GMAT Math : Algebra

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Example Questions

Example Question #1171 : Problem Solving Questions

Simplify:

$\frac{(x^3y^4z)^2}{x^{\frac{1}{2}}y^9}$

Possible Answers:

$\frac{x^3z^2}{y}$

$\frac{x^{\frac{11}{2}}z^2}{y}$

$\frac{x^3z}{y^5}$

$\frac{x^{\frac{5}{2}}z^2}{y^5}$

$\frac{x^5z^2}{y^{10}}$

Correct answer:

$\frac{x^{\frac{11}{2}}z^2}{y}$

Explanation:

The first step is two distribute the squared exponent across the numerator:

$\frac{(x^3y^4z)^2}{x^{\frac{1}{2}}y^9} = \frac{x^6y^8z^2}{x^{\frac{1}{2}}y^9}$

We can then subtract the denominator's exponents from the numerator's leaving us with the answer:

$\frac{x^6y^8z^2}{x^{\frac{1}{2}}y^9} = \frac{x^{\frac{11}{2}} z^2}{y}$

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Example Question #61 : Exponents

The first two terms of a geometric sequence are and $C ^{3}$ , in that order. Give the tenth term.

(Assume is positive.)

Possible Answers:

$C^{11}$

$C^{19}$

$C^{21}$

$C^{27}$

$C^{30}$

Correct answer:

$C^{19}$

Explanation:

The common ratio of the geometric sequence can be found by dividing the second term by the first:

$\frac{C^{3}}{C} = C^{2}$

The tenth term of the sequence is therefore

$a_{10} = a_{1}r^{10-1}=C \cdot \left ( C^{2}\right ) ^{9} = C \cdot C^{18} = C^{19}$

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Example Question #1176 : Gmat Quantitative Reasoning

$7^{3x+2} = 49 ^{y - 12 }$

Express in terms of .

Possible Answers:

y = 6x - 8

y = 6x+16

$y = \frac{3}{2} x+25$

$y = \frac{3}{2} x-11$

$y = \frac{3}{2} x+13$

Correct answer:

$y = \frac{3}{2} x+13$

Explanation:

$7^{3x+2} = 49 ^{y - 12 }$

$7^{3x+2} = \left (7^{2} \right ) ^{y - 12 }$

$7^{3x+2} = 7^{2 \cdot (y - 12 )}$

$7^{3x+2} = 7^{2 y - 24}$

2y-24 = 3x+2

2y-24 + 24= 3x+2 + 24

2y = 3x+2 6

$\frac{1}{2}\cdot 2y = \frac{1}{2}\cdot (3x+2 6)$

$y = \frac{3}{2} x+13$

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Example Question #1177 : Gmat Quantitative Reasoning

$4^{t} = \frac{2^{x+3}}{8^{y - 5}}$

Which of the following is a true statement?

Possible Answers:

$t= \frac{1}{2} x - \frac{3}{2} y-6$

t = 2x-6y- 24

t = 2x-6y+ 36

t = 2x-6y+12

$t= \frac{1}{2} x - \frac{3}{2} y+9$

Correct answer:

$t= \frac{1}{2} x - \frac{3}{2} y+9$

Explanation:

$4^{t} = \frac{2^{x+3}}{8^{y - 5}}$

$(2^{2}) ^{t} = \frac{2^{x+3}}{(2^{3}) ^{y - 5}}$

$2^{2t} = \frac{2^{x+3}}{2^{3(y-5)}}$

$2^{2t} = \frac{2^{x+3}}{2^{3y-15}}$

$2^{2t} = 2^{(x+3)- (3y-15)}$

2t=(x+3)- (3y-15)

2t=x+3- 3y+15

2t=x - 3y+18

$\frac{1}{2} \cdot 2t= \frac{1}{2} \cdot ( x - 3y+18 )$

$t= \frac{1}{2} x - \frac{3}{2} y+9$

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Example Question #1178 : Gmat Quantitative Reasoning

$0.25 ^{t} = 2 ^{3y}$

Express in terms of .

Possible Answers:

$t = -\frac{2}{3}y$

$t = -\frac{3}{2}y$

$t = \sqrt{3y}$

t = 3y+2

$t = \sqrt[3]{2y}$

Correct answer:

$t = -\frac{3}{2}y$

Explanation:

$0.25 ^{t} = 2 ^{3y}$

$\left ( \frac{1}{4} \right )^{t} = 2 ^{3y}$

$\left ( 2 ^{-2 }\right )^{t} = 2 ^{3y}$

$2 ^{-2t} = 2 ^{3y}$

-2t = 3y

$\frac{-2t }{-2 }= \frac{3y}{-2}$

$t = -\frac{3}{2}y$

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Example Question #71 : Exponents

$0.04 ^{t} = 25 ^{x+2}$

Express in terms of .

