GMAT Math : GMAT Quantitative Reasoning

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 #29 : Real Numbers

Define an operation $\bigstar$ $\displaystyle \bigstar$ on the positive integers as follows:

If $\displaystyle a$ and $\displaystyle b$ are both prime integers, then $a \bigstar b =|a- b|$ $\displaystyle a \bigstar b =|a- b|$.

If $\displaystyle a$ and $\displaystyle b$ are not both prime integers, then $a \bigstar b = 0$ $\displaystyle a \bigstar b = 0$.

Evaluate $M \bigstar N$ $\displaystyle M \bigstar N$.

Statement 1: M= 2 $\displaystyle M= 2$.

Statement 2: $\displaystyle M$ is a factor of $\displaystyle N$.

Possible Answers:

EITHER statement ALONE is 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.

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:

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

Explanation:

Assume Statement 1 alone. A prime number is an integer with exaclty two factors - 1 and the number itself. 2 has only two factors, 1, and 2, and is therefore prime. However, we do not know $\displaystyle N$. If $\displaystyle N$ is not prime, then $M \bigstar N =2 \bigstar N = 0$ $\displaystyle M \bigstar N =2 \bigstar N = 0$. If $\displaystyle N$ is prime, then $M \bigstar N =2 \bigstar N = |2 -N|$ $\displaystyle M \bigstar N =2 \bigstar N = |2 -N|$, which cannot be calculated without knowing $\displaystyle N$.

Assume Statement 2 alone.

Unless both numbers are primes, the second definition of $a \bigstar b$ $\displaystyle a \bigstar b$ is used, and $M \bigstar N = 0$ $\displaystyle M \bigstar N = 0$.

The only way for both numbers to be primes and $\displaystyle M$ to be a factor of $\displaystyle N$ is for both $\displaystyle M$ and $\displaystyle N$ to be the same prime number. If this is the case, the first definition is used:

$M \bigstar N =|M -N| = |N -N| = |0| = 0$ $\displaystyle M \bigstar N =|M -N| = |N -N| = |0| = 0$.

Therefore, $M \bigstar N = 0$ $\displaystyle M \bigstar N = 0$ regardless.

Report an Error

Example Question #21 : Real Numbers

Define an operation $\bigstar$ $\displaystyle \bigstar$ on the real numbers as follows:

If both $\displaystyle a$ and $\displaystyle b$ are integers, then $a \bigstar b = a+b$ $\displaystyle a \bigstar b = a+b$.

If $\displaystyle a$ and $\displaystyle b$ are not both integers, then $a \bigstar b = a-b$ $\displaystyle a \bigstar b = a-b$.

Evaluate $M \bigstar N$ $\displaystyle M \bigstar N$.

Statement 1: M = N $\displaystyle M = N$

Statement 2: $\displaystyle 1< M < 2$ and $\displaystyle 1< N < 2$

Possible Answers:

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.

EITHER statement ALONE is 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:

Assume Statement 1 alone. The defintion that will be used to calculate $M \bigstar N$ $\displaystyle M \bigstar N$ is not clear, since it is not known whether the numbers are integers. For example, if

$\displaystyle M = N = 2$,

since both are integers, the definition $a \bigstar b = a+b$ $\displaystyle a \bigstar b = a+b$ will be used, and

$M \bigstar N = 2 \bigstar 2 = 2+2 = 4$ $\displaystyle M \bigstar N = 2 \bigstar 2 = 2+2 = 4$.

If $M = N = \frac{1}{2}$ $\displaystyle M = N = \frac{1}{2}$, the defintion $a \bigstar b = a-b$ $\displaystyle a \bigstar b = a-b$. will be used, and

$M \bigstar N = \frac{1}{2} \bigstar \frac{1}{2} =\frac{1}{2} - \frac{1}{2} =0$ $\displaystyle M \bigstar N = \frac{1}{2} \bigstar \frac{1}{2} =\frac{1}{2} - \frac{1}{2} =0$.

