13$

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. $a+b$

6. $f(x)=4x+8$, $f(c+3)=8$, $f(c)=$

1. $-8$
2. $0$
3. $3$
4. $8$

7. $5^{n}.125^{m}=78,125$, $n+3m=$

1. $5$
2. $6$
3. $7$
4. $8$

8. $\frac{3b^{2}}{a^{3}}=27a^{2}$

1. $9a^{3}$
2. $\frac{1}{9a^{3}}$
3. $\frac{1}{a^{3}}$
4. $\frac{1}{3a^{3}}$

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. $xy=1$
2. $x=-y$
3. $y>x$
4. $x=y$

10. What is the length of the side of a cube whose volume is 125 cubic units?

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

PCAT Quantitative Practice Questions -2

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. $6$

2. If $x=-1$, then $x^{5}+x^{4}+x^{3}+x^{2}-5=$

1. $-10$
2. $-6$
3. $-5$
4. $-3$

3. If $f(x)=2^{x}+7x$, then $f(4)=$

1. $24$
2. $36$
3. $44$
4. $54$

4. If $x-3=y$, then $(y-x)^{3}=$

1. $27$
2. $54$
3. $-54$
4. $-27$

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

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. $x^{4}y^{8}$

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. $1$

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. $\frac{72}{17}$
2. $-72$
3. $72$
4. $\frac{17}{72}$

9. If $\sqrt{\frac{49}{x}}=\frac{7}{3}$

1. $6$
2. $9$
3. $25$
4. $49$

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 \% $ 1 B 2 C 3 C 4 D 5 C 6 A 7 C 8 D 9 B 10 C PCAT Quantitative Practice Questions -1 Pharmacy College Admission Test 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 \% $2. If$\frac{xyz}{t}=w$and$x$and$t$are doubled, what happens to the value of w 1. The value of$w$is halved. 2. The value of$w$is four times greater. 3. The value of$w$is doubled 4. The value of$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}$4. If$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. 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}$6. If$x=-\frac{1}{4}$, then$(-x)^{-3}+(\frac{1}{x})^{2}=$1.$-64$2.$16 $3.$64$4.$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} $8.$x^{2}+2xy+y^{2}=169$,$-|-(x+y)|=$9. How many distincts factors does 900 have? 1.$2$2.$ 3$3.$ 4$4.$ 5$10. If$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$ 1 C 2 D 3 C 4 D 5 B 6 D 7 3 8 -13 9 B 10 B Monday, August 15, 2011 CLEP Precalculus Practice Questions - Algebra review 1. Factor$3a^{2}+3ab-6b^{2}$2. Factor$x^{3}-4x^{2}+2x-8$3. Factor$25a^{2}-36b^{2}$4. Resolve into factors$x^{2}-ax+bx-ab$5. Resolve into factors$6x^{2}-9ax+4bx-6ab$6. Resolve into factors$x^{2}+11x+24$7. Resolve into factors$x^{2}-10x+24$8. Resolve into factors$x^{2}-10ax+10a^{2}$Monday, August 1, 2011 CLEP College Algebra Practice Questions - 12 & 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.$30$ 1 B 2 D 3 B 4 B 5 D 6 A 7 E 8 125 9 D 10 A CLEP College Algebra Practice Questions - 11 & Answer Key 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.$20$ 1 D 2 B 3 E 4 C 5 E 6 D 7 B 8 A 9 D 10 B CLEP College Algebra Practice Questions - 10 & Answer Key 1.$2(5x-5)+5(2x+2)=$1.$0$2.$20x$3.$20x-10$4.$20x+10$5.$10x^{2}+20+x+20$2. If$x=a+2$, and$y=-8-a$then$x+y=$1.$6$2.$10$3.$2a-6$4.$-10$5.$-6$3. If$x \ne -5$, then$\frac{x^{2}+3x-10}{x+5}-(x-2)=$4. If$(a-\frac{1}{a})^{2}=8$, then$a^{2}+\frac{1}{a^{2}}=$1.$8$2.$6$3.$10$4.$12$5.$100$5.$(x+y)^{2}=16$, and$x^{2}+y^{2}=6$then$xy=$1.$5$2.$10$3.$6$4.$4$5.$16$6.$(x+y)=2$, and$x^{2}-y^{2}=6$then$x-y=$1.$12$2.$4$3.$6$4.$\frac{1}{3}$5.$3$7.$\frac{15y+3}{3}-5y=$1.$1$2.$0$3.$10y+1$4.$3$5.$3y+1$8. if$b^{2}-a^{2}=9$then$5(a-b)(a+b)=$1.$45$2.$\frac{9}{5}$3.$4$4.$50$5.$-45$9. When$c \ne 3$, then$\frac{c^{2}-9}{c-3}=$1.$c-3$2.$1$3.$c+3$4.$3-c$5.$o$10. If$b>0$, and$b^{2}-1=10 \times 12$, then$b=$1.$9$2.$1$3.$12$4.$10$5.$11$ 1 B 2 E 3 0 4 C 5 A 6 D 7 A 8 E 9 C 10 E CLEP College Algebra Practice Questions - 9 & Answer Key 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$ 1 D 2 E 3 D 4 B 5 D 6 D 7 C 8 E 9 E 10 B CLEP College Algebra Practice Questions - 8 & Answer Key 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. $30 \%$