Possible Answers:

t = -x+2

t = -x-2

$t = \frac{1}{x+2}$

$t = \frac{-1}{x+2}$

t = x-2

Correct answer:

t = -x-2

Explanation:

$0.04 ^{t} = 25 ^{x+2}$

$\left ( \frac{1}{25} \right )^{t} = 25 ^{x+2}$

$\left ( 25 ^{-1} \right )^{t} = 25 ^{x+2}$

$25 ^{- t} = 25 ^{x+2}$

-t = x+2

t = -x-2

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Example Question #91 : Algebra

The first and third terms of a geometric sequence are and $K ^{4}$ , in that order. Give the eighth term.

(Assume is positive.)

Possible Answers:

$K^{11 } \sqrt{K}$

$K^{25}$

$K^{10} \sqrt{K}$

$K^{22}$

$K^{14}$

Correct answer:

$K^{11 } \sqrt{K}$

Explanation:

Let be the common ratio of the geometric sequence. Then the third term is $r^{2}$ times the first, so

$r^{2} = \frac{K^{4}}{K} = K^{3}$

and

$r = \sqrt{K^{3}} = K^ { \frac{3}{2}}$ .

The eighth term of the sequence is

$a_{8} = a_{1} \cdot r ^{7}$

$= K \cdot (K^{\frac{3}{2}} )^{7}$

$= K \cdot K^{\frac{21}{2}}$

$= K^{\frac{23}{2}}$

$= K^{11 \frac{1}{2}}$

$= K^{11} \cdot K^{ \frac{1}{2}}$

$= K^{11 } \sqrt{K}$

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Example Question #1181 : Problem Solving Questions

Simplify: $\frac{x^6y^{-4}z^0}{x^{-5}y^{10}z^{-6}}$

Possible Answers:

$\frac{x^{11}z^{6}}{y^{14}}$

$\frac{y^{14}}{x^{11}z^6}$

xy^6z^6

$\frac{xz^6}{y^{14}}$

$\frac{x^{11}}{y^{14}}$

Correct answer:

$\frac{x^{11}z^{6}}{y^{14}}$

Explanation:

To solve, we must first simplify the negative exponents by shifting them to the other side of the fraction:

$\frac{x^6y^{-4}z^0}{x^{-5}y^{10}z^{-6}} = \frac{x^6x^5z^0z^6}{y^{10}y^4}$

Then we can simply the multiplied like bases by adding their exponents:

$\frac{x^6x^5z^0z^6}{y^{10}y^4} = \frac{x^{11}z^6}{y^{14}}$

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Example Question #71 : Understanding Exponents

$\frac{(2^6 \cdot 2^7)^3}{2^{40}} =$

Possible Answers:

$\frac{1}{16}$

$\frac{1}{4}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

First we can simplify the numerator's parentheses by adding the like bases' exponents:

$\frac{(2^6 \cdot 2^7)^3}{2^{40}} = \frac{(2^{13})^3}{2^{40}}$

We can then simplify the numerator further by multiplying the base's exponent by the exponent to which it is raised:

$\frac{(2^{13})^3}{2^{40}} = \frac{2^{39}}{2^{40}}$

We can then subtract the denominator's exponent from the numerator's:

$\frac{1}{2^1} = \frac{1}{2}$

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Example Question #71 : Understanding Exponents

Simplify the following expression:

$\frac{343y^7}{49y^4}-9y^3$

Possible Answers:

3y^2

2y^3

-2y^3

285y^3

Correct answer:

-2y^3

Explanation:

Simplify the following expression:

$\frac{343y^7}{49y^4}-9y^3$

Let's begin by simplifying the fraction. Recall that when dividing exponents of similar base, we need to subtract the exponents. We can treat the 343 and the 49 just like regular fractions.

$\frac{343y^7}{49y^4}-9y^3=7y^3-9y^3=-2y^3$

Note that then we perform the subtraction step to get our final answer:

-2y^3

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GMAT Math : Algebra

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1171 : Problem Solving Questions

Example Question #61 : Exponents

Example Question #1176 : Gmat Quantitative Reasoning

Example Question #1177 : Gmat Quantitative Reasoning

Example Question #1178 : Gmat Quantitative Reasoning

Example Question #71 : Exponents

Example Question #91 : Algebra

Example Question #1181 : Problem Solving Questions

Example Question #71 : Understanding Exponents

Example Question #71 : Understanding Exponents

All GMAT Math Resources

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