GRE Math : Linear / Rational / Variable Equations

Study concepts, example questions & explanations for GRE Math

Create An Account

All GRE Math Resources

13 Diagnostic Tests 452 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #84 : How To Find The Solution To An Equation

Ben is walking three dogs that weigh an average of 75 pounds each. Ben begins to walk a fourth dog, and the average weight of the dogs decreases to 70 pounds. What is the weight in pounds of the fourth dog?

Possible Answers:

$50$

$40$

$60$

$55$

$45$

Correct answer:

$55$

Explanation:

The total weight of the first three dogs is 225 pounds. This amount, plus the weight of the fourth dog, divided by total number of dogs, is the new average weight:

$\frac{d + 225}{4} = 70$

$d + 225 = 280$

$d = 55 lbs$

Report an Error

Example Question #85 : How To Find The Solution To An Equation

Pets Plus makes bird houses. Their monthly fixed expenses are $750. The cost for each bird house is $15. The bird houses sell for $40.

What is the monthly break-even point at Pets Plus?

Possible Answers:

$30$

$25$

$40$

$50$

$35$

Correct answer:

$30$

Explanation:

Let $x=$ the number of bird houses sold each month.

$Revenue = 40x$

$Costs=15x+750$

The break-even point is where the revenue is the same as the costs:

$Revenue=Costs$

$40x=15x+750$

Solve for $x$ :

$x=30$

Therefore, Pets Plus must sell 30 bird houses to break-even.

Report an Error

Example Question #91 : How To Find The Solution To An Equation

Pets Plus makes bird houses. Their monthly fixed expenses are $750. The cost for each bird house is $15. The bird houses sell for $40.

If Pets Plus sells 50 bird houses, what is the profit?

Possible Answers:

$\$625$

$\$300$

$\$500$

$\$750$

$\$250$

Correct answer:

$\$500$

Explanation:

Let $x$ = the number of birdhouses sold each month.

$Revenue=40x$

$Costs=15x+750$

$Profit = Revenue-Costs$

$=40x-15x-750$

$=25x-750$

Substituting in 50 for $x$ gives an answer of 500, so the profit on 50 birdhouses is $500.

Report an Error

Example Question #52 : Algebra

George is three times older than Joey. The sum of their ages is 16. What is the product of their ages?

Possible Answers:

Correct answer:

Explanation:

Let = Joey's age and = George's age.

Then the equation to solve becomes x + 3x = 16 .

4x=16

x=4

Therefore, Joey is 4 years old and George is 12 years old, so the product of their ages is 48.

Report an Error

Example Question #53 : Algebra

Three consecutive even numbers add to 42. What is the middle number?

Possible Answers:

$18$

$16$

$14$

$10$

$12$

Correct answer:

$14$

Explanation:

Let $x$ = 1st even number, $x+2$ = 2nd even number, and $x+4$ = 3rd even number.

Then the equation to solve becomes $x+(x+2)+(x+4)=42$ .

$3x+6=42$

Thus $x=12,x+2=14,\ and\ x+4=16$ , so the middle number is 14.

Report an Error

Example Question #51 : Equations / Inequalities

Consider the following equation:

$\left | 2x-9 \right | = x-3$

Which of the following must be true?

$I) \quad x=6$

$II) \quad x \mbox{ is positive }$

$III) \quad x \mbox{ is even }$

Possible Answers:

$II \mbox{ only }$

$\mbox{ none of these }$

$II \mbox{ and } III \mbox{ only }$

$III \mbox{ only }$

$I, II \mbox{ and } III$

Correct answer:

$II \mbox{ and } III \mbox{ only }$

Explanation:

The quantity inside the absolute value brackets must equal either x-3 or -(x-3) , depending on whether the quantity inside the brackets is positive or negative. We therefore have two seperate equations:

2x-9 = x-3

2x-9 =-(x-3)

To solve the first equation, add 9 to both sides:

2x = x+6

Subtract from both sides:

x=6

This is the first solution. Now let's look at the second equation. The distributive law gives us:

2x-9 =-x+3

Add 9 to both sides:

2x =-x+12

Add to both sides:

3x = 12

Divide both sides by 3:

x=4

Therefore, is either 4 or 6.

Statement does NOT have to be true because can also equal 4.

Statement must be true because both 4 and 6 are positive .

Finally, statement III always holds because 4 and 6 are both even.

Report an Error

Example Question #51 : Algebra

$5\textup{,}100 = 300(2v + 7)$ ,

then v =

Possible Answers:

500

$\frac{1}{5}$

Correct answer:

Explanation:

Divide both sides by 300 to get 17 = 2v + 7 . Subtract 7 and divide by two to get v = 5 .

Report an Error

Example Question #151 : Gre Quantitative Reasoning

If b – 3 = a, then (a – b)² =

Possible Answers:

–9

–3

The answer cannot be determined from the given information.

Correct answer:

Explanation:

The quantity can be regrouped to be –3 = a – b. Thus, (a – b)² = (–3)² = 9.

Report an Error

All GRE Math Resources

13 Diagnostic Tests 452 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Biology Tutors in Houston, GMAT Tutors in San Francisco-Bay Area, GRE Tutors in Miami, GRE Tutors in Dallas Fort Worth, Calculus Tutors in Philadelphia, MCAT Tutors in Seattle, Physics Tutors in Philadelphia, French Tutors in Philadelphia, Reading Tutors in Dallas Fort Worth, GMAT Tutors in Boston

Popular Courses & Classes

LSAT Courses & Classes in Denver, LSAT Courses & Classes in Houston, GMAT Courses & Classes in Phoenix, ACT Courses & Classes in Phoenix, MCAT Courses & Classes in Houston, SSAT Courses & Classes in Washington DC, GRE Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in San Diego, ISEE Courses & Classes in San Diego, Spanish Courses & Classes in San Diego

Popular Test Prep

GMAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Philadelphia, ACT Test Prep in San Diego, ISEE Test Prep in Seattle, LSAT Test Prep in New York City, GRE Test Prep in Denver, ACT Test Prep in Phoenix, LSAT Test Prep in Seattle, ISEE Test Prep in Dallas Fort Worth, MCAT Test Prep in San Diego

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:

GRE Math : Linear / Rational / Variable Equations

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #84 : How To Find The Solution To An Equation

Example Question #85 : How To Find The Solution To An Equation

Example Question #91 : How To Find The Solution To An Equation

Example Question #52 : Algebra

Example Question #53 : Algebra

Example Question #51 : Equations / Inequalities

Example Question #51 : Algebra

Example Question #151 : Gre Quantitative Reasoning

All GRE Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details