GMAT Math : DSQ: Simplifying algebraic expressions

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 : Simplifying Algebraic Expressions

Evaluate the expression $(x+y)^{2}-x(x+3y)+xy$

1) x = 3

2) y = 2

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is not sufficient.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient.

Explanation:

Simplify the expression:

$(x+y)^{2}-x(x+3y)+xy$

$= x^{2}+2xy+y^{2}-x^{2}-3xy+xy$

$= x^{2}-x^{2} +xy+2xy-3xy+y^{2}$

$= y^{2}$

Therefore, we only need to know - If we know y = 2 , we calculate that $(x+y)^{2}-x(x+3y)+xy = y^{2} = 2^{2} = 4$

The answer is that Statement 2 alone is sufficient to answer the question, but Statement 1 is not.

Report an Error

Example Question #2 : Simplifying Algebraic Expressions

Evaluate: $\frac{(x+y)^{2}-(x-y)^{2}}{x}$

Statement 1: x = 5

Statement 2: y=3

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Correct answer:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Explanation:

$\frac{(x+y)^{2}-(x-y)^{2}}{x} = \frac{(x^{2}+2xy+y^{2})-(x^{2}-2xy+y^{2})}{x} = \frac{4xy}{x}= 4y$

Therefore, you only need to know the value of to evaluate this; knowing the value of is neither necessary nor helpful.

Report an Error

Example Question #3 : Dsq: Simplifying Algebraic Expressions

Evaluate the expression for positive x,y :

$\frac{4x^{2}}{y^{-4}} \cdot \frac{3x^{2}y^{2}}{8} \cdot \frac{5}{(2x^{2}y^{2})^{2}}$

Statement 1: x = 3

Statement 2: y = 4

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Correct answer:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Explanation:

$\frac{4x^{2}}{y^{-4}} \cdot \frac{3x^{2}y^{2}}{8} \cdot \frac{5}{(2x^{2}y^{2})^{2}}$

$= \frac{4x^{2}}{y^{-4}} \cdot \frac{3x^{2}y^{2}}{8} \cdot \frac{5}{2^{2} (x^{2})^{2}(y^{2})^{2}}$

$= \frac{4x^{2}}{y^{-4}} \cdot \frac{3x^{2}y^{2}}{8} \cdot \frac{5}{4 x^{2\cdot 2}y^{2\cdot 2}}$

$= \frac{4x^{2}}{y^{-4}} \cdot \frac{3x^{2}y^{2}}{8} \cdot \frac{5}{4 x^{4}y^{4}}$

$= \frac{4x^{2}\cdot 3x^{2}y^{2}\cdot 5}{y^{-4}\cdot 8\cdot 4 x^{4}y^{4}}$

$= \frac{4 \cdot 3\cdot 5 \cdot x^{2}\cdot x^{2}\cdot y^{2}}{8\cdot 4 \cdot x^{4} \cdot y^{4}\cdot y^{-4}}$

$= \frac{60 \cdot x^{2+2}\cdot y^{2}}{32 \cdot x^{4} \cdot y^{4-4}}$

$= \frac{60 \cdot x^{4}\cdot y^{2}}{32 \cdot x^{4}}$

Cancel the $x^{4}$ from both halves:

$= \frac{60 y^{2}}{32 } = \frac{15 y^{2}}{8 }$

As can be seen by the simplification, it turns out that only the value of , which is given only in Statement 2, affects the value of the expression.

Report an Error

Example Question #4 : Dsq: Simplifying Algebraic Expressions

What is the value of x+y ?

(1) 7x=7-7y

(2) 13x+13y=13

Possible Answers:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.

Statement 1 ALONE is sufficient to answer the question, but the other statement alone is not sufficient

EACH statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are not sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but the other statement alone is not sufficient

Correct answer:

EACH statement ALONE is sufficient to answer the question.

Explanation:

(1) Add to both sides to make 7x+7y=7 . Then divide through by 7 to get

x+y=1 . This statement is sufficient.

(2) Divide both sides by 13. The equation becomes x+y=1 . This statement is sufficient.

Report an Error

Example Question #5 : Dsq: Simplifying Algebraic Expressions

Is d > e ?

(1.) d = e + 5

(2.) $\frac{d}{6} = e - 2$

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but the other statement alone is not sufficient.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.

BOTH statements TOGETHER are not sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but the other statement alone is not sufficient.

EACH statement ALONE is sufficient to answer the question.

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but the other statement alone is not sufficient.

Explanation:

(1) Since 5 must be added to to make it equal to , it follows that d>e . This statement is sufficient.

(2) Multiply both sides by 6 to obtain d = 6e - 12 . Thus, whether d > e or

d < e depends on the value selected for and . For instance, e = 0 implies

d = -12 , (such that e > d ) but e = 20 implies d = 108 ,

(such that e < d ). Therefore, this statement is insufficient.

Report an Error

Example Question #6 : Dsq: Simplifying Algebraic Expressions

True or false?

$\frac{(x + y)^{2} - (x - y)^{2} }{y} \geq \frac{(x + y)^{2} + (x - y)^{2} }{x^{2}+y^{2}}$

Statement 1: x = 10

Statement 2: y = 7

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Explanation:

Simplify each expression.

