GMAT Math : Algebra

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

Example Question #1372 : Problem Solving Questions

Consider the incomplete equation

$10(N - 18) + 5N = \square (N-12 )$

What number replaces the box in order to form an equation with no solution?

Possible Answers:

None of the other choices yields a correct answer.

Correct answer:

None of the other choices yields a correct answer.

Explanation:

Set to be the number that replaces the box.

Simplify first:

10(N - 18) + 5N =A (N-12 )

10N - 180+ 5N =A (N-12 )

15N - 180 =A N-12A

15N - 180+180-AN=A N-12A +180 - AN

15N -AN= 180 - 12A

Now solve for in terms of :

$\left (15 -A \right )N= 180 - 12A$

$N=\frac{ 180 - 12A}{15 -A }$

The only possible value of that might preclude the existence of a solution is A = 15 , since it makes the denominator 0. However, let us test this value in the original equation:

10(N - 18) + 5N =15 (N-12 )

15N - 180 = 15N - 180

As it turns out, replacing the box with 15 yields an identity, not a contradiction, so the solution set is the set of all real numbers. There is no number that fits the description.

Report an Error

Example Question #11 : Solving Linear Equations With One Unknown

Consider the incomplete equation

$4x + 17 = 6\left ( \square x - 16 \right ) - 4x$

Which of the following numbers can replace the box to form an equation whose one and only solution is 2?

Possible Answers:

None of the other responses gives a correct answer.

$\frac{4}{3}$

$\frac{113}{4}$

$- \frac{79}{12}$

$\frac{129}{12}$

Correct answer:

$\frac{129}{12}$

Explanation:

Rewrite this equation as

$4x + 17 = 6\left ( A x - 16 \right ) - 4x$

If 2 is a solution of the equation, then we can substitute 2 for to make a true arithmetic equation. Replace with 2 and solve for :

$4 \cdot 2 + 17 = 6\left ( A \cdot 2- 16 \right ) - 4 \cdot 2$

$8+ 17 = 6\left (2 A - 16 \right ) - 8$

$25 = 12 A - 96 \right ) - 8$

25 = 12 A - 104

129 = 12 A

$A = \frac{129}{12}$

This number replaces the box in order to form the equation

$4x + 17 = 6\left ( \frac{129}{12}x - 16 \right ) - 4x$

Report an Error

Example Question #11 : Solving Linear Equations With One Unknown

Solve the following equation for

$\frac{6x}{4} +7 = 18 +x$

Possible Answers:

x=11

x=33

x=22

x=7

x=0

Correct answer:

x=22

Explanation:

We proceed as follows

$\frac{6x}{4} +7 = 18 +x$ (Start)

6x +28 = 72 +4x (Multiply both sides by 4. Remember to distribute the 4 to both summands on both sides.)

6x = 44 +4x (Subtract 28 from both sides)

2x = 44 (Subtract 4x from both sides)

x =22 (Divide both sides by 2)

Report an Error

Example Question #291 : Algebra

Define a function as follows:

f(x) = 8x - 35

If f(N)= 47 , evaluate .

Possible Answers:

N = 10.25

N = 341

N = 96

N = 1.5

N = 656

Correct answer:

N = 10.25

Explanation:

Since f(N)= 47 , we can plug N in for x and 47 in for f(N) to get the following equation,

8N - 35 = 47

From here, we want to solve for N therefore we must isolate N on one side of the equation and all other numbers on the other side.

8N = 47 + 35

8N = 82

$N = 82 \div 8$

N = 10.25

Report an Error

Example Question #11 : Linear Equations, One Unknown

Lisa went to a bargain bookstore where books were sold for dollars and magazines for (x-2) dollars. After buying six books and four magazines, she only spent $30.00. How much did the books and magazines cost?

Possible Answers:

Books: $4.20; Magazines: $2.20

Books: $1.80; Magazines: $3.80

Books: $3.80; Magazines: $5.80

Books: $3.80; Magazines: $1.80

Correct answer:

Books: $3.80; Magazines: $1.80

Explanation:

We must first write out the equation to this problem.

If we set to be the cost of books then we can set to represent the cost of magazines.
She purchased books which means she spent on books.
She also bought magazines which means she spent on magazines.
The total spent was so when these two values are added together they must equal :

6x+4(x-2)=30

We can now solve for :

6x+4x-8=30

10x-8=30

10x=38

x=3.80

Remember: the cost of magazines was x-2 so we must plug in the value to find our answer.

3.80-2=1.80

So, our answer is that books cost $ 3.80 and magazines cost $ 1.80 .

