GMAT Math : Problem-Solving Questions

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 #25 : Discrete Probability

Three boxes contain marbles, each one either red or white.

Box 1 contains 20 red marbles and 10 white marbles.

Box 2 contains 30 red marbles and 10 white marbles.

Box 3 conatins 40 red marbles and 10 white marbles.

One of three boxes is selected at random, and one marble is selected from that box at random. What is the probability that a white marble will be selected?

Possible Answers:

$\frac{47}{90}$

$\frac{47}{120}$

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{47}{180}$

Correct answer:

$\frac{47}{180}$

Explanation:

This is a conditional probability problem.

Each box can be selected with probability $\frac{1}{3}$ .

If Box 1 is selected, the probability of selecting a white marble is $\frac{10}{30} =\frac{1}{3}$ . The overall probability of selecting Box 1, then a white marble, is $\frac{1}{3} \cdot \frac{1}{3} = \frac{1}{9}$ .

If Box 2 is selected, the probability of selecting a white marble is $\frac{10}{40} =\frac{1}{4}$ . The overall probability of selecting Box 2, then a white marble, is $\frac{1}{3} \cdot \frac{1}{4} = \frac{1}{12}$ .

If Box 3 is selected, the probability of selecting a white marble is $\frac{10}{50} =\frac{1}{5}$ . The overall probability of selecting Box 2, then a white marble, is $\frac{1}{3} \cdot \frac{1}{5} = \frac{1}{15}$ .

The overall probability of selecting a white marble is the sum of these probabilities:

$\frac{1}{9} +\frac{1}{12} + \frac{1}{15} = \frac{20}{180} +\frac{15}{180} + \frac{12}{180}= \frac{47}{180}$

Report an Error

Example Question #21 : Calculating Discrete Probability

Two fair six-sided dice are altered. One of them has its "6" changed to a "1"; the other has its "1" changed to a "6". The dice are tossed and their sum is noted.

What is the probability that the sum will be 7?

Possible Answers:

$\frac{1}{6}$

$\frac{2}{9}$

$\frac{1}{3}$

$\frac{7}{36}$

$\frac{1}{4}$

Correct answer:

$\frac{2}{9}$

Explanation:

We will call the faces of the first die (the one with two 1's and no 6) 1A, 1B, 2, 3, 4, 5; we will call the faces of the second die (the one with two 6's and no 1) 2, 3, 4, 5, 6A, 6B.

A seven can be rolled in the following ways - with the outcome of the first die and the second die listed in that order:

$\left \{ 1A, 6A\right \}$

$\left \{ 1A, 6B\right \}$

$\left \{ 1B, 6A\right \}$

$\left \{ 1B, 6B\right \}$

$\left \{ 2,5\right \}$

$\left \{ 3,4\right \}$

$\left \{ 4,3\right \}$

$\left \{ 5,2\right \}$

Note that a 6 cannot be rolled on the first die, nor can a 1 be rolled on the second.

This makes 8 rolls out of 36 that can result in a 7; since the dice are fair, the probability of rolling one of these results is $\frac{8}{36} = \frac{2}{9}$

Report an Error

Example Question #1821 : Problem Solving Questions

What is the probability of drawing a red king in a standard card deck?

Possible Answers:

$\frac{1}{13}$

$\frac{1}{26}$

$\frac{4}{13}$

$\frac{1}{52}$

Correct answer:

$\frac{1}{26}$

Explanation:

There are red kings in a standard deck of cards, therefore the probability of drawing red kings is $\frac{2}{52}$ which simplifies to $\frac{1}{26}$ .

Report an Error

Example Question #1821 : Gmat Quantitative Reasoning

A box contains tickets numbered 01-50 . What is the probability of randomly selecting a ticket that has a in the ones place?

Possible Answers:

$20\%$

$50\%$

$5\%$

$10\%$

Correct answer:

$10\%$

Explanation:

From 01-50 , there are tickets that will have a in the ones place: 2,12,22,32,42 .

Therefore the probability of drawing a ticket with a in the ones place is $\frac{5}{50}$ which is 10%.

Report an Error

Example Question #23 : Discrete Probability

If N is a number chosen at random from the set [3, -7, 12, 8, 11] , and P is a number chosen at random from the set [1, 2, 0, 9] , what is the probability that

N+P=12 ?

Possible Answers:

0.12

0.24

0.25

0.85

0.15

Correct answer:

0.15

Explanation:

The total possible pairs of numbers for the two sets is 20, since there are 5 numbers in the first set and 4 numbers in the second set. Total possible outcomes are found by multiplying the number of terms in each set together.

5x4=20, so there are 20 possible pairs.

How many pairs sum to 12?

There are three pairs that work: 3 from the first set and 9 from the second, 12 from the first set and 0 from the second, and 11 from the first set and 1 from the second.

Since 3 out of 20 pairs sum to twelve, the probability of N+P=12 is:

$\frac{3}{20}=0.15$

Report an Error

Example Question #23 : Discrete Probability

Jane has toy cars. of them are trucks and are race cars. are blue, are green, are orange, and are red.

What is the probability of having a blue car OR a race car?

