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# Overview of GMAT Math Question Types and Patterns on the GMAT

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Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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A complete breakdown of GMAT Math question types and its history

What should you study more? Arithmetic? Geometry? Probability? All?
When preparing for GMAT, test-takers often ask about Math that is covered on the GMAT and about the most common question types that appear in the actual test. Therefore, in this article, I will not only delve into the past trends, but also into the current trend of the GMAT Math test. Also, I will discuss the types of questions that appear on the test every month. You can also find our observations about the hardest question types that appear on the test here: The Ultimate Q51 Guide

The scope of Math Tested on the GMAT

1. Topics that appear frequently on the GMAT - This is what you need to study and know:

• Integer: Question in this section involves dividing an integer n with 5 or 10, solving the units digits for an integer n, finding the remainder of an integer n after dividing it by 3 or 9 and solving factor prime factor.
• Geometry: Questions in this section involve Pythagoras Theorem, special angles ($$1:1:\sqrt{2}$$, $$1: \sqrt{3}:2$$), solving an area for different figures.
• Statistics: Questions in this section involve finding the average, standard deviation, median, and range.
• Speed Rate: Questions in this section involve solving average speed rate.
• Inequality: Questions in this section involve inequality questions that ignore squares and DS questions related to inclusion relation.
• Equation: Questions in this section involve calculation using $$(a-b) (a+b) =a^2-b^2$$.
• DS questions: Common Mistake Type questions

NOTE: Please refer to the table below for additional types of questions that appear in the test. However, remember that types that are mentioned above are the most common types of questions.

 Quant Topics and Types of Questions Tested on the GMAT Today Topic Proportion Questions that appear frequently Questions that appear occasionally Questions that appear once in a while Integer 30% Remainder, factor, multiple Remainder questions after dividing the number by 4 or 8, terminating decimal questions Modula questions Statistics 18% Median, Range, Mean Harmonic mean Standard Normal Distribution Geometry 10% Pythagoras Theorem Questions involving special angles and area of circles Questions involving areas of parallelogram and trapezoid. Equation 10% $$a^2-b^2=(a-b)(a+b)$$ $$(a+b)^2=a^2+b^2+2ab$$ $$(a+b+c)^2$$ Inequality 7% Questions that ignore squares DS questions with inclusion relation Questions that require the substitution of the positive and negative number and that involve changes in signs of inequality with 1 as a standard. Absolute Value 5% N/A Questions involving the definition of absolute value Questions involving a relationship between A and |A|. Exponent 5% Basics of quotient (an)m=anm N/A Probability 3% Combination Permutation ‘At least’ questions. Work Rate 3% Together and alone Inversely proportional relationship between work rate and time. N/A Ratio 2% Percent change questions N/A N/A Speed Rate 2% Average speed Speed*Time=Distance Traveling in the same time Sequence 2% Sum of sequence Compound and simple interests Geometric series, sum of reciprocal series Set 1% N/A Intersection of two sets Intersection of three sets Function 1% N/A Straight line and discriminant questions Questions involving a definition of a function Proportion 1% $$a:b:c=1:2:3$$ Axiom questions N/A

2. Mathematical concepts that are partially covered

In case of sequence, only fundamental concepts such as arithmetic sequence and geometric sequence are included within the scope of the test. This means more complex concepts like difference sequence will not be tested.

There are also questions regarding probability and statistics, but those questions will rather be simple. In other words, concepts like the combination with repetition, conditional probability, discriminating distribution and average deviation will not be on the test. In the end, test-takers are not trying to go to a graduate program in mathematics!

3. TREND: Dead questions from previous tests have reappeared recently

Moreover, some questions can be categorized into two types: dead questions (those questions that appeared in previous tests, but later disappeared) and live questions (those questions appear in today’s tests). Recently, we have discovered that some dead questions, which appeared in early 2000, are being reused in today’s tests. Here is an example of the type of the question:

• Example 1:
On a certain transatlantic crossing, 40 percent all passengers held round-trip tickets. Additionally, they also took their laptops aboard the ships. If 20 percent of the passengers with round-trip tickets did not take their laptops aboard the ship, what percent of the ship’s passengers held round-trip tickets?
A. 33.3%
B. 45%
C. 50%
D. 65%
E. 66.6%

• Example 2:
40 percent of the ducks included in a certain side effects study were male. If some of the ducks had side effects during the study and 30 percent of the ducks who had side effects were male, what was the ratio of the side effect rate for the male ducks to the side effect rate for the female ducks?
A. 1/4
B. 9/14
C. 2/3
D. 7/8
E. 8/7

