GRE Math : Arithmetic

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 #451 : Arithmetic

Choose the answer below which best expresses the following decimal as a fraction (choose the answer which has been reduced/simplified the most):

0.97

Possible Answers:

$\frac{97}{10}$

$\frac{34}{10}$

$\frac{34}{50}$

$\frac{97}{100}$

$\frac{9}{10}$

Correct answer:

$\frac{97}{100}$

Explanation:

To convert from a decimal to a fraction, simply put the digits over one followed by a number of zeroes equal to the number of digits:

$0.97=0.97\cdot \frac{100}{100}=\frac{97}{100}$

You cannot reduce, as one of the numbers in the fraction is prime, so that's your final answer.

Report an Error

Example Question #1035 : Gre Quantitative Reasoning

Choose the answer below which best expresses the following decimal as a fraction (choose the answer which has been reduced/simplified the most):

0.82

Possible Answers:

$\frac{82}{100}$

$\frac{51}{100}$

$\frac{820}{1000}$

$\frac{41}{50}$

$\frac{82}{1000}$

Correct answer:

$\frac{41}{50}$

Explanation:

To convert from a decimal to a fraction, simply put the digits over one followed by a number of zeroes equal to the number of digits:

$0.82=0.82\cdot \frac{100}{100}=\frac{82}{100}$

Then, you can reduce for your final answer:

$\frac{82}{100}=\frac{2\cdot 41}{2\cdot 50}=\frac{41}{50}$

Report an Error

Example Question #1 : Operations

What is the result of adding $20\%$ of $\frac{2}{7}$ to $\frac{1}{4}$ ?

Possible Answers:

$\frac{43}{140}$

$\frac{23}{11}$

$\frac{3}{28}$

$\frac{47}{140}$

$\frac{3}{39}$

Correct answer:

$\frac{43}{140}$

Explanation:

Let us first get our value for the percentage of the first fraction. 20% of 2/7 is found by multiplying 2/7 by 2/10 (or, simplified, 1/5): (2/7) * (1/5) = (2/35)

Our addition is therefore (2/35) + (1/4). There are no common factors, so the least common denominator will be 35 * 4 or 140. Multiply the numerator and denominator of 2/35 by 4/4 and the numerator of 1/4 by 35/35.

This yields:

(8/140) + (35/140) = 43/140, which cannot be reduced.

Report an Error

Example Question #2 : Operations

Reduce to simplest form: $\frac{1}{4}+(\frac{4}{3}\times \frac{3}{8})-(\frac{1}{4}\div \frac{3}{8})$

Possible Answers:

$\frac{3}{8}$

$\frac{3}{4}$

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{1}{12}$

Correct answer:

$\frac{1}{12}$

Explanation:

Simplify expressions inside parentheses first: $\dpi{100} \small \left (\frac{4}{3} \times \frac{3}{8} \right ) = \frac{12}{24} = \frac{1}{2}$ and $\dpi{100} \small \left (\frac{1}{4} \div \frac{3}{8} \right ) = \left (\frac{1}{4} \times \frac{8}{3} \right ) = \frac{8}{12} = \frac{2}{3}$

Now we have: $\frac{1}{4} + \frac{1}{2} - \frac{2}{3}$

Add them by finding the common denominator (LCM of 4, 2, and 3 = 12) and then multiplying the top and bottom of each fraction by whichever factors are missing from this common denominator:

$\dpi{100} \small \frac{1\times 3}{4\times 3} + \frac{1\times 6}{2\times 6} - \frac{2\times 4}{3\times 4} =\frac{3}{12} + \frac{6}{12} - \frac{8}{12} = \frac{1}{12}$

Report an Error

Example Question #31 : Fractions

Quantity A: $\frac{15}{x}+\frac{12}{y}$

Quantity B: $\frac{15y+12x}{xy}$

Which of the following is true?

Possible Answers:

The relationship between the two quantities cannot be determined.

The two quantities are equal.

Quantity B is larger.

Quantity A is larger.

Correct answer:

The two quantities are equal.

Explanation:

Start by looking at Quantity A. The common denominator for this expression is . To calculate this, you perform the following multiplications:

$\frac{15}{x}*\frac{y}{y}+\frac{12}{y}*\frac{x}{x}$

This is the same as:

$\frac{15y}{xy}+\frac{12x}{xy}$ , or $\frac{15y+12x}{xy}$

This is the same as Quantity B. They are equal!

