GMAT Math : Understanding real numbers

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 #401 : Arithmetic

Solve $\dpi{100} \small 2x-3> 0$ for x.

Possible Answers:

$\dpi{100} \small x\geq \frac{3}{2}$

$\dpi{100} \small x> \frac{-3}{2}$

$\dpi{100} \small x< \frac{3}{2}$

$\dpi{100} \small x> \frac{3}{2}$

$\dpi{100} \small x\leq \frac{3}{2}$

Correct answer:

$\dpi{100} \small x> \frac{3}{2}$

Explanation:

$\dpi{100} \small 2x-3> 0$

Add 3 to both sides: $\dpi{100} \small 2x> 3$

Divide both sides by 2: $\dpi{100} \small x> \frac{3}{2}$

Report an Error

Example Question #1953 : Problem Solving Questions

Of 200 students, 80 take biology, 40 take chemistry, 60 take physics, 13 take two science courses, and no one takes three science courses. How many students are not taking a science course?

Possible Answers:

180

Correct answer:

Explanation:

To calculate the number of students taking at least 1 science course, add the number of students who are taking each course and subtract the number of students who are taking 2 (to ensure they're not counting twice).

$\small 80\ +\ 40\ +\ 60\ -\ 13\ =167$

To calculate the number of students NOT taking a class, subtract this number by the total number of students.

$\small 200\ -\ 167\ =\ 33$

Report an Error

Example Question #3 : Understanding Real Numbers

Which of the following expressions is equal to $\sqrt[3]{4} \cdot \sqrt{2}$

Possible Answers:

$4 \sqrt[6]{2}$

$\sqrt[6]{8}$

$2 \sqrt[6]{2}$

$\sqrt[8]{8}$

$4 \sqrt[6]{4}$

Correct answer:

$2 \sqrt[6]{2}$

Explanation:

$\small \sqrt[3]{4} \cdot \sqrt{2} = 4^{\frac{1}{3}} \cdot 2^{\frac{1}{2}} = (2^{2})^{\frac{1}{3}} \cdot 2^{\frac{1}{2}} = 2^{2\; \cdot \frac{1}{3}} \cdot 2^{\frac{1}{2}}= 2^{ \frac{2}{3}} \cdot 2^{\frac{1}{2}}= 2^{ \frac{2}{3} + \frac{1}{2}}$

$\small = 2^{ \frac{7}{6} }} = \sqrt[6]{2^7} = 2\sqrt[6]{2}$

Report an Error

Example Question #1 : Real Numbers

Given that $\small \small x + y = 9$ , $\small xy = 16$ , and $\small \small x < y$ , evaluate $\small \frac{1}{x}-\frac{1}{y}$ .

Possible Answers:

Not enough information is given to answer the question

$\small \small \frac{{17}}{16}$

$\small \small \small \frac{{9}}{16}$

$\small \frac{\sqrt{17}}{16}$

$\small \small \small \small \frac{{3}}{16}$

Correct answer:

$\small \frac{\sqrt{17}}{16}$

Explanation:

$\small \frac{1}{x}-\frac{1}{y} = \frac{y-x}{xy}$

To find $\small y - x$ :

$\small \small \small y + x = 9$ ,

so $\small \small \left (y + x \right )^{2} =y^{2} + 2xy +x^{2} = 81$

$\small \small y^{2} + 2xy +x^{2} - 4xy= 81 - 4 \cdot 16$

$\small \small y^{2} - 2xy +x^{2} = (y - x)^{2}= 17$

$\small \small y - x = \pm \sqrt{17}$

Since $\small \small x < y$ , $\small \small \small \small y - x > 0$

and we choose the positive square root

$\small \small \small y - x = \sqrt{17}$

$\small \small \small \frac{1}{x}-\frac{1}{y} = \frac{y-x}{xy}= \frac{\sqrt{17}}{16}$

Report an Error

Example Question #5 : Understanding Real Numbers

Today, Becky's age (B) is 3 times Charlie's age. In 3 years, what will Charlie's age be in terms of B?

Possible Answers:

$\small \frac{B+3}{3}$

$\small \frac{B}{3}+3$

$\small 3(B+3)$

$\small 3B+3$

$\small 3(B+3)$

$\small 3B+3$

Correct answer:

$\small \frac{B}{3}+3$

Explanation:

Today, $\small C=\frac{B}{3}$ . In 3 years, $\small C=\frac{B}{3}+3$ .

Report an Error

Example Question #1 : Real Numbers

Given that $6 \leq A \leq 12$ and $4 \leq B \leq 6$ , what is the range of possible values for $\frac{A}{B}$ ?

