GRE Math : Algebra

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Example Questions

Example Question #441 : Gre Quantitative Reasoning

$11-3x=\frac{5x}{2}$ , solve for .

Possible Answers:

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

x=11

x=22

x=1

x=2

Correct answer:

x=2

Explanation:

The first step is to multiple each side by and that leaves you with

22-6x=5x .

The next step will be to add to both sides resulting in

22=11x .

Finally divide both sides by giving answer of x=2 .

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Example Question #441 : Algebra

For which value of are the following two functions equal?

$F(x)=2x+3^x+\frac{9x}{3}$

$G(x)=\frac{2^x+4^x}{2}-4x-5x+1$

Possible Answers:

Correct answer:

Explanation:

It is important to follow the order of operations for this equation and find a solution that satisfies both F(x) and G(x).

Recall the order of operations is PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

The correct answer is 4 because

F(x) = 2x + 3^x+ (9x/3) = 2(4) + 3⁴ + ((9 * 4)/3) = 101, and

G(x) = (((2⁴ + 4⁴)/2) - 4 * 4) – 5(4) + 1 = 101.

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Example Question #1132 : Algebra

The function is defined as f(x) = 3x^2 + 6x + 27 . What is f(-1) ?

Possible Answers:

-36

Correct answer:

Explanation:

Substitute -1 for in the given function.

$f(-1)=3(-1)^{2}+6(-1)+27$

f(-1)=3(1)-6+27

f(-1)=3-6+27

f(-1)=24

If you didn’t remember the negative sign, you will have calculated 36. If you remembered the negative sign at the very last step, you will have calculated -36; however, if you did not remember that (-1)^2 is 1, then you will have calculated 18.

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Example Question #1133 : Algebra

If the function h(x) is created by shifting f(x) up four units and then reflecting it across the x-axis, which of the following represents h(x) in terms of f(x) ?

Possible Answers:

f(x-4)

f(x+4)

f(x)+4

-f(x+4)

-f(x)-4

Correct answer:

-f(x)-4

Explanation:

We can take each of the listed transformations of f(x) one at a time. If f(x) is to be shifted up by four units, increase every value of f(x) by 4.

$f(x)_{\textup{shifted up by 4}}=f(x)+4$

Next, take this equation and reflect it across the x-axis. If we reflect a function across the x-axis, then all of its values will be multiplied by negative one. So, h(x) can be written in the following way:

h(x)=-(f(x)+4)

Lastly, distribute the negative sign to arrive at the final answer.

h(x)=-f(x)-4

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Example Question #1 : How To Divide Exponents

Simplify

$\dpi{100} \small \frac{20x^{4}y^{-3}z^{2}}{5z^{-1}y^{2}x^{2}}=$

Possible Answers:

None

$\dpi{100} \small {4x^{5}y^{-2}}$

$\dpi{100} \small 15x^{2}y^{2}z^{2}$

$\dpi{100} \small 15x^{-2}y^{-2}z^{-2}$

$\dpi{100} \small \frac{4x^{2}z^{3}}{y^{5}}$

Correct answer:

$\dpi{100} \small \frac{4x^{2}z^{3}}{y^{5}}$

Explanation:

Divide the coefficients and subtract the exponents.

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Example Question #1 : How To Divide Exponents

Which of the following is equal to the expression Equationgre , where

xyz ≠ 0?

Possible Answers:

z/(xy)

xyz

1/y

Correct answer:

1/y

Explanation:

(xy)⁴ can be rewritten as x⁴y⁴ and z⁰ = 1 because a number to the zero power equals 1. After simplifying, you get 1/y.

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Example Question #11 : How To Divide Exponents

If $c\neq 0$ , then $\frac{(c^3)^2}{c^2c^4}=?$

Possible Answers:

c^4

Cannot be determined

c^2

Correct answer:

Explanation:

Start by simplifying the numerator and denominator separately. In the numerator, (c³)² is equal to c⁶. In the denominator, c²* c⁴ equals c⁶ as well. Dividing the numerator by the denominator, c⁶/c⁶, gives an answer of 1, because the numerator and the denominator are the equivalent.

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Example Question #2 : How To Divide Exponents

If $a\not\equiv0$ , which of the following is equal to $\frac{(a^6*a^2)^3}{a^6}$ ?

Possible Answers:

a⁶

The answer cannot be determined from the above information

a⁴

a¹⁸

Correct answer:

a¹⁸

Explanation:

The numerator is simplified to a^8 (by adding the exponents), then cube the result. a²⁴/a⁶ can then be simplified to $a^{18}$ .

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Example Question #1 : Exponential Operations

[64^1/2 + (–8)^1/3] * [4³/16 – 3¹⁷¹/3¹⁶⁹] =

Possible Answers:

–5

–30

Correct answer:

–30

Explanation:

Let's look at the two parts of the multiplication separately. Remember that (–8)^1/3 will be negative. Then 64^1/2 + (–8)^1/3= 8 – 2 = 6.

For the second part, we can cancel some exponents to make this much easier. 4³/16 = 4³/4² = 4. Similarly, 3¹⁷¹/3¹⁶⁹ = 3^171–169 = 3² = 9. So 4³/16 – 3¹⁷¹/3¹⁶⁹= 4 – 9 = –5.

Together, [64^1/2 + (–8)^1/3] * [4³/16 – 3¹⁷¹/3¹⁶⁹] = 6 * (–5) = –30.

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Example Question #1 : Exponential Operations

Evaluate:

$\frac{(2x^3y^{-2}a^6z^4)^5}{(4xy^4a^{-3}z^4)^2}$

Possible Answers:

$\frac{5x^{13}y-2az^{12}}{4y}$

$\frac{5x^{13}y-2az^{12}}{4}$

$\frac{2x^{13}z^{12}}{y^{18}a^{36}}$

$\frac{2x^{13}a^{36}z^{12}}{y^{18}}$

$2x^{13}-18a-36z^{12}$

Correct answer:

$\frac{2x^{13}a^{36}z^{12}}{y^{18}}$

Explanation:

Distribute the outside exponents first:

$\frac{2^5x^{15}y^{-10}a^{30}z^{20}}{4^2x^2y^8a^{-6}z^8}$

Divide the coefficient by subtracting the denominator exponents from the corresponding numerator exponents:

$\frac{2x^{13}a^{36}z^{12}}{y^{18}}$

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GRE Math : Algebra

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #441 : Gre Quantitative Reasoning

Example Question #441 : Algebra

Example Question #1132 : Algebra

Example Question #1133 : Algebra

Example Question #1 : How To Divide Exponents

Example Question #1 : How To Divide Exponents

Example Question #11 : How To Divide Exponents

Example Question #2 : How To Divide Exponents

Example Question #1 : Exponential Operations

Example Question #1 : Exponential Operations

All GRE Math Resources

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