Possible Answers:

$\frac{12}{20}$

$\frac{17}{20}$

$\frac{3}{20}$

$\frac{7}{20}$

$\frac{7}{10}$

Correct answer:

$\frac{7}{10}$

Explanation:

P(Blue Car OR Race Car) = P(Blue Car) + P(Race Car) - P(Blue Race Car)

P(Blue Car) = 5/20

P(Race Car) = 12/20

P(Blue Race Car) $= 5/20 \times 12/20 = 1/4 \times 3/5 = 3/20$

So P(Blue Car OR Race Car) = 5/20 + 12/20 - 3/20 = (5+12-3)/20 = 14/20 = 7/10

Report an Error

Example Question #1822 : Problem Solving Questions

In a 10,000 students university, in students will drop out of college. What is the probability that a randomly selected student will not drop out of college?

Possible Answers:

$\frac{3}{4}$

$\frac{3}{5}$

$\frac{1}{4}$

$\frac{2}{5}$

Correct answer:

$\frac{3}{4}$

Explanation:

The probability of students who will drop out is 1/4.

Therefore, we are looking for the probability that a student will NOT drop out, which is 3/4.

A randomly selected student will not drop out of college with a probability of 3/4.

$p=1-\frac{1}{4}=\frac{3}{4}$

The fact that there is 10,000 students in the school is not relevant to calculate this probability.

Report an Error

Example Question #1823 : Problem Solving Questions

Of 100 students accepted for a masters degree program this fall semester, 30 do not have any work experience, 10 have two years of work experience, 15 have four years of work experience, and all of the other students have over seven years of work experience. What is the probability that a randomly selected student in the 100 who have been accepted for the program will have at least four years of work experience?

Possible Answers:

0.15

0.6

0.45

0.4

0.3

Correct answer:

0.6

Explanation:

The number of students who have over seven years of experience is:

100-30-10-15=100-55=45

The probability that a randomly selected student has at least four years of experience is:

Formula

Substituting in our values for these variables, we get:

$\frac{15+45}{100}=\frac{60}{100}=0.6$

Report an Error

Example Question #1821 : Problem Solving Questions

An auto insurer underwrites its 60 customers and classifies them in 3 mutually exclusive risk classes. 15 of the customers are in the high-risk class, 35 are in the moderate-risk class, and 10 are in the low-risk class. What is the probability that a randomly selected customer will be in the moderate- or high-risk class?

Possible Answers:

$\frac{2}{3}$

$\frac{1}{6}$

$\frac{7}{48}$

$\frac{1}{2}$

$\frac{5}{6}$

Correct answer:

$\frac{5}{6}$

Explanation:

The probability that a randomly selected customer is in the moderate- or high-risk class is simply the sum of the number of clients in the moderate-risk class and the number of clients in the high-risk class divided by the total number of clients:

$\frac{15+35}{60}=\frac{50}{60}=\frac{5}{6}$

This is also equivalent to just summing up the probability of being in the high-risk class and the probability of being in the moderate-risk class. Since the 3 classes are mutually exclusive, we do not have to worry about subtracting the probability of mutual elements.

$\frac{15}{60}+\frac{35}{60}=\frac{5}{6}$

Report an Error

Example Question #1822 : Problem Solving Questions

A university received 1000 applications for their MBA program this semester. Of all applicants, 150 had a GMAT score above 720. 620 applicants had a GMAT score between 640 and 720. 80 applicants had a score between 560 and 640. All other applicants had a score lower than 560. What is the probability that a randomly selected applicant will have a score lower than 560?

Possible Answers:

0.12

0.10

0.08

0.16

0.15

Correct answer:

0.15

Explanation:

The probability that a randomly selected applicant has a score lower than 560 is:

$\frac{1000-150-620-80}{1000}=\frac{150}{1000}=0.15$

Report an Error

All GMAT Math Resources

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

Popular Subjects

Physics Tutors in New York City, GRE Tutors in Philadelphia, Math Tutors in Seattle, SAT Tutors in San Francisco-Bay Area, LSAT Tutors in San Diego, English Tutors in Miami, GMAT Tutors in Chicago, SSAT Tutors in Washington DC, Computer Science Tutors in Miami, SSAT Tutors in Boston

Popular Courses & Classes

SAT Courses & Classes in Washington DC, ACT Courses & Classes in Los Angeles, SSAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Phoenix, MCAT Courses & Classes in Boston, MCAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Chicago, SSAT Courses & Classes in Denver, SSAT Courses & Classes in Phoenix, Spanish Courses & Classes in San Francisco-Bay Area

Popular Test Prep

LSAT Test Prep in Denver, SAT Test Prep in Los Angeles, GMAT Test Prep in Phoenix, ISEE Test Prep in Boston, SAT Test Prep in Chicago, MCAT Test Prep in Houston, ACT Test Prep in Los Angeles, SSAT Test Prep in New York City, GRE Test Prep in Dallas Fort Worth, GMAT 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 : Problem-Solving Questions

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #25 : Discrete Probability

Example Question #21 : Calculating Discrete Probability

Example Question #1821 : Problem Solving Questions

Example Question #1821 : Gmat Quantitative Reasoning

Example Question #23 : Discrete Probability

Example Question #23 : Discrete Probability

Example Question #1822 : Problem Solving Questions

Example Question #1823 : Problem Solving Questions

Example Question #1821 : Problem Solving Questions

Example Question #1822 : Problem Solving Questions

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details