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Tuesday, August 30, 2011

PCAT Quantitative Practice Questions -8

Pharmacy College Admission Test

    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. Answer Key
      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

Pharmacy College Admission Test

  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. $c+a-b$
    Answer Key
    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

Pharmacy College Admission Test

  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. $15$

    Answer Key
    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

Pharmacy College Admission Test

  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. $-80$

    Answer Key
    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

Pharmacy College Admission Test

  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. $11$


    Answer Key
    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

Pharmacy College Admission Test

  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$
    Answer Key
    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

Pharmacy College Admission Test

  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 \% $

    Answer Key
    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. $n-x$


    Answer Key
    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. $30$

    Answer Key
    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. $20$

    Answer Key
    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. $11$


    Answer Key
    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$
    Answer Key
    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 \% $

    Answer Key
    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} $


    Answer Key
    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. $\frac{b}{ac}$
    Answer Key
    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. $11$


    Answer Key
    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. $20$

    Answer Key
    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. $30$

    Answer Key
    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. $\frac{b}{ac}$
    Answer Key
    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} $


    Answer Key
    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 \% $

    Answer Key
    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$
    Answer Key
    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$
    Answer Key
    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 \% $

    Answer Key
    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} $


    Answer Key
    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. $\frac{b}{ac}$
    Answer Key
    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. $30$

    Answer Key
    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. $20$

    Answer Key
    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. $11$


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