GMAT Math : Solving equations

Study concepts, example questions & explanations for GMAT Math

Create An Account

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 6 7 8 Next →

Example Question #1427 : Problem Solving Questions

Solve for . Give all real solutions:

$x - \sqrt{x} - 20 = 0$

Possible Answers:

The equation has no real solution.

$x = -16 \textrm{ or }x = 25$

x = -16

x = 25

$x = -25 \textrm{ or }x = 25$

Correct answer:

x = 25

Explanation:

One way is to substitute $t = \sqrt{ x}$ , and, subsequently, $t ^{2} = x$

$x - \sqrt{x} - 20 = 0$

$t^{2}- t - 20 = 0$

(t-5)(t+4)= 0

Set each binomial to 0 and solve separately:

t-5 = 0

t = 5

$\sqrt{x}= 5$

x = 25

t+4= 0

t=-4

$\sqrt{x}=-4$

Since no real number has as its principal square root, this yields no solution.

The only solution is x = 25 .

Report an Error

Example Question #1428 : Problem Solving Questions

Solve for , giving all solutions, real and imaginary:

$x^{3} - 4x^{2}+ 3x - 12 = 0$

Possible Answers:

$x \in \left \{ -3,3,4\right \}$

$x \in \left \{ -\sqrt{3 }, \sqrt{3 },4\right \}$

$x \in \left \{-4,3,4\right \}$

$x \in \left \{ 4, i \sqrt{3 }, -i \sqrt{3 }\right \}$

$x \in \left \{ -3i,3i,4\right \}$

Correct answer:

$x \in \left \{ 4, i \sqrt{3 }, -i \sqrt{3 }\right \}$

Explanation:

Factor the expression:

$x^{3} - 4x^{2}+ 3x - 12 = 0$

$\left ( x^{3} - 4x^{2} \right ) +\left ( 3x - 12 \right )= 0$

$x^{2} \left ( x - 4 \right ) + 3 \left ( x - 4 \right )= 0$

$\left (x^{2}+ 3 \right ) \left ( x - 4 \right ) = 0$

Rewrite:

x- 4 = 0

x=4

$x^{2} +3 =0$

$x^{2} = -3$

$x = \pm \sqrt{ -3} = \pm i \sqrt{3}$

Report an Error

Example Question #1429 : Problem Solving Questions

Solve for :

$6 ^{2x+5} =\left ( \frac{1}{36} \right )^{x-3}$

Possible Answers:

The equation has no solution.

$x =2 \frac{3}{4}$

x = 4

$x = \frac{1}{4}$

$x = \frac{4}{11}$

Correct answer:

$x = \frac{1}{4}$

Explanation:

$\frac{1}{36} = 6 ^{-2}$ , so the equation can be rewritten as follows:

$6 ^{2x+5} =\left ( \frac{1}{36} \right )^{x-3}$

$6 ^{2x+5} =\left ( 6 ^{-2} \right )^{x-3}$

$6 ^{2x+5} = 6 ^{-2\left ( x-3 \right )}$

Set the exponents equal to each other:

2x+5 = -2 ( x-3 )

2x+5 = -2 x+6

2x+5 +2x-5 = -2 x+6+2x-5

4x = 1

$x = \frac{1}{4}$

Report an Error

Example Question #1430 : Problem Solving Questions

Daniel has candy bars. Andy has three more candy bars than the double of Daniel's candy bars.

How many candy bars does Andy have?

Possible Answers:

Correct answer:

Explanation:

Let A be the number of Andy's candy bars and D be the number of Daniel's candy bars.

We start by setting up the equation:

$A = 3 + 2 \cdot D$

and

D = 7

$A = 3 + 2 \cdot 7 = 3 + 14 = 17$

Report an Error

Example Question #31 : Solving Equations

$\frac{2}{(5^{-1})x+0.1}=5$

What is the value of ?

Possible Answers:

1.7

1.5

1.6

1.9

1.8

Correct answer:

1.5

Explanation:

To find the value of x we need to isolate x on one side of the equation and the rest of the numbers on the other side.

$\frac{2}{(5^{-1})x+0.1}=5$

First, we multiply what is in the denominator on the left had side by the numerators on both sides.

$2=5\times((5^{-1})x +0.1)$

Then we distribute the 5 to both terms in the binomial. Doing this we get a zero in the exponent.

$2=(5^{0})x+0.5$

Anything raised to the zero just becomes one.

2=x+0.5

From here we subtract 0.5 from each side to solve for x.

x=2-0.5

x=1.5

Report an Error

Example Question #32 : Solving Equations

Define $f (x) = x \cdot |x |$ . Which of the following would be a valid alternative way of expressing the definition of ?

Possible Answers:

$f (x) = \left\{\begin{matrix}0 & \textrm{ if } x < 0\\ x^{2} & \textrm{ if } x \geq 0 \end{matrix}\right.$

$f (x) = \left\{\begin{matrix} -x^{2} & \textrm{ if } x < 0\\ x^{2} & \textrm{ if } x \geq 0 \end{matrix}\right.$

$f (x) = \left\{\begin{matrix} 0 & \textrm{ if } x < 0\\ -x^{2} & \textrm{ if } x \geq 0 \end{matrix}\right.$

$f (x) = \left\{\begin{matrix} x^{2} & \textrm{ if } x < 0\\ -x^{2} & \textrm{ if } x \geq 0 \end{matrix}\right.$

$f (x) = -x^{2}$

Correct answer:

$f (x) = \left\{\begin{matrix} -x^{2} & \textrm{ if } x < 0\\ x^{2} & \textrm{ if } x \geq 0 \end{matrix}\right.$

Explanation:

By definition:

If $x \geq 0$ , then |x| = x ,and subsequently, $f (x) = x \cdot |x | = x \cdot x= x^{2}$

If x < 0 , then |x| = -x ,and subsequently, $f (x) = x \cdot |x | = x \cdot \left (- x \right )= - x^{2}$

Report an Error

Example Question #33 : Solving Equations

$125^{N} = x$

Which of the following expressions is equal to $\log_{25}x$ ?

