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

Example Question #1 : Solving Equations

If $\dpi{100} \small 5x+4=19$ , what is the value of $\dpi{100} \small 4x^{2}-5$ ?

Possible Answers:

$\dpi{100} \small 139$

$\dpi{100} \small 10$

$\dpi{100} \small 19$

$\dpi{100} \small 31$

$\dpi{100} \small 3$

Correct answer:

$\dpi{100} \small 31$

Explanation:

First, we need to solve for $\dpi{100} \small x$ from the first equation in order to calculate the second quadratic function. To solve for $\dpi{100} \small x$ , we need to subtract four on each side of the equation, then we will get

$\dpi{100} \small 5x=15$

The answer for $\dpi{100} \small x$ would be $\dpi{100} \small \frac{15}{5}$ , which is $\dpi{100} \small 3$ .

So now we can calculate the function by plugging in $\dpi{100} \small x=3$ .

$\dpi{100} \small 3^{2}=9$ , and $\dpi{100} \small 9\times 4=36$ .

$\dpi{100} \small 36-5=31$

Report an Error

Example Question #2 : Solving Equations

A tractor spends 5 days plowing $\dpi{100} \small x$ number of fields. How many days will it take to plow $\dpi{100} \small y$ number of fields at the same rate?

Possible Answers:

$\frac{5x}{y}$

$\frac{y}{5x}$

$\frac{5}{xy}$

$\frac{xy}{5}$

$\frac{5y}{x}$

Correct answer:

$\frac{5y}{x}$

Explanation:

The equation that will be used is (rate * number of days = number of fields plowed). From the first part of the question, number of fields plowed $\dpi{100} \small (x)$ is calculated as:

$rate \cdot 5 = x$

To solve for rate both sides are divided by 5.

$rate = \frac{x}{5}$

This rate is used for the second part of the problem. $\frac{x}{5} * days = y$ . To solve for days, both sides are divided by $\frac{x}{5}$ , which is the same as multiplying by $\frac{5}{x}$ , cancelling out the $\frac{x}{5}$ and giving the answer of $days = \frac{5y}{x}$ .

Report an Error

Example Question #3 : Solving Equations

A 70 ft long board is sawed into two planks. One plank is 30 ft longer than the other, how long (in feet) is the shorter plank?

Possible Answers:

$\dpi{100} \small 40$

$\dpi{100} \small 30$

$\dpi{100} \small 50$

$\dpi{100} \small 15$

$\dpi{100} \small 20$

Correct answer:

$\dpi{100} \small 20$

Explanation:

Let $\dpi{100} \small x$ = length of the short plank and $\dpi{100} \small x+30$ = length of the long plank.

$\dpi{100} \small x+x+30=70$ is the length of the pre-cut board, or combined length of both planks.

$\dpi{100} \small 2x+30=70$

$\dpi{100} \small 2x=40$

$\dpi{100} \small x=20$

Report an Error

Example Question #4 : Solving Equations

Solve $2x^{2} - 8x - 24 = 0.$

Possible Answers:

$\dpi{100} \small x=-12\ or\ x=-4$

$\dpi{100} \small x=2\ or\ x=-2$

$\dpi{100} \small x=-6\ or\ x=2$

$\dpi{100} \small x=6\ or\ x=-6$

$\dpi{100} \small x=6\ or\ x=-2$

Correct answer:

$\dpi{100} \small x=6\ or\ x=-2$

Explanation:

$2x^{2} - 8x - 24 = 2(x^{2}-4x-12)=0$

Divide both sides by 2: $x^{2}-4x-12=0$ . We need to find two numbers that multiply to $\dpi{100} \small -12$ and sum to $\dpi{100} \small -4$ . The numbers $\dpi{100} \small -6$ and $\dpi{100} \small 2$ work.

$x^{2}-4x-12= (x-6)(x+2)=0$

$\dpi{100} \small x-6=0$

$\dpi{100} \small x=6$

$\dpi{100} \small or\ x+2=0$

$\dpi{100} \small x=-2$

Report an Error

Example Question #5 : Solving Equations

If $1-\frac{4}{a}=2-\frac{7}{a}$ then $a=$

Possible Answers:

$3$

$\frac{2}{3}$

$\frac{1}{3}$

$2$

$-1$

Correct answer:

$3$

Explanation:

Multiply both sides of the equation by a: $a-4=2a-7$

Then, solve for $a$ .

Report an Error

Example Question #6 : Solving Equations

$\dpi{100} \small 4y+7=3x+5$

Solve for x.

Possible Answers:

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

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

not enough information

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

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

Correct answer:

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

Explanation:

We need to solve for x in terms of y by isolating x.

3x=4y+2

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

Report an Error

Example Question #7 : Solving Equations

Which of the following is a solution to the equation x+2y-3z=4 ?

Possible Answers:

x=8,y=1,z=2

x=3,y=2,z=1

x=2,y=-1,z=5

x=1,y=2,z=3

two of the answer choices are correct

Correct answer:

two of the answer choices are correct

Explanation:

We need to plug in the answer choices and see which produce the value 4.

1. x=3,y=2,z=1:3+2(2)-3(1)=3+4-3=4 , correct

2. x=1,y=2,z=3:1+2(2)-3(3)=1+4-9=-4 , incorrect

3. x=8,y=1,z=2:8+2(1)-3(2)=8+2-6=4 , correct

4. x=2,y=-1,z=5:2+2(-1)-3(5)=2-2-15=-15 , incorrect

Therefore two of the answer choices are correct.

