GMAT Math : Graphing

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 #11 : Coordinate Geometry

Let and be real numbers.

From the number a + bi , subtract its complex conjugate. What is the result?

Statement 1: a = 7

Statement 2: b = 12

Possible Answers:

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.

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.

EITHER 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 complex conjugate of an imaginary number a + bi is a - bi , and

(a + bi)- (a - bi) = a -a +bi+bi = 2bi .

Therefore, it is necessary and sufficient to know in order to answer the question. Statement 1 does not give this value, and is unhelpful here; Statement 2 does give this value.

Report an Error

Example Question #12 : Coordinate Geometry

Let and be real numbers.

What is the sum of a + bi and its complex conjugate?

Statement 1: a = 12

Statement 2: b= 18

Possible Answers:

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 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.

EITHER statement ALONE is sufficient 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:

The complex conjugate of an imaginary number a + bi is a - bi , and the sum of the two numbers is

(a + bi)+ (a - bi) = 2a .

Therefore, it is necessary and sufficient to know in order to answer the question. Statement 1 alone gives this information; Statement 2 does not, and it is unhelpful.

Report an Error

Example Question #13 : Coordinate Geometry

Let be a positive integer.

True or false: $i^{N} = 1$

Statement 1: is a prime number.

Statement 2: is a two-digit number ending in a 7.

Possible Answers:

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 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.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

If is a positive integer, then $i^{N} = 1$ if and only if is a multiple of 4.

It follows that if $i^{N} = 1$ , cannot be a prime number. Also, every multiple of 4 is even, so as an even number, cannot end in 7. Contrapositively, if Statement 1 is true and is prime, or if Statement 2 is true and if ends in 7, it follows that is not a multiple of 4, and $i^{N} \ne 1$ .

Report an Error

Example Question #14 : Coordinate Geometry

Let and be real numbers.

What is the product of a + bi and its complex conjugate?

Statement 1: a = 12

Statement 2: $b = \sqrt{2}$

Possible Answers:

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.

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.

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

The complex conjugate of an imaginary number a + bi is a - bi , and

$(a + bi)(a - bi) = a^{2}+b^{2}$ .

Therefore, it is necessary and sufficient to know the values of both and in order to answer the problem. Each statement alone gives only one of these values, so each statement alone provides insufficient information; the two together give both, so the two statements together provide sufficient information.

Report an Error

Example Question #15 : Coordinate Geometry

Let and be real numbers.

What is the sum of a + bi and its complex conjugate?

Statement 1: $a ^{2}+ b^{2}= 50$

Statement 2: $a ^{2}= b^{2}$

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.

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:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

The complex conjugate of an imaginary number a + bi is a - bi , and

(a + bi)+ (a - bi) = 2a .

We show, however, that the two statements are insufficient to determine the sum by examining two scenarios.

Case 1: a = b= 5 .

$a ^{2}+ b^{2}=5^{2}+ 5^{2} = 25+25 = 50$ , and since a = b= 5 , $a ^{2} = b^{2}=5 ^{2} =25$ . The conditions of both statements are satisfied.

The sum of the numbers is $2a = 2 \cdot 5 = 10$ .

Case 2: a = b= -5 .

$a ^{2}+ b^{2}=(-5)^{2}+ (-5)^{2} = 25+25 = 50$ , and since a = b= -5 , $a ^{2} = b^{2}=(-5) ^{2}= 25$ . The conditions of both statements are satisfied.

The sum of the numbers is $2a = 2 \cdot (-5) = - 10$ .

In both cases, the conditions of both statements are satisfied, but the sum of the number and its complex conjugate differs between the two.

Report an Error

Example Question #16 : Coordinate Geometry

Let and be real numbers.

What is the product of a + bi and its complex conjugate?

Statement 1: a + b = 12

Statement 2: a - b = 16

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 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.

EITHER statement ALONE is sufficient 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:

The complex conjugate of an imaginary number a + bi is a - bi , and

$(a + bi)(a - bi) = a^{2}+b^{2}$ .

Statement 1 alone provides insufficient information, as seen in these two scenarios, both of which feature values of and that add up to 12:

Case 1: a = b= 6

Then a + bi = 6+6i , and the product of this number and its complex conjugate is $a^{2}+b^{2} = 6^{2}+6^{2} =36+36 = 72$ .

Case 2: a =5, b = 7

Then a + bi = 5+7i , and the product of this number and its complex conjugate is $a^{2}+b^{2} = 5^{2}+7^{2} =25+49= 74$ .

The two cases result in different products.

For a similar reason, Statement 2 alone provides insufficient information.

If both statements are assumed to be true, they form a system of equations that can be solved as follows:

a + b = 12

$\underline{a - b = 16}$

=28

a = 14

Backsolve:

14 + b = 12

b=-2

Since we know that a = 14 and b=-2 , then we know that the desired product is $a^{2}+b^{2} =14 ^{2}+(-2)^{2} =196+4 = 200$ .