[Side effect rate for ducks of a certain sex = (number of ducks of that sex which had side effects) / (total number of ducks of that sex)]

4. Questions/Topics that Never Appear

The level of GMAT Math is generally what people learn in High School.
This means that the scope of GMAT Math does not include difficult concepts like trigonometrical function, logarithm, differentiation, integration or limits. Also, even though basic concepts such as calculating volume and area of space figure and finding diagonal length appear in the test, more difficult concepts like vector or inner product do not appear.
During the past 15 years of experience in teaching GMAT Math, I have encountered only 2 matrix questions. Due to its infrequency, we can say matrix is not included within the scope of GMAT Math. Additionally, a question on an imaginary number - a complex number $$(\sqrt{(-1)}=i)$$- also is not included on GMAT Math.

NOTE: From 15 years of experience in teaching GMAT Math, I have found some patterns on the GMAT test. It was that some questions, which were on the test in 2001, have reappeared recently. Even though I cannot give any assurance to whether GMAC - the question bank of GMAT Math – reutilizes its questions, I believe that it occasionally uses some of the previously-appeared questions along with new questions it makes every year.

History and Evolution of GMAT Math

In this part, I will analyze GMAT Math trends beginning from 2001, the year when I started teaching.

• Most common types of questions

First of all, questions involving integer and statistics are the most common types of questions. Please note that you can make your score go up as high as 50 only by excelling in these two sections. If you feel like you have not enough time to study for the test, you might want to focus on mastering integer and statistics sections.
Regarding integer, questions involving remainder and factor appear almost every month.

1. Example 3:
When both positive integers a and b are divided by 7, both have a remainder of 4. What is the remainder when ab3 is divided by 7?
A. 6
B. 5
C. 4
D. 3
E. 2

Regarding statistics, questions involving median, mean and range appear almost every month.

2. Example 4:
The numbers of defects in the first 5 vehicles to be produced through a new production line are 8, 6, 9, 3, and 5 respectively. If the 6-th vehicle produced through the production line has either 2, 6, or 11 defects, which of these values does the mean number of defects per vehicle for the first 6 vehicles equal the median?

I. 2
II. 6
III. 11

A. I only
B. II only
C. III only
D. I and III
E. I, II, and III

• GMAT Math trends from 2001 to 2005

Rather simple types of questions took the major portion of tests between 2001 and 2005. Especially, basic concepts such as factorization formula, area formula and basic formula appear for an equation, figure and index questions respectively. Hence, as you can see, GMAT tests between 2001 and 2005 mostly included the very basic mathematical concepts. Additionally, during this period, GMAT Math gradually increased the portion of integer and statistics sections, and these took about 25% of all experimental questions (questions that have no influence on actual test scores). Also, some questions even included 2 answers or no answers at all.

• Example 5:
If n and k are integers, is $$(-1)^{4n+k}$$ less than 0?
(1) n is an even number
(2) k is an odd number

• Example 6: (statistics)

Is the median of class A and class B combined greater than the mean of class A and class B combined?

(1) a+b=69
(2) a=37, b=32

• Example 7:
When -1<x<0, which of the following is the smallest?
A. $$x^2$$
B. $$1-x$$
C. $$1-(\frac{1}{x^2})$$
D. $$1-(\frac{1}{x})$$
E. $$\frac{1}{x}$$

• GMAT Math trends from 2005 to 2011

Many applied questions began to appear in the test. Unlike simple calculation problems, these questions require additional steps in the calculation. Besides, GMAT Math started to contain longer questions. From my experience, I remember that, in 2001, I was able to generate equations quickly from the original condition and the question. However, this crucial step to solving a problem became a little more challenging since questions got longer. Also, questions did not only become longer but also became wordy. In other words, from 2005 to 2011, as integer and statistics began to take significant portions of the test, long and wordy questions began to appear in other parts.

• Example 8:
Of all of the apples inspected last week at a certain orchard, 4.5 percent failed to pass inspection. Of the apples that failed inspection, 2/3 of them were rotten and the rest was unmatured. If all of the apples that were rotten or unmatured failed inspection, how many of apples inspected last week at the plant were unmatured?
(1) 450 of apples inspected last week at the orchard failed to pass inspection.
(2) 9,550 of apples inspected last week at the orchard passed inspection.

• Example 9:
Stations M and N are connected by two separate, straight and parallel rail lines that are 500 miles long. Freight train A and freight train B simultaneously left Station M and Station N, respectively, and each freight train traveled to the other’s point of departure. The two freight trains passed each other after traveling for 4 hours. When the two freight trains passed, which train was nearer to its destination?

(1) At the time when the two freight trains passed, freight train A had averaged a speed of 60 miles per hour.
(2) Freight train B averaged a speed of 130 miles per hour for the entire trip.

• GMAT Math trends from 2012 to 2015

The recent trend of all standardized tests in the United States is that questions nowadays contain characteristics of our daily lives. In other words, questions feature daily activities such as tipping in restaurants and purchasing movie tickets in theaters. For example:

• Example 10:
Whenever Tom pays an amount of 2-digit integer in a cafeteria, he calculates the dollar amount of the tip as 3imes the tens digit of the amount of his bill. If the amount of Tom’s most recent cafeteria bill was 2-digit integer, was the tip calculated by Tom on this bill greater than 20 percent of the amount of the bill?

(1) The amount of the bill excluding tip was over $20 (2) The tip calculated by Tom was at least$4

Additionally, the number of questions involving figures is increasing as well. Even though trigonometrical functions will not appear in the test, since some advanced figure questions do appear in the test, it may be worth spending some time studying this type of problems.
• Example 11:

There is a right-angled triangle yard ABC. A and B are where sprinklers are located, and the radius of the range of sprinklers is 20 as shown in the above figure. What is the area of parts of the yard where water from the sprinklers does not reach?
A. $$384-100\pi$$
B. $$384-10\pi$$
C. $$284-100\pi$$
D. $$384-80\pi$$
E. $$284-80\pi$$

Also, the number of questions related to data interpretation has increased as well. Not only does the DS part include this type of questions, but the number of the similar type of questions is increasing in PS part as well. NOTE: This question type requires test-takers to read and analyze data.
• Example 12

On last Wednesday, each of the 45 members of a certain task force team spent some time working on a project A. The above graph shows the number of hours and the number of members, who spent that number of hours working on the project A on last Wednesday. What was the median number of hours that the members of the task force team spent working on the project A on last Wednesday?
A. 3
B. 4
C. 5
D. 6
E. 7

Also, DS questions have become more difficult and weigh more than they did before. In the past, PS part contained most of the tough questions, yet, nowadays, the trend is that difficult questions in DS part have become unprecedentedly challenging. Questions involving Common Mistake Type are especially increasing in number. Thus, it can be stated that, due to increasing difficulty level of problems, the conventional method of approach to GMAT Math problems will not be as effective as it has been before. This also means that questions are becoming so difficult that even those who are good at Math and those who have majored in Math in college will struggle to solve 37 problems in just 75 minutes.

It is also vital to note that, for inequality section, the number of maximum and minimum questions is increasing. For example, this type of questions asks, “If x has to be the minimum, what is the value of x?”

• Example 13:
A certain state with a population of 130,000 is to be divided into 11 new districts, and no district has a population that is more than 20 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?
A. 9,900
B. 10,000
C. 10,200
D. 10,400
E. 10,600

 Evolution of Topics Tested Since 2001 2001 - 2005 2005 - 2011 2011 - Today NOTE arithmetic 40% 40% 30% Has been consistent algebra 35% 30% 30% Has been consistent geometry 10% 10% 15% The number of questions is increasing, and the questions are becoming harder. Word problems 5% 5% 5% DATA interpretation 5% 5% 10% The number of questions is increasing, and questions have characteristics related to daily lives. Common Mistake Type (CMT) 5% 5% 10% The number of questions is increasing, and the questions are becoming harder.

Note: This is a table I made based on my 15 years of experience.

• Example 14:
When a positive integer n is divided by 3, what is the remainder?

(1) The sum of the digits of n is 11.
(2) When n is divided by 9, the remainder is 2.

• Example 15:
If the average (arithmetic mean) of positive integers x, y, and z is 15, what is the greatest possible value of z?
A. 18
B. 20
C. 30
D. 43
E. 45

• Example 16:
When the product of the digits of the two-digit positive integer x is 3, what is the value of x?

(1) x is greater than 30.
(2) The tens digi of x is greater than the units digit of x.

Conclusion

I want to emphasize that it would be especially helpful for those who prepare GMAT Math to focus on mastering integer and statistics section. In fact, I have seen students who get every integer and statistics question right in prep tests (mock tests distributed freely by GMAC) and get 50. Additionally, I want to advise test-takers to focus on studying questions that appear every month.

As explained earlier, integer questions are the most common types of questions (not only the number of questions, but the number of types of integer questions are numerous). Hence, spending more time learning these areas than any other concepts would be an effective and time-efficient way to tackle GMAT Math.

Also, the recent trend of GMAT Math is that questions nowadays contain characteristics of our daily lives. Thus, it would be helpful for test-takers to have a general understanding of the culture of the United States. Besides, questions involving figures are increasing in number. I want to advise test-takers to spend some time learning this part.

As mentioned earlier, questions are becoming wordy. So, while studying the Official Guide, please spend some time observing the trend and styles of questions. It is vital for test-takers to regularly exercise generating equations after reading difficult and wordy questions.

As many test-takers are already aware of, solving 37 questions in just 75 minutes is very challenging. Therefore, it is important to have strategies for time management. Many people can solve simple questions in just about 1 minute with no problems. However, those who solve questions with the conventional method of approach take about 5 minutes in solving just one difficult question. Thus, it is very helpful to learn various techniques and tips that can guide test-takers to solve difficult questions in just about 2 minutes.

The average GMAT score is 38 (it is 33 for the United States alone). However, I strong believe that if test-takers clearly understand about GMAT Math trends and the history of the test, they will not only be able to exceed the average score, but will be able to score at least 45 or even get a score of 49 to 51. Thank you so much for reading this article, and I wish you the best luck.

*** We are math experts and if you find any grammatical issues – that is because we spend all of our time focusing on math; sorry grammar. Note that the information herein is based on the knowledge and experience of Max Lee, who taught 30,000+ students and solved 100,000+ problems in the past 15 years. He discovered and analyzed types of GMAT Math questions based on continuous and numerous interviews with students after the actual GMAT exam. Thus, please note that the information is herein based solely on experience of Max Lee. Due to the nature of the test and lack of transparency about the algorithm, this guide is a best efforts attempt based on the best information available. If you have any questions or other information to share, please feel free to post it here for the benefit of the community.
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14 Jan 2016, 11:09
Please tell Books for exhaustive practice for the sections

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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15 Jan 2016, 04:26
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MathRevolution , can you please explain the solution of the below question.

When both positive integers a and b are divided by 7, both have a remainder of 4. What is the remainder when ab3 is divided by 7?
A. 6
B. 5
C. 4
D. 3
E. 2

Can we assume that a and b and single digit integers, since abc3 is a three-digit integer?

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16 Jan 2016, 13:28
is it possible to get an explanation of the solutions for #1, 2, 3, 6, 9, 11, 12, 13?

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16 Jan 2016, 21:36
oishik2910! We currently have our own book for internal teaching purpose for our own members but we are planning to publish the 3 books through Amazon by the end of Feb. Or, if you are interested in free videos and free core theory, you may join the membership in our site.
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16 Jan 2016, 21:42
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nycgirl212! As this section is for general GMAT strategies and questions, if you want to know how to solve these questions, you may post the questions in Math Forum then we can post reply.
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ruhibhatia wrote:
MathRevolution , can you please explain the solution of the below question.

When both positive integers a and b are divided by 7, both have a remainder of 4. What is the remainder when ab3 is divided by 7?
A. 6
B. 5
C. 4
D. 3
E. 2

Can we assume that a and b and single digit integers, since abc3 is a three-digit integer?

Hi ruhi,
there are two things which ab3 can mean..a three digit number or a*b*3..
1)if ab3 is three digit number, as you have said a and b should be a single digits..
so a and b have to be 4, as the next number to leave a remainder of 4 would be 11, which is not a single digit number..
so our number is 443.. and remainder when 443 is divided by 7 is 6..
2)if ab3 actually meant a*b*3...
remainder will be 4*4*3=48..
48 when divided by 7 leaves a remainder 6..

Hope it helps u
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16 Jan 2016, 22:52
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nycgirl212 wrote:
is it possible to get an explanation of the solutions for #1, 2, 3, 6, 9, 11, 12, 13?

Example 1:
On a certain transatlantic crossing, 40 percent all passengers held round-trip tickets. Additionally, they also took their laptops aboard the ships. If 20 percent of the passengers with round-trip tickets did not take their laptops aboard the ship, what percent of the ship’s passengers held round-trip tickets?
A. 33.3%
B. 45%
C. 50%
D. 65%
E. 66.6%

The Q no 1 is not correct..
on one hand we are already given "40% all passengers held round-trip tickets." and then we are asked 'what percent of the ship’s passengers held round-trip tickets"...
so what is intended to ask is not clear as the answer is already given as 40%..

MathRevolution,
you will require to look into the Q..
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17 Jan 2016, 02:01
hi chetan2u, thanks a lot for the explanation. I also followed similar approach and got 6 as my answer, but the post above has mentioned option C (i.e. 4) as the right answer.

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This question is frequently on GMAT Math lately, which is 2 by 2 question.
Attachment:

GCDS overview of GMAT에 대한 댓글답변 (20160118).jpg [ 33.78 KiB | Viewed 42481 times ]

On the above, suppose all the passengers 100p(if there is %, use 100 since it is per cent. p is an initial for passengers). Passengers who brought a round ticket and a laptop is 40% of the total passengers, which is 40p. However, what 20% means is that x=10 is derived from 40p:xp=80%:20%=4:1. That is, 40p+10p=50p, which means 50% of the passengers have round tickets. Therefore, the answer is C.
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If you are serious about hitting 49-51, you may find this post useful (Ultimate Guide Q51)
the-ultimate-q51-guide-209801.html#p1641408
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19 Feb 2016, 21:33
The understandable explanation. It is really helps to me

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Questions related to geometry are continuously increasing. Let’s have a look at the example of the recent trend.

(ex 4)
Attachment:

GEOMETRY.jpg [ 2.98 KiB | Viewed 40068 times ]

If n regular pentagons are tangent each other in points of a circle as above figure, n=?

A. 8
B. 9
C. 10
D. 11
E. 12
[Reveal] Spoiler:

Questions like the above are increasing. Therefore, students preparing for GMAT should focus on geometry more intensively.
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Furthermore, not only simple but also analysing questions are also frequently given. Let's have a look at the question below.
(ex 5)

There is Fi.
A) If i is an even number, the inner figure is a horizontal rectangle. If i is an odd number, the inner figure is a vertical rectangle.
B) If remainders are 2,1,0, dividing i with 3, each outer figure is circle, triangle, and rectangle.
C) If i is an even number and an inbetween area of 2 figures is an odd number, it is an area of an inner figure.
Which one is possible for the figure of F32?

Attachment:

FIGURE.jpg [ 8.17 KiB | Viewed 39904 times ]

[Reveal] Spoiler:

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11 Mar 2016, 06:16
Moreover, the mistake type 3 and 4 are substantially increasing. Let's have a look at a recent question.

(ex 6) If a and b are positive integers, what is the greatest common factor of a and b?
1) a=b+1
2) a=26

In this case, C is an answer though you should apply the mistake type 4(A) as it is an integer question, which is one of the key questions. For 1), GCD(a,b)=1. That is, it is always 1, which is unique and sufficient.

For these reasons, with increase of geometry and the mistake 3 and 4 questions, you should study in an organised and logical way.

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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13 Mar 2016, 22:44
In addition, for highly advanced integer questions are on the similar level of the question below.

(ex 6) If m is a positive integer, is √13m an integer?
1) 117m is the square of an integer.
2) m/117 is the square of an integer.

In this case, the answer is D since there is 1 variable. If you actually encounter a question like this, you might be confused. The advanced level of integer questions like this are frequently given.
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Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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20 Mar 2016, 18:11
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Also, geometry questions are rising continuously. Let's take the recent question as an example.

(ex 4)
Attachment:

yin yang.jpg [ 4.6 KiB | Viewed 39145 times ]

There is a yin-yang symbol shown as above figure such that its radius is 2. What is the area of the region shaded?
1) Both arc MNO and arc OCD are the same semi-circles.
2) The area of region shaded is half of the area of the circle

[Reveal] Spoiler:

In this case, 1) and 2) are the same, which makes D the answer. Just like the question above, slightly difficult and deriving 1)=2) questions which make D the answer are frequently given as well. This type of geometry questions are steadily on an upward tendency.

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Last edited by MathRevolution on 22 Mar 2016, 18:17, edited 1 time in total.

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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21 Mar 2016, 09:41
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Hello Math Revolution Team,

Many Thanks !

Posted from my mobile device

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24 Mar 2016, 17:06
Plus, inequality questions disregarding square frequently appear as well. Let’s have a look at the question below.

(ex 5) If xy2z3<0, is xyz>0?
1) y<0
2) x<0

In this case, if you disregard square in the original condition, ‘If xz<0’ is derived and ‘is xyz>0’ becomes ‘is y<0?’, which makes A the answer.
This type of question is frequently given.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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27 Mar 2016, 01:58
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Also, the highly advanced hidden integer questions frequently appear on exams.

(ex 6) Tom, who has 50 math questions, will get 5 points per question if he chooses a correct answer. If he chooses a wrong answer to a question or skips one, he will lose 2 points per question. Then, which of the following can be the score if he solves all the 50 questions?

A. 192
B. 193
C. 194
D. 195
E. 196

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT   [#permalink] 27 Mar 2016, 01:58

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