Report an Error

Example Question #8 : Solving Equations

Which is NOT a solution to the equation 2x-4y+z=8

Possible Answers:

(2,4,6)

$(\frac{11}{2},1,1)$

(6,1,0)

$(\frac{7}{2},0,1)$

$(4+2a-\frac{b}{2},a,b)$

Correct answer:

(2,4,6)

Explanation:

To solve this, we need to plug the answer choices into the equation and see which choice does NOT work. Let's go through the answer choices.

$\dpi{100} (2,4,6):2(2)-4(4)+6=-6$

This is the correct answer. If this had been a solution to the equation, the equation would have produced 8.

$\dpi{100} (\frac{11}{2},1,1):2(\frac{11}{2}) -4(1)+1)=8$

(6,1,0):2(6)-4(1)+0=8

$(\frac{7}{2},0,1):2(\frac{7}{2})-4(0)+1=8$

$(4+2a-\frac{b}{2}):$

Let's let a=1 and b=0 . Then this ordered pair becomes (6,1,0) .

2(6)-4(1)+0=8 . Any other answer choices of this form will also work.

Report an Error

Example Question #9 : Solving Equations

Given the equation $x\cdot(x+k)=-7$ , if can be any integer, how many different sets of integer solutions are there for ?

Possible Answers:

Infinitely many

Correct answer:

Explanation:

$x\cdot(x+k)=-7$ is the same as x^2 + kx + 7 = 0 .

For solutions sets of integers, we are able to divide it as: $(x+\_\_)(x+\_\_) = 0$

When we multiply this, we notice that the constants must return 7. Since 7 is a prime number, we now know that these constants are 1 and 7. The signs of these can still switch however. If both of the numbers are negative, it will also return a product of positive 7. These are the only ways to make the constant term work. If they are both positive numbers, then we get k=8 . If they're both negative numbers then k= -8 .

For the values of , we simply notice the only way for the overall product to be 0 is for one (or both) of the pieces to be zero. This is done by having equal the additive inverse of the constant piece.

Thus we have 2 integer solution sets: $\left\{1,7\right\}$ and $\left\{-1,-7\right\}$

Report an Error

Example Question #10 : Solving Equations

The volume of a fixed mass of gas varies inversely as the atmospheric pressure, as measured in millibars, acting on it, and directly as the temperature, as measured in kelvins, acting on it.

A balloon is filled to capacity at a point in time at which the atmospheric pressure is 104 millibars and the temperature is 295 kelvins. Six hours later, the temperature has increased to 305 kelvins, but the volume of the gas has not changed at all. What is the current atmospheric pressure?

Possible Answers:

$108 \textrm{ mbar}$

$112 \textrm{ mbar}$

$104 \textrm{ mbar}$

The information provided is insufficient to answer this question.

$101 \textrm{ mbar}$

Correct answer:

$108 \textrm{ mbar}$

Explanation:

The following variation equation can be set up:

$\frac{V_{1} P _{1}}{T_{1}} = \frac{V_{2} P _{2}}{T_{2}}$

But since the initial volume and the current volume are equal, or, equivalently, $V_{1} = V_{2}$ ,

$\frac{V_{1} P _{1}}{T_{1}} \div V_{1} = \frac{V_{2} P _{2}}{T_{2}}\div V_{2}$

$\frac{P _{1}}{T_{1}}= \frac{P _{2}}{T_{2}}$

We substitute $P _{1}= 104, T_{1}=295 ,T_{2}=305$ , and solve for $P _{2}$ :

$\frac{104}{295}= \frac{P _{2}}{305}$

$\frac{104}{295}\cdot 305 = \frac{P _{2}}{305} \cdot 305$

$P_{2} = \frac{104}{295}\cdot 305 \approx 108 \textrm{ mbar}$

Report an Error

All GMAT Math Resources

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

Popular Subjects

GRE Tutors in Houston, French Tutors in Chicago, LSAT Tutors in Chicago, SAT Tutors in Phoenix, Computer Science Tutors in Boston, Computer Science Tutors in Denver, LSAT Tutors in San Francisco-Bay Area, SAT Tutors in Seattle, Biology Tutors in Miami, Statistics Tutors in New York City

Popular Courses & Classes

ISEE Courses & Classes in New York City, GRE Courses & Classes in Phoenix, LSAT Courses & Classes in San Diego, SSAT Courses & Classes in Phoenix, ACT Courses & Classes in Denver, SAT Courses & Classes in Philadelphia, MCAT Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Philadelphia, ISEE Courses & Classes in Washington DC, MCAT Courses & Classes in Boston

Popular Test Prep

GMAT Test Prep in Miami, GMAT Test Prep in Dallas Fort Worth, SAT Test Prep in San Diego, GRE Test Prep in Seattle, GRE Test Prep in Phoenix, MCAT Test Prep in Phoenix, SAT Test Prep in Washington DC, GRE Test Prep in Chicago, SSAT Test Prep in New York City, SSAT 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 : Solving equations

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Solving Equations

Example Question #2 : Solving Equations

Example Question #3 : Solving Equations

Example Question #4 : Solving Equations

Example Question #5 : Solving Equations

Example Question #6 : Solving Equations

Example Question #7 : Solving Equations

Example Question #8 : Solving Equations

Example Question #9 : Solving Equations

Example Question #10 : Solving Equations

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details