Report an Error

Example Question #453 : Arithmetic

Solve for :

$\frac{x}{4}=\frac{3x}{8}-12$

Possible Answers:

Correct answer:

Explanation:

Begin by isolating the factors:

$\frac{x}{4}-\frac{3x}{8}=-12$

Now, the common denominator of these two fractions is . Therefore, multiply $\frac{x}{4}$ by $\frac{2}{2}$ :

$\frac{2}{2}*\frac{x}{4}-\frac{3x}{8}=-12$

$\frac{2x}{8}-\frac{3x}{8}=-12$

Now, you can subtract the left values:

$-\frac{x}{8}=-12$

Now, multiply both sides by :

x=96

Report an Error

Example Question #454 : Arithmetic

Simplify:

$\frac{15}{12}-\frac{2}{9}$

Possible Answers:

$\frac{13}{21}$

$\frac{37}{36}$

$\frac{21}{22}$

$\frac{5}{9}$

$\frac{13}{3}$

Correct answer:

$\frac{37}{36}$

Explanation:

Just like adding fractions, when you subtract fractions, you need to find a common denominator. For and , the least common denominator is . In order to do your subtraction, you need to multiply appropriately to give your fractions this denominator:

$\frac{15}{12}-\frac{2}{9}=\frac{15}{12}*\frac{3}{3}-\frac{2}{9}*\frac{4}{4}$

Which is the same as...

$\frac{45}{36}-\frac{8}{36}$

Now, you can subtract the numerators and retain the denominator:

$\frac{37}{36}$

Report an Error

Example Question #1 : How To Subtract Fractions

Which of the following is true?

Quantity A: $\frac{12}{7}-\frac{3}{5}$

Quantity B: $\frac{11}{6}-\frac{7}{8}$

Possible Answers:

The relationship between the quantities cannot be determined.

Quantity A is larger.

Quantity B is larger.

The two quantities are equal.

Correct answer:

Quantity A is larger.

Explanation:

First, consider each quantity separately.

Quantity A

$\frac{12}{7}-\frac{3}{5}$

These two fractions do not have a common factor. Their common denominator is . Thus, we multiply the fractions as follows to give them a common denominator:

$\frac{12}{7}*\frac{5}{5}-\frac{3}{5}*\frac{7}{7}$

This is the same as:

$\frac{60}{35}-\frac{21}{35}=\frac{39}{35}$

Quantity B

$\frac{11}{6}-\frac{7}{8}$

The common denominator of these two values is . Therefore, you multiply the fractions as follows to give them a common denominator:

$\frac{11}{6}*\frac{4}{4}-\frac{7}{8}*\frac{3}{3}$

This is the same as:

$\frac{44}{24}-\frac{21}{24}=\frac{23}{24}$

Since Quantity A is larger than and Quantity B is a positive fraction less than , we know that Quantity A is larger without even using a calculator.

Report an Error

Example Question #1 : How To Multiply Fractions

There are 340 students at Saint Louis High School in the graduating senior class. Of these students, 9/10 are going to college. Of those going to college, 2/5 are going to Saint Louis University. How many students are going to Saint Louis University?

Possible Answers:

122

The answer cannot be determined from the given information.

136

103

306

Correct answer:

122

Explanation:

122 students are going to Saint Louis University. To answer this question, the following equation can be used: 340*(9/10)*(2/5) . This is then rounded down to 122 students attending Saint Louis University.

Report an Error

Example Question #3 : Operations

If $\frac{4}{7}$ of a number is , what is $\frac{6}{7}$ of that number?

Possible Answers:

Correct answer:

Explanation:

The least common multiple of 4 and 6 is 12.

So we know if $\frac{4}{7}$ of the number is then

$3\cdot \frac{4}{7}=\frac{12}{7}$ of the number is

$3\cdot 22=66$ .

So then it follows that

$\frac{1}{2}\cdot \frac{12}{7}=\frac{12}{14}=\frac{6}{7}$ of the number is

$\frac{1}{2}\cdot 66=33$ .

Report an Error

All GRE Math Resources

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

Popular Subjects

ISEE Tutors in Los Angeles, Physics Tutors in Denver, Computer Science Tutors in Atlanta, Math Tutors in Miami, Spanish Tutors in San Diego, Calculus Tutors in Miami, Spanish Tutors in Miami, Biology Tutors in Washington DC, Chemistry Tutors in San Diego, Calculus Tutors in Denver

Popular Courses & Classes

GRE Courses & Classes in Miami, SSAT Courses & Classes in San Diego, GMAT Courses & Classes in Chicago, ACT Courses & Classes in Seattle, GRE Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in New York City, GMAT Courses & Classes in Philadelphia, GRE Courses & Classes in Phoenix, MCAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Los Angeles

Popular Test Prep

GMAT Test Prep in Philadelphia, MCAT Test Prep in Phoenix, GMAT Test Prep in Phoenix, GRE Test Prep in Philadelphia, LSAT Test Prep in Los Angeles, LSAT Test Prep in Atlanta, SAT Test Prep in Chicago, SAT Test Prep in Boston, SSAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Chicago

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 : Arithmetic

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #451 : Arithmetic

Example Question #1035 : Gre Quantitative Reasoning

Example Question #1 : Operations

Example Question #2 : Operations

Example Question #31 : Fractions

Example Question #453 : Arithmetic

Example Question #454 : Arithmetic

Example Question #1 : How To Subtract Fractions

Example Question #1 : How To Multiply Fractions

Example Question #3 : Operations

All GRE Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details