Report an Error

Example Question #1376 : Problem Solving Questions

Students at a local college decide to make and sell t-shirts in order to raise money for their activities. They will pay the manufacturer $\$6.00$ per t-shirt made and a fixed fee of $\$200.00$ . If they sell each t-shirt for $\$16.00$ , how many t-shirts would they have to make and sell to raise $\$1600.00$ ?

Possible Answers:

180

200

160

140

120

Correct answer:

180

Explanation:

We set up the following equation:

16x-6x-200=1600

10x=1800

x=180

The students will need to make and sell 180 t-shirts in order to raise $\$1600.00$ .

Report an Error

Example Question #12 : Solving Linear Equations With One Unknown

Solve for : $\frac{1}{2}x+6=34$

Possible Answers:

x=40

x=-56

x=56

x=52

x=68

Correct answer:

x=56

Explanation:

In order to solve for , we must isolate on one side of the equation:

$\frac{1}{2}x+6=34$

$\frac{1}{2}x=28$

x=56

Report an Error

Example Question #11 : Linear Equations, One Unknown

What is the value of in the following equation when y=-343 ?

y=-7x+49

Possible Answers:

343

Correct answer:

Explanation:

When solving algebraic equations with one unknown, it is often easier to rearrange the equation first so that you have the unknown variable isolated.

So this:

y=-7x+49

becomes this when we subtract from both sides:

y-49=-7x

Then, divide both sides by to get all by itself:

$\frac{y-49}{-7}=x$

To finish, simply plug in for and simplify.

$x=\frac{-343-49}{-7}=\frac{-392}{-7}=56$

Thus, is our answer!

Report an Error

Example Question #1381 : Problem Solving Questions

Solve for : 9x-11=70

Possible Answers:

x=9

x=6

x=8

x=5

x=11

Correct answer:

x=9

Explanation:

In order to solve for , isolate on one side of the equation:

9x-11=70

9x=81

x=9

Report an Error

Example Question #292 : Algebra

Solve for : $\frac{3}{2}x+\frac{1}{3}=\frac{5}{9}$ .

Possible Answers:

$x=-\frac{27}{4}$

$x=-\frac{4}{27}$

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

$x=\frac{4}{27}$

$x=\frac{27}{4}$

Correct answer:

$x=\frac{4}{27}$

Explanation:

To solve for , we need to isolate on one side of the equation:

$\frac{3}{2}x+\frac{1}{3}=\frac{5}{9}$

$\frac{3}{2}x=\frac{5}{9}-\frac{1}{3}$

$\frac{3}{2}x=\frac{5}{9}-\frac{3}{9}$

$\frac{3}{2}x=\frac{2}{9}$

$x=\frac{2}{9}\times\frac{2}{3}$

$x=\frac{4}{27}$

Report an Error

All GMAT Math Resources

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

Popular Subjects

Statistics Tutors in Miami, Spanish Tutors in Miami, Chemistry Tutors in Chicago, GRE Tutors in Phoenix, English Tutors in Phoenix, ACT Tutors in Los Angeles, MCAT Tutors in Boston, English Tutors in Denver, Calculus Tutors in Atlanta, Physics Tutors in Washington DC

Popular Courses & Classes

ACT Courses & Classes in Boston, GMAT Courses & Classes in Seattle, SAT Courses & Classes in Seattle, ACT Courses & Classes in Denver, GMAT Courses & Classes in Chicago, LSAT Courses & Classes in Atlanta, ISEE Courses & Classes in Atlanta, ACT Courses & Classes in Chicago, GRE Courses & Classes in Houston, SSAT Courses & Classes in New York City

Popular Test Prep

GMAT Test Prep in Seattle, SSAT Test Prep in Phoenix, SSAT Test Prep in Philadelphia, GRE Test Prep in Phoenix, ACT Test Prep in Boston, GMAT Test Prep in Washington DC, ACT Test Prep in Chicago, ISEE Test Prep in Washington DC, GRE Test Prep in Chicago, GMAT Test Prep in Phoenix

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 : Algebra

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1372 : Problem Solving Questions

Example Question #11 : Solving Linear Equations With One Unknown

Example Question #11 : Solving Linear Equations With One Unknown

Example Question #291 : Algebra

Example Question #11 : Linear Equations, One Unknown

Example Question #1376 : Problem Solving Questions

Example Question #12 : Solving Linear Equations With One Unknown

Example Question #11 : Linear Equations, One Unknown

Example Question #1381 : Problem Solving Questions

Example Question #292 : Algebra

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details