Assume Statement 2 alone. Both numbers fall between two consecutive integers, so neither is an integer, and the definition $a \bigstar b = a-b$ $\displaystyle a \bigstar b = a-b$ will be used. However, the value of $M \bigstar N$ $\displaystyle M \bigstar N$ cannot be calculated, since $\displaystyle M$, $\displaystyle N$, and their difference are unknown.

Now assume both statements to be true. From Statement 2, the definition $a \bigstar b = a-b$ $\displaystyle a \bigstar b = a-b$ will be used. Since M = N $\displaystyle M = N$,

$M \bigstar N = M - N= M- M = 0$ $\displaystyle M \bigstar N = M - N= M- M = 0$

Report an Error

Example Question #31 : Dsq: Understanding Real Numbers

Define an operation $\bigstar$ $\displaystyle \bigstar$ on the real numbers as follows:

If both $\displaystyle a$ and $\displaystyle b$ are both positive, then $a \bigstar b = a+b$ $\displaystyle a \bigstar b = a+b$.

If both $\displaystyle a$ and $\displaystyle b$ are not both positive, then $a \bigstar b = a-b$ $\displaystyle a \bigstar b = a-b$.

Evaluate $M \bigstar N$ $\displaystyle M \bigstar N$.

Statement 1: M = -N $\displaystyle M = -N$.

Statement 2: M < N $\displaystyle M < N$.

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.

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.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Assume both statements to be true. From Statement 1, N = -M $\displaystyle N = -M$, so $\displaystyle M$ and $\displaystyle N$ are each other's opposites. Either one is positive and one is negative, or both are equal to 0; either way, the definition of $a \bigstar b$ $\displaystyle a \bigstar b$ for $\displaystyle a$ and $\displaystyle b$ not both positive is used, and

$M \bigstar N = M - N$ $\displaystyle M \bigstar N = M - N$

$M \bigstar (-M) = M - (-M) = 2M$ $\displaystyle M \bigstar (-M) = M - (-M) = 2M$

Statement 2 tells us nothing except that M < N $\displaystyle M < N$, so it can only be deduced that $\displaystyle M$ is negative, and so is $\displaystyle 2M$.

With no further information, $M \bigstar N = M - N$ $\displaystyle M \bigstar N = M - N$ cannot be evaluated.

Report an Error

Example Question #1261 : Data Sufficiency Questions

At Branchwood Middle School, there are 4 sixth graders for every 5 seventh graders and 6 seventh graders for every 5 eighth graders. How many sixth graders are there?

1. The ratio of sixth graders to eighth graders is 24:25

2. There are 75 eighth graders at the middle school.

Possible Answers:

EACH statement ALONE is sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Correct answer:

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Explanation:

Statement 1: This information can already be determined from the original information.

Statement 2: The two ratios can be connected by the common element of seventh graders. Convert the two ratios so that the seventh grade value is the same in both. The ratio of sixth graders: seventh graders:eighth graders = 24:30:25.

Therefore, $\displaystyle 24x + 30x + 25x = total students$

$\displaystyle 25x = 75$

x=3 $\displaystyle x=3$

$\displaystyle Sixth graders =24x = 24(3)=72$

Report an Error

Example Question #1 : Dsq: Calculating Ratio And Proportion

Fred is looking at a map and is wondering how far it is from Washington City to Bush Corner. He sees that on the map, they are three and a half inches apart. From the map distance between the two, how far is it in actual miles?

Statement 1: The distance from Adamsville to Clinton Ridge on the map is four and a half inches.

Statement 2: In actuality, it is 85 miles from Adamsville to Clinton Ridge.

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:

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

Explanation:

Fred needs to know the ratio of actual miles to map inches to solve this problem; once he knows this, he can multiply this ratio by the map distance from Washington City to Bush Corner. Neither of the facts alone about the other two cities are helpful, but if he knows both, he can determine the ratio he needs to achieve his goal.

Report an Error

Example Question #3 : Ratio & Proportions

Last year, a computer shop had an average of 75 computers in stock at the start of each day, and it sold an average of 300 computers each week.

