An introduction to GMAT math
The GMAT exam has a section on Math, also called quantitative section. This Math section contributes towards the final score. The final points carry half of its weight-age from the Math section. The other half comes from verbal section. In the GMAT quantitative section there are 37 multiple-choice questions and the allotted time is 75 minutes.
GMAT Math - Why is it difficult
Test-takers find the GMAT Math as the most intimidating portion of the exam. Having had little or no practice of the math after high school days, most of them are apprehensive about taking the test. The methods that are taught to solve most of the problems are not intuitive or straightforward. And the type and format of the question asked in the exam does not help them either. Therefore, often, one has to train oneself to do well in the test. Further, the exam is Computer Adaptive Test (CAT) making the experience challenging for every individual who takes the test. (More on CAT explained later in this article)
GMAT Math - Old and new ways of learning
The GMAT Math is the most difficult part of the test. Not surprisingly, the test prep market is full of textbooks & CDs, online material, review courses and private tuition. However no method is perfect, and one may require help from more than one source besides putting in considerable self-study. The other problem with most of the resource materials presently available in the market is that they are either expensive or utilize poor methods of instruction. For example, on the one hand a good private tutor for GMAT Math may charge over $50 per hour. On the other, an inexpensive textbook on GMAT Math presents math methods in text format which, if you are learning on your own, cannot substitute a teacher. In recent years, however, some enterprising instructors have put together the best of classroom or private sessions in an online video gmat course. Now that high speed internet connection is readily available in most of the homes and offices, it has become possible to learn from some of the best instructors at an affordable rate.
GMAT Math Test Format - Questions, Time, Date, and Difficulty
Questions & Time: The quantitative section of the GMAT test has 37 multiple-choice objective questions, and one is permitted only 75 minutes to answer them. Further, the test is always taken on a computer at special test centers throughout the world.
Difficulty & CAT: The test being computer adaptive (CAT), is also known as GMAT-CAT. It is extremely important to note that there is no fixed set of questions in the test. The question you see on the screen and its difficulty level depends on your performance in the previous question. When you begin the test, the first question you see on the computer screen is of medium difficulty. If you answer that correctly, the next question will of slightly higher level (and your score has gone up). If however, you choose the wrong answer for the first question, the second problem will be of lower difficulty (and your score has gone down). This process continues till the very end. Therefore your final score is largely dependent on your level. Hence it is possible for a test taker to get the final score higher even when he/she made mistakes. On the other hand a test-taker may get a lower score if one correctly answered most of the questions but was operating at a lower level.
Date & Venue: The GMAT test is taken through out the year at special centers. One can find more details on the Internet. However it is advised to take the exam several months before the application deadline. In doing so, one will have the opportunity and chance to re-take the test if not satisfied with the first score.
GMAT Math - Types of questions
Problem solving: About two-third of the questions in the test are of this type. It is a straightforward type that you may have seen in your high school. A question is followed by a five-answer option. The test-taker solves the questions and chooses the right answer. You confirm your answer on the screen and then proceed to the next question.
Data Sufficiency: This is a unique type of question and may seem very difficult. Here a question is followed by two statements. One has to figure out which of the statements are required to sufficiently answer the question. Experts feel that test-takers must train themselves well in order to score well in this section.
Math Topics and subtopics
The GMAT Math test asks questions from topics and sub-topics you may have seen in your high school days. They can be broadly classified as Arithmetic, Algebra, Geometry and Miscellaneous. Subtopics for Each one of these are listed below
ARITHMETIC
Number Properties - Integers, even/odd numbers, power or exponents, number line
Percent - Calculate percent, percent change, profit and loss percent
Average - Mean, weighted mean, median, mode, range and standard deviation
Ratio & proportions - direct and indirect relationships, two or three variables
Distance & Rate problems - distance-rate-time problems, average speed, work and rate problems
ALGEBRA
Equations - Solving simple equations, linear equations, two equations etc.
Advance - Quadratic equations, inequalities, multiple equations, logical word related problems
GEOMETRY
Angles & Triangles - Lines and angles, acute & obtuse angles, properties of triangle, right triangles, special right triangles
Quadrilaterals - Squares, rectangles, parallelogram, calculation of area and perimeters
Circles - Diameters, radius, area, circumference, partial circles, tangents, sectors, arcs
Solid geometry - Cylinder, cube, cuboids, surface area, volume, mixed figures
Coordinate geometry - Coordinate points, lines, distance, slope, relationships
MISCELLANEOUS
Word problems - Above topics and sub-topics in word or language format
Other topics - Venn diagram, probability, counting principles, permutation and combination etc.
GMAT Math Summary
Questions = 37 Time = 75 minutes Test Date = Through out the year Difficulty level = Computer adaptive (CAT) Importance = Half of the total final score Type of questions = (1) Problem Solving (2) Data Sufficiency Topics = (1) Arithmetic, (2) Algebra, (3) Geometry, and (4) Miscellaneous
GMAT Math: Sample questions/tests
There are plenty of sample questions available on the internet. A simple search is all that is needed to get access to the best of the gmat resources for problem solving and data sufficiency .
Example problems:
Question 1:
In a mixture of 28 pounds, the ratio of beans and nuts is 5:2. If 2 pounds of nuts is added to the mixture, find the ratio of beans and nuts in the new mixture?
4:13:12:11:11:2
Solution 1:
Beans in the given mixture = (28) (5/7) = