GRE Math : GRE Quantitative Reasoning

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Example Questions

Example Question #1 : How To Find The Radius Of A Sphere

If a sphere has a volume of 268.08 cubic inches, what is the approximate radius of the sphere?

Possible Answers:

64 in

5.9 in

8 in

4.5 in

4 in

Correct answer:

4 in

Explanation:

The formula for the volume of a sphere is

$v=\frac{4}{3}(\pi r^3)$ where is the radius of the sphere.

Therefore,

$r=\sqrt[3]{\frac{3v}{(4\pi)}}$

$r=\sqrt[3]{\frac{3(268.08)}{(4\pi)}}=\sqrt[3]{63.999}=3.999$ , giving us $r\approx4$ .

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Example Question #2 : How To Find The Radius Of A Sphere

A rectangular prism has the dimensions $9\textup{ x }6\textup{ x }12$ . What is the volume of the largest possible sphere that could fit within this solid?

Possible Answers:

$288\pi$

$972\pi$

$2304\pi$

$36\pi$

Correct answer:

$36\pi$

Explanation:

For a sphere to fit into the rectangular prism, its dimensions are constrained by the prism's smallest side, which forms its diameter. Therefore, the largest sphere will have a diameter of , and a radius of .

The volume of a sphere is given as:

$\frac{4}{3}\pi r^3$

And thus the volume of the largest possible sphere to fit into this prism is

$\frac{4}{3}\pi (3)^3=36\pi$

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Example Question #1541 : Gre Quantitative Reasoning

What is the radius of a sphere with volume $36\pi$ cubed units?

Possible Answers:

Correct answer:

Explanation:

The volume of a sphere is represented by the equation $\frac{4}{3}\pi r^3$ . Set this equation equal to the volume given and solve for r:

$36\pi=\frac{4}{3}\pi r^3$

$36\pi\cdot \frac{3}{4}=\pi r^3$

$27\pi=\pi r^3$

27=r^3

r=3

Therefore, the radius of the sphere is 3.

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Example Question #1 : Exponential Operations

Simplify

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

Possible Answers:

None

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

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

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

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

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 #472 : Algebra

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

xyz ≠ 0?

Possible Answers:

xyz

z/(xy)

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 #473 : Algebra

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

Possible Answers:

Cannot be determined

c^2

c^4

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 #1 : 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

a¹⁸

a⁴

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 #1542 : Gre Quantitative Reasoning

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

Possible Answers:

–30

–5

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 #1543 : Gre Quantitative Reasoning

Evaluate:

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

Possible Answers:

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

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

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

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

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

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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Example Question #41 : Exponents

$\dpi{100} \small \frac{7^{10}-7^{8}}{7^{9}-7^{7}}=$

Possible Answers:

$\dpi{100} \small 49$

$\dpi{100} \small 28$

$\dpi{100} \small 7$

$\dpi{100} \small 42$

$\dpi{100} \small 343$

Correct answer:

$\dpi{100} \small 7$

Explanation:

The easiest way to solve this is to simplify the fraction as much as possible. We can do this by factoring out the greatest common factor of the numerator and the denominator. In this case, the GCF is 7^7 .

$\frac{7^7\left ( 7^3-7^1\right)}{7^7\left ( 7^2-1\right)}$

Now, we can cancel out the 7^7 from the numerator and denominator and continue simplifying the expression.

$\frac{7^7\left ( 7^3-7^1\right)}{7^7\left ( 7^2-1\right)}=\frac{7^3-7^1}{7^2-1}=\frac{343-7}{49-1}=\frac{336}{48}=7$

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GRE Math : GRE Quantitative Reasoning

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : How To Find The Radius Of A Sphere

Example Question #2 : How To Find The Radius Of A Sphere

Example Question #1541 : Gre Quantitative Reasoning

Example Question #1 : Exponential Operations

Example Question #472 : Algebra

Example Question #473 : Algebra

Example Question #1 : How To Divide Exponents

Example Question #1542 : Gre Quantitative Reasoning

Example Question #1543 : Gre Quantitative Reasoning

Example Question #41 : Exponents

All GRE Math Resources

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