This year, the shop is expecting to sell an average of 732 computers each week. The computer store wants to use last year's ratio of computers in stock to computers sold to decide how many computers to have in stock each day. What should this target number be?

Possible Answers:

2,928 $\displaystyle 2,928$

30.5 $\displaystyle 30.5$

132 $\displaystyle 132$

198 $\displaystyle 198$

183 $\displaystyle 183$

Correct answer:

183 $\displaystyle 183$

Explanation:

We can set up a proportion to solve for the number of computers the store should keep in stock each day:

$\frac{75}{300}=\frac{x}{732}$ $\displaystyle \frac{75}{300}=\frac{x}{732}$

Cross-multiply:

$300x=75\times 732$ $\displaystyle 300x=75\times 732$

$\displaystyle 300x=54,900$

Divide both sides by 300:

x=183 $\displaystyle x=183$

The store should aim to have 183 computers in stock at the start of each day.

Report an Error

Example Question #1 : Dsq: Calculating Ratio And Proportion

Eleanor has a a scale model of the Voyager I probe. What is the radius of the dish in the model?

I) The length of the antennae on the model is $\frac{1}{60}$ $\displaystyle \frac{1}{60}$ the length of the actual antennae.

II) The radius of the dish on the actual probe is $\displaystyle 5$ feet.

Possible Answers:

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.

Neither statement is sufficient to answer the question. More information is needed.

Both statements are needed to answer the question.

Either statement is sufficient to answer the question.

Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.

Correct answer:

Both statements are needed to answer the question.

Explanation:

The secret to this problem is to set up a proportion.

We are given the ratio of one part of the model from Statement I, and asked to find the length of another part.

We need both I) and II) to set up the following proportion.

$\frac{1}{60}=\frac{x}{5}$ $\displaystyle \frac{1}{60}=\frac{x}{5}$

$\frac{5}{60}=\frac{1}{12}=x$ $\displaystyle \frac{5}{60}=\frac{1}{12}=x$

So both statements are needed.

Report an Error

Example Question #5 : Ratio & Proportions

In a car dealership there are $\displaystyle 7$ SUVs to every $\displaystyle 8$ sedans, and $\displaystyle 6$ sedans to every $\displaystyle 5$ sports car. How many sedans are there?

There are $\displaystyle 84$ SUVs.
There are $\displaystyle 80$ sport cars.

Possible Answers:

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

Statement 1 and 2 are not sufficient, and additional data is needed to answer the question.

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

Each statement alone is sufficient.

Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

Correct answer:

Each statement alone is sufficient.

Explanation:

We can combine the given ratios into one ratio by using the least common mulitiple of 8 and 6, which is 24.

In order to arrive to 24, we need to multiply the first ratio by 3 and the second ratio by 4. We can then arrive to a single ratio of $\displaystyle 21:24:20$

Using our ratio, we have an equation: $\displaystyle 21x + 24x + 20x =total$

Statement 1: 21x=84 $\displaystyle 21x=84$

x=4 $\displaystyle x=4$

then $\displaystyle 24(4)=96$ sedans

so Statement 1 is sufficient to answer the question

Statement 2: 20x=80 $\displaystyle 20x=80$

x=4 $\displaystyle x=4$

then $\displaystyle 24(4)=96$ sedans

so Statement 2 is also sufficient to answer the question

Report an Error

Example Question #1 : Percents

What percent of students in a school are freshmen with glasses?

(1) Of the freshmen in the school, 10% wear glasses.

(2) Of the non-freshmen in the school, 20% wear glasses.

Possible Answers:

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

EACH statement ALONE is sufficient to answer the question asked.

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Correct answer:

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Explanation:

To answer this question, it is necessary to know the total number of students in the school and the number of freshmen with glasses.

(1) This indicates that 10% of the freshmen have glasses; neither the total number of freshmen nor the total number of students in the school is provided $\dpi{100} \small \rightarrow$ $\displaystyle \dpi{100} \small \rightarrow$ NOT sufficient.

(2) Provides the percent of non-freshmen who wear glasses (irrelevant to the question at hand). It does not provide the total number of students in the school or the number of freshmen with glasses $\dpi{100} \small \rightarrow$ $\displaystyle \dpi{100} \small \rightarrow$ NOT sufficient.