$\frac{(x + y)^{2} - (x - y)^{2} }{y}$

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

$= \frac{4xy }{y} = 4x$

$\frac{(x + y)^{2} + (x - y)^{2} }{x^{2}+y^{2}}$

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

$= \frac{2x^{2} + 2y^{2}}{x^{2}+y^{2}} = \frac{2 \left ( x^{2} + y^{2} \right ) }{x^{2}+y^{2}} = 2$

The inequality, therefore, is equivalent to

$4x \geq 2$ ,

the truth or falsity of which depends only on the value of

Report an Error

Example Question #101 : Algebra

True or false?

$\frac{(x + 4y)^{2} - (x - 4y)^{2} }{y} < \frac{(x + 3y)^{2} - (x - 3y)^{2} }{x}$

Statement 1: x = 7

Statement 2: y = 4

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

Simplify both expressions algebraically.

$\frac{(x + 4y)^{2} - (x - 4y)^{2} }{y}$

$=\frac{(x^{2} + 2\cdot x\cdot 4y+ (4y)^{2} ) - (x^{2} - 2\cdot x\cdot 4y+ (4y)^{2} ) }{y}$

$=\frac{(x^{2} + 8 xy+ 16y^{2} ) - (x^{2} -8 xy+ 16y^{2} ) }{y}$

$=\frac{16xy }{y} =16x$

Using similar algebra, you can simplify the other expression:

$\frac{(x + 3y)^{2} - (x - 3y)^{2} }{x} = 12y$

The question, assuming the variables have nonzero values, is equivalent to asking whether 16x<12y is true. Since we need to know the values of both variables to answer this, both statements are necessary and sufficient.

Report an Error

Example Question #1 : Simplifying Algebraic Expressions

The figure below shows a trinomial with its exponents replaced by shapes:

$x^{\bigcirc } + x^{\square} + x^{\bigtriangleup }$

Each shape replaces a whole number.

Is this a simplified expression?

Statement 1: The sum of the three exponents is 10.

Statement 2: The circle and the triangle are replacing different numbers.

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Assume both statements are true.

$x^{2} + x^{3} + x^{5 }$ and $x^{2} + x^{4} + x^{4 }$ each fits the conditions of both statements. However, the first polynomial, having no like terms - three different exponents - is a simplified expression; the second, having like terms - both with exponent 4 - is not.

Report an Error

Example Question #102 : Algebra

The figure below shows a binomial with its coefficients and exponents replaced by shapes:

$\square x^{\bigcirc } + \lozenge x ^{ \bigtriangleup }$

Each shape replaces a whole number.

Is this a simplified expression?

Statement 1: The square and the circle are replacing the same integer.

Statement 2: The diamond and the triangle are replacing different integers.

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Both statements together are insufficient.

$2x^{2}+ 3x^{2}$ and $2x^{2}+ 2x^{3}$ each match the conditions of both statements. However, the former is the sum of like terms - the exponents are the same - and can be simplified; the latter is the sum of unlike terms - the exponents are different - and cannot.

Report an Error

Example Question #3 : Simplifying Algebraic Expressions

Stephanie was challenged by her teacher to create a monomial of degree 5 by filling in the square and the circle in the figure below.

$\square x^{\bigcirc }$

Did Stephanie succeed?

Statement 1: Stephanie wrote a 5 in the square.

Statement 2: Stephanie wrote a 7 in the circle.

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Correct answer:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Explanation:

The degree of a monomial with one variable is the exponent of that variable. Therefore, only the number Stephanie wrote in the circle is relevant. Statement 1 is unhelpful; Statement 2 alone proves that Stephanie was unsuccessful.

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 San Diego, Spanish Tutors in Chicago, Computer Science Tutors in Denver, French Tutors in Seattle, SAT Tutors in Chicago, Statistics Tutors in Atlanta, Physics Tutors in San Diego, Computer Science Tutors in New York City, Statistics Tutors in Chicago, ACT Tutors in Dallas Fort Worth

Popular Courses & Classes

GMAT Courses & Classes in Denver, GRE Courses & Classes in Denver, GMAT Courses & Classes in Los Angeles, Spanish Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Philadelphia, MCAT Courses & Classes in Denver, SAT Courses & Classes in Miami, ACT Courses & Classes in Los Angeles, MCAT Courses & Classes in Seattle, LSAT Courses & Classes in Miami

Popular Test Prep

GRE Test Prep in Los Angeles, ISEE Test Prep in San Diego, ISEE Test Prep in Philadelphia, GMAT Test Prep in Atlanta, LSAT Test Prep in Miami, GMAT Test Prep in Chicago, MCAT Test Prep in Chicago, MCAT Test Prep in New York City, SSAT Test Prep in Phoenix, GRE 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:

GMAT Math : DSQ: Simplifying algebraic expressions

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Simplifying Algebraic Expressions

Example Question #2 : Simplifying Algebraic Expressions

Example Question #3 : Dsq: Simplifying Algebraic Expressions

Example Question #4 : Dsq: Simplifying Algebraic Expressions

Example Question #5 : Dsq: Simplifying Algebraic Expressions

Example Question #6 : Dsq: Simplifying Algebraic Expressions

Example Question #101 : Algebra

Example Question #1 : Simplifying Algebraic Expressions

Example Question #102 : Algebra

Example Question #3 : Simplifying Algebraic Expressions

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details