Report an Error

Example Question #17 : Coordinate Geometry

Let and be real numbers.

From the number a + bi , subtract its complex conjugate. What is the result?

Statement 1: $a ^{2}- b^{2}= 36$

Statement 2: a +b = 12

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 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 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:

The complex conjugate of an imaginary number a + bi is a - bi , and

(a + bi)- (a - bi) = a -a +bi+bi = 2bi .

Therefore, it is necessary and sufficient to know in order to answer the question. Neither statement alone gives this information. However, the first statement can be rewritten by factoring out $a ^{2}- b^{2}$ as a difference of squares:

$a ^{2}- b^{2}= 36$

(a+b)(a-b)= 36

Since a +b = 12 , then by substitution,

12(a-b)= 36

$\frac{12(a-b)}{12}= \frac{36}{12}$

a -b=3

A system of linear equations has now been formed; subtract both sides of the equations as follows:

a +b = 12

$-\underline{(a -b=3)}$

= 9

We need go no further; since 2b=9 , the desired difference is (2b)i = 9i .

Report an Error

Example Question #8 : Dsq: Graphing Complex Numbers

Let be a positive integer.

Evaluate $i^{N}$ .

Statement 1: is a multiple of 16.

Statement 2: is a multiple of 20.

Possible Answers:

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.

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 to answer the question.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

The value of $i^{N}$ , a positive integer, is equal to $i^{R}$ , where is the remainder of the division of by 4. Either statement alone is enough to prove that is divisible by 4, since, if a number is divisible by a given number (16 or 20 in these statements), it is divisible by any factor of that number (with 4 being a factor of both).

Report an Error

Example Question #9 : Dsq: Graphing Complex Numbers

Let and be real numbers.

What is the sum of a + bi and its complex conjugate?

Statement 1: $a+ b = 12\sqrt{2}$

Statement 2: $a - b = 4\sqrt{2}$

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 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.

EITHER statement ALONE is sufficient 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:

The complex conjugate of an imaginary number a + bi is a - bi , and

(a + bi)+ (a - bi) = 2a .

Therefore, it is necessary and sufficient to know in order to answer the question. Neither statement alone gives this information. However, the two statements together form a linear system that can be solved as follows:

$a+ b = 12\sqrt{2}$

$+( \underline{a - b = 4\sqrt{2}})$

$=16 \sqrt{2}$

We need go no further; since $2a=16 \sqrt{2}$ , this is the desired sum.

Report an Error

Example Question #11 : Coordinate Geometry

Let and be real numbers.

From the number a + bi , subtract its complex conjugate. What is the result?

Statement 1: a+b= 10

Statement 2: a -b = 4

Possible Answers:

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.

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.

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

The complex conjugate of an imaginary number a + bi is a - bi , and

(a + bi)- (a - bi) = a -a +bi+bi = 2bi .

a+b= 10

$- \underline{(a -b = 4)}$

We need go no further; since 2b=6 , the desired sum is (2b)i = 6i .

Report an Error

All GMAT Math Resources

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

Popular Subjects

MCAT Tutors in New York City, Calculus Tutors in Los Angeles, LSAT Tutors in Denver, Math Tutors in San Diego, SAT Tutors in Atlanta, SSAT Tutors in San Diego, Algebra Tutors in Phoenix, Calculus Tutors in Houston, MCAT Tutors in Chicago, French Tutors in San Francisco-Bay Area

Popular Courses & Classes

MCAT Courses & Classes in Denver, LSAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Washington DC, ISEE Courses & Classes in Phoenix, SAT Courses & Classes in Houston, ACT Courses & Classes in Houston, SAT Courses & Classes in New York City, MCAT Courses & Classes in Los Angeles, MCAT Courses & Classes in New York City, ISEE Courses & Classes in Houston

Popular Test Prep

ACT Test Prep in New York City, LSAT Test Prep in Seattle, GRE Test Prep in Chicago, ISEE Test Prep in Denver, ACT Test Prep in Houston, SSAT Test Prep in Chicago, ISEE Test Prep in Houston, MCAT Test Prep in Phoenix, ISEE Test Prep in Dallas Fort Worth, GMAT Test Prep in Washington DC

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 : Graphing

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #11 : Coordinate Geometry

Example Question #12 : Coordinate Geometry

Example Question #13 : Coordinate Geometry

Example Question #14 : Coordinate Geometry

Example Question #15 : Coordinate Geometry

Example Question #16 : Coordinate Geometry

Example Question #17 : Coordinate Geometry

Example Question #8 : Dsq: Graphing Complex Numbers

Example Question #9 : Dsq: Graphing Complex Numbers

Example Question #11 : Coordinate Geometry

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details