Possible Answers:

$\frac{3}{2}N$

$\sqrt[3]{N^2}$

$\frac{2}{3}N$

$N \ln 5$

$N \sqrt{N }$

Correct answer:

$\frac{3}{2}N$

Explanation:

$5 ^{2} = 25$ , so $5 = \sqrt{25}$ , and $125 = 5 ^{3}= \left (\sqrt{25} \right )^{3} = 25^\frac{3}{2}$ .

$x= 125^{N} = \left ( 25^\frac{3}{2} \right )^{N} =25^{\frac{3}{2}N} \right$

$\log_{25} x = \frac{3}{2}N$

Report an Error

Example Question #1431 : Problem Solving Questions

A factory makes barrels of the same shape but different sizes; the amount of water they hold varies directly as the cube of their height. The four-foot-high barrel holds 20 gallons of water; how much water would the six-foot-high barrel hold?

Possible Answers:

$67 \frac{1}{2}\textrm{ gal}$

$45\textrm{ gal}$

$80\textrm{ gal}$

$64\textrm{ gal}$

$30\textrm{ gal}$

Correct answer:

$67 \frac{1}{2}\textrm{ gal}$

Explanation:

Let be the height of a barrel and be its volume. Since varies directly as the cube of , the variation equation is

$V = k h^{3}$

for some constant of variation .

We find by substituting V = 20, h= 4 from the smaller barrels:

$20 = k \cdot 4^{3}$

$20 = k \cdot 64$

$k = \frac{20 }{64}= \frac{5 }{16}$

Then the variation equation is:

$V = \frac{5 }{16} h^{3}$

Now we can substitute h = 6 to find the volume of the larger barrel:

$V = \frac{5 }{16} \cdot 6^{3} = \frac{5 }{16} \cdot 216 = \frac{5 }{16} \cdot \frac{216}{1} = \frac{5 }{2} \cdot \frac{27}{1} = \frac{135 }{2}= 67 \frac{1 }{2}$

The larger barrel holds $67 \frac{1 }{2}$ gallons.

Report an Error

Example Question #1431 : Problem Solving Questions

Solve for .

-x-3xy+4>0

Possible Answers:

$x>\frac{4}{1+3y}$

$x<\frac{4}{1+3y}$

$x<\frac{-4}{1+3y}$

$x>\frac{-4}{1+3y}$

Correct answer:

$x<\frac{4}{1+3y}$

Explanation:

$-x-3xy+4>0\Rightarrow 4>x+3xy$

$4>x(1+3y) \Rightarrow \frac{4}{1+3y}>x$

Report an Error

Example Question #353 : Algebra

To convert Celsius temperature to the equivalent in Fahrenheit temperature , use the formula

$F = \frac{9}{5}C + 32$

To the nearest tenth of a degree, convert $70^{\circ } C$ to degrees Fahrenheit.

Possible Answers:

$158.0 ^{\circ } F$

$94.0 ^{\circ } F$

$183.6 ^{\circ } F$

$68.4 ^{\circ } F$

$21.1 ^{\circ } F$

Correct answer:

$158.0 ^{\circ } F$

Explanation:

$F = \frac{9}{5}C + 32 = \frac{9}{5} \cdot 70 + 32 = 126 + 32 = 158$

Report an Error

← Previous 1 2 3 4 5 6 7 8 Next →

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in Denver, ISEE Tutors in Houston, Biology Tutors in Boston, Computer Science Tutors in Dallas Fort Worth, SAT Tutors in Dallas Fort Worth, Biology Tutors in San Diego, Chemistry Tutors in Boston, GRE Tutors in Boston, Physics Tutors in San Diego, Biology Tutors in Atlanta

Popular Courses & Classes

MCAT Courses & Classes in Atlanta, ACT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Seattle, GMAT Courses & Classes in Los Angeles, MCAT Courses & Classes in Phoenix, Spanish Courses & Classes in Denver, ISEE Courses & Classes in Los Angeles, Spanish Courses & Classes in Seattle, SAT Courses & Classes in Los Angeles, Spanish Courses & Classes in Miami

Popular Test Prep

GMAT Test Prep in Los Angeles, ACT Test Prep in Dallas Fort Worth, ACT Test Prep in Chicago, LSAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Phoenix, ACT Test Prep in New York City, SAT Test Prep in Chicago, GMAT Test Prep in Washington DC, GRE Test Prep in Denver, LSAT Test Prep in New York City

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

Email address:
Your name:
Feedback:

GMAT Math : Solving equations

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1427 : Problem Solving Questions

Example Question #1428 : Problem Solving Questions

Example Question #1429 : Problem Solving Questions

Example Question #1430 : Problem Solving Questions

Example Question #31 : Solving Equations

Example Question #32 : Solving Equations

Example Question #33 : Solving Equations

Example Question #1431 : Problem Solving Questions

Example Question #1431 : Problem Solving Questions

Example Question #353 : Algebra

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details