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

CLEP College Algebra Practice Questions - 7 & Answer Key

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. $\frac{x}{n}$

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

CLEP College Algebra Practice Questions - 6 & Answer Key

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. $\frac{b}{ac}$
 1 B 2 B 3 B 4 E 5 A 6 D 7 B 8 E 9 C 10 C

GRE Practice Questions - 10 & Answer Key

1. $2(5x-5)+5(2x+2)=$
1. $0$
2. $20x$
3. $20x-10$
4. $20x+10$
5. $10x^{2}+20+x+20$

2. If $x=a+2$, and $y=-8-a$ then $x+y=$

1. $6$
2. $10$
3. $2a-6$
4. $-10$
5. $-6$

3. If $x \ne -5$, then $\frac{x^{2}+3x-10}{x+5}-(x-2)=$

4. If $(a-\frac{1}{a})^{2}=8$, then $a^{2}+\frac{1}{a^{2}}=$

1. $8$
2. $6$
3. $10$
4. $12$
5. $100$

5. $(x+y)^{2}=16$, and $x^{2}+y^{2}=6$ then $xy=$

1. $5$
2. $10$
3. $6$
4. $4$
5. $16$

6. $(x+y)=2$, and $x^{2}-y^{2}=6$ then $x-y=$

1. $12$
2. $4$
3. $6$
4. $\frac{1}{3}$
5. $3$

7. $\frac{15y+3}{3}-5y=$

1. $1$
2. $0$
3. $10y+1$
4. $3$
5. $3y+1$

8. if $b^{2}-a^{2}=9$ then $5(a-b)(a+b)=$

1. $45$
2. $\frac{9}{5}$
3. $4$
4. $50$
5. $-45$

9. When $c \ne 3$, then $\frac{c^{2}-9}{c-3}=$

1. $c-3$
2. $1$
3. $c+3$
4. $3-c$
5. $o$

10. If $b>0$, and $b^{2}-1=10 \times 12$, then $b=$

1. $9$
2. $1$
3. $12$
4. $10$
5. $11$

 1 B 2 E 3 0 4 C 5 A 6 D 7 A 8 E 9 C 10 E

GRE Practice Questions - 9 & Answer Key

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. $20$

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

GRE Practice Questions - 8 & 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. $30$

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

GRE Practice Questions - 7 & Answer Key

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. $\frac{b}{ac}$
 1 B 2 B 3 B 4 E 5 A 6 D 7 B 8 E 9 C 10 C

GRE Practice Questions - 6 & Answer Key

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. $\frac{x}{n}$

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

GRE Practice Questions - 5 & Answer Key

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 \% $ 1 B 2 C 3 C 4 D 5 C 6 A 7 C 8 E 9 B 10 C GRE Practice Questions - 4 & Answer Key 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$4.$-3$5.$8$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$ 1 D 2 E 3 D 4 B 5 D 6 D 7 C 8 E 9 E 10 B GMAT Practice Questions - 12 & Answer Key 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$ 1 D 2 E 3 D 4 B 5 D 6 D 7 C 8 E 9 E 10 B GMAT Practice Questions - 11 & Answer Key 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. $30 \%$

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

GMAT Practice Questions - 10 & Answer Key

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. $\frac{x}{n}$

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

GMAT Practice Questions - 9 & Answer Key

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. $\frac{b}{ac}$
 1 B 2 B 3 B 4 E 5 A 6 D 7 B 8 E 9 C 10 C

GMAT Practice Questions - 8 & 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. $30$

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

GMAT Practice Questions - 7 & Answer Key

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. $20$

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

GMAT Practice Questions -6 & Answer Key

1. $2(5x-5)+5(2x+2)=$
1. $0$
2. $20x$
3. $20x-10$
4. $20x+10$
5. $10x^{2}+20+x+20$

2. If $x=a+2$, and $y=-8-a$ then $x+y=$

1. $6$
2. $10$
3. $2a-6$
4. $-10$
5. $-6$

3. If $x \ne -5$, then $\frac{x^{2}+3x-10}{x+5}-(x-2)=$

4. If $(a-\frac{1}{a})^{2}=8$, then $a^{2}+\frac{1}{a^{2}}=$

1. $8$
2. $6$
3. $10$
4. $12$
5. $100$

5. $(x+y)^{2}=16$, and $x^{2}+y^{2}=6$ then $xy=$

1. $5$
2. $10$
3. $6$
4. $4$
5. $16$

6. $(x+y)=2$, and $x^{2}-y^{2}=6$ then $x-y=$

1. $12$
2. $4$
3. $6$
4. $\frac{1}{3}$
5. $3$

7. $\frac{15y+3}{3}-5y=$

1. $1$
2. $0$
3. $10y+1$
4. $3$
5. $3y+1$

8. if $b^{2}-a^{2}=9$ then $5(a-b)(a+b)=$

1. $45$
2. $\frac{9}{5}$
3. $4$
4. $50$
5. $-45$

9. When $c \ne 3$, then $\frac{c^{2}-9}{c-3}=$

1. $c-3$
2. $1$
3. $c+3$
4. $3-c$
5. $o$

10. If $b>0$, and $b^{2}-1=10 \times 12$, then $b=$

1. $9$
2. $1$
3. $12$
4. $10$
5. $11$

 1 B 2 E 3 0 4 C 5 A 6 D 7 A 8 E 9 C 10 E