Possible Answers:

$\frac{1}{2} \leq \frac{A}{B} \leq \frac{2}{3}$

$1 \leq \frac{A}{B} \leq 3$

$0 \leq \frac{A}{B} \leq 3$

$\frac{3}{2} \leq \frac{A}{B} \leq 2$

$24 \leq \frac{A}{B} \leq 72$

Correct answer:

$1 \leq \frac{A}{B} \leq 3$

Explanation:

The lowest possible value of $\frac{A}{B}$ is the lowest possible value of divided by the highest possible value of :

$\frac{A}{B} \geq 6 \div 6 = 1$

The highest possible value of $\frac{A}{B}$ is the highest possible value of divided by the lowest possible value of :

$\frac{A}{B} \leq 12 \div 4 = 3$

Report an Error

Example Question #1961 : Problem Solving Questions

If and are composite integers, which of the following can be prime?

Possible Answers:

None of these can be prime.

x^2-y^2

$x\cdot y$

x^2y+2y

x^2+y^2

Correct answer:

x^2+y^2

Explanation:

x^2-y^2 = (x-y)(x+y) so this is a composite number for all and .

$x\cdot y$ is by definition a composite number.

$x^2y+2y = y\cdot (x^2+2)$ the product of 2 numbers.

This leaves just x^2+y^2 . For a number to be prime, it must be odd (except for 2) so we need to have either or be odd (but not both). The first composite odd number is 9. 9^2 = 81 . The smallest composite number is 4. 4^2 = 16 .

81+16 = 97 is a prime number.

So the answer is x^2+y^2

Report an Error

Example Question #3 : Number Theory

If $\frac{122}{x-3}$ is a real number, which of the following CANNOT be a value for x?

Possible Answers:

122

-3

-122

125

Correct answer:

Explanation:

The definition of the set of real numbers is the set of all numbers that can fit into a/b where a and b are both integers and b does not equal 0.

So, since we see a fraction here, we know a non-real number occurs if the denominator is 0. Therefore we can find where the denominator is 0 by setting x-3 =0 and solving for x. In this case, x=3 would create a non-real number. Thus our answer is that x CANNOT be 3 for our expression to be a real number.

Report an Error

Example Question #1963 : Problem Solving Questions

Let be the product of integers from 18 to 33, inclusive. If g=2x , how many more unique prime factors does have than ?

Possible Answers:

Greater than

Not enough information given.

Correct answer:

Explanation:

This question does not require any calculation. Given that 32 (an even number) is a factor of , then 2 must be a prime factor. If is then multiplied by 2 (to get ) then has no additional unique prime factors (its only additional prime factor, 2, is NOT unique).

Report an Error

Example Question #4 : Number Theory

If $\dpi{100} \small x\ and\ y$ are both negative, then $\dpi{100} \small \frac{x+y}{-xy}$ could NOT be equal to....

Possible Answers:

$\dpi{100} \small 5$

$\dpi{100} \small \frac{\sqrt{8}}{4}$

$\dpi{100} \small -5$

$\dpi{100} \small \frac{3}{4}$

Correct answer:

$\dpi{100} \small -5$

Explanation:

$\dpi{100} \small x+y$ is negative and $\dpi{100} \small xy$ is positive

$\dpi{100} \small \frac{Negative}{-Positive} = \frac{Negative}{Negative} = Positive$

Therefore, the solution cannot be negative.

Report an Error

All GMAT Math Resources

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

Popular Subjects

ISEE Tutors in Chicago, LSAT Tutors in Phoenix, Chemistry Tutors in Denver, French Tutors in Atlanta, Statistics Tutors in Miami, English Tutors in Los Angeles, SAT Tutors in San Francisco-Bay Area, Statistics Tutors in New York City, Biology Tutors in Miami, Statistics Tutors in Atlanta

Popular Courses & Classes

Spanish Courses & Classes in New York City, GMAT Courses & Classes in Philadelphia, SSAT Courses & Classes in Miami, SAT Courses & Classes in Chicago, SSAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Denver, MCAT Courses & Classes in Atlanta, ACT Courses & Classes in Washington DC, SSAT Courses & Classes in Chicago, ACT Courses & Classes in New York City

Popular Test Prep

SAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Miami, ACT Test Prep in Washington DC, SSAT Test Prep in Los Angeles, ACT Test Prep in Los Angeles, MCAT Test Prep in Los Angeles, GMAT Test Prep in Denver, ISEE Test Prep in Atlanta, LSAT Test Prep in Denver, GMAT Test Prep in Philadelphia

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 : Understanding real numbers

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #401 : Arithmetic

Example Question #1953 : Problem Solving Questions

Example Question #3 : Understanding Real Numbers

Example Question #1 : Real Numbers

Example Question #5 : Understanding Real Numbers

Example Question #1 : Real Numbers

Example Question #1961 : Problem Solving Questions

Example Question #3 : Number Theory

Example Question #1963 : Problem Solving Questions

Example Question #4 : Number Theory

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details