From (1) and (2), the percent of non-freshmen with glasses is known and the percent of the freshmen with glasses is known, but not the percent of the school who are freshmen with glasses.

For example:

If there are 100 freshmen, including 10 freshmen with glasses, and 100 non-freshmen, including 20 non-freshmen with glasses, then $\dpi{100} \small \frac{10}{200}=5\%$ $\displaystyle \dpi{100} \small \frac{10}{200}=5\%$ of the school are freshmen with glasses.

If there are 300 freshmen, including 30 freshmen with glasses and 100 non-freshmen, including 20 non-freshmen with glasses, then $\dpi{100} \small \frac{30}{400}=7.5\%$ $\displaystyle \dpi{100} \small \frac{30}{400}=7.5\%$ of the school are freshmen with glasses.

Both statements together are not sufficient.

Report an Error

Example Question #1 : Dsq: Calculating Percents

In 2013 there are 300 employees at Company ABC. If the number of employees at Company ABC increased by 200% from 1993 to 2013, by what percent did the number of employees at Company ABC increase from 2003 to 2013?

(1) In 2003 there were 160 employees at Company ABC.

(2) From 1993 to 2003 the number of employees increased by 60% at Company ABC.

Possible Answers:

D. EACH statement ALONE is sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Correct answer:

D. EACH statement ALONE is sufficient.

Explanation:

For statement (1), since we know the numbers of employees in 2003 and 2013, we can directly calculate the percentage change: $\frac{(300 - 160)}{160}= 87.5\%$ $\displaystyle \frac{(300 - 160)}{160}= 87.5\%$.

For statement (2), since we know the percentage change from 1993 to 2013 and the percentage change from 1993 to 2003, we can set the percentage change from 2003 to 2013 to be $\displaystyle x$ and then calculate $\displaystyle x$ from the following:

$(1 + 60\%) \cdot (1 + x) = 1+200\%$ $\displaystyle (1 + 60\%) \cdot (1 + x) = 1+200\%$.

Solve $\displaystyle x$ and we can get $x = 87.5\%$ $\displaystyle x = 87.5\%$.

Report an Error

All GMAT Math Resources

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

Popular Subjects

Reading Tutors in San Francisco-Bay Area, Chemistry Tutors in San Diego, Computer Science Tutors in Dallas Fort Worth, MCAT Tutors in Atlanta, Algebra Tutors in Seattle, Chemistry Tutors in San Francisco-Bay Area, MCAT Tutors in Dallas Fort Worth, Reading Tutors in Phoenix, Algebra Tutors in Washington DC, Algebra Tutors in San Diego

Popular Courses & Classes

ISEE Courses & Classes in Philadelphia, ISEE Courses & Classes in Boston, SAT Courses & Classes in Boston, MCAT Courses & Classes in Chicago, SAT Courses & Classes in Washington DC, Spanish Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Denver, GRE Courses & Classes in Houston, GMAT Courses & Classes in Atlanta, ISEE Courses & Classes in Miami

Popular Test Prep

GRE Test Prep in Miami, GRE Test Prep in New York City, GMAT Test Prep in Seattle, ISEE Test Prep in Los Angeles, SAT Test Prep in Boston, MCAT Test Prep in Seattle, LSAT Test Prep in Dallas Fort Worth, SAT Test Prep in Washington DC, ACT Test Prep in Washington DC, SSAT Test Prep in Los Angeles

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 : GMAT Quantitative Reasoning

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #29 : Real Numbers

Example Question #21 : Real Numbers

Example Question #31 : Dsq: Understanding Real Numbers

Example Question #1261 : Data Sufficiency Questions

Example Question #1 : Dsq: Calculating Ratio And Proportion

Example Question #3 : Ratio & Proportions

Example Question #1 : Dsq: Calculating Ratio And Proportion

Example Question #5 : Ratio & Proportions

Example Question #1 : Percents

Example Question #1 : Dsq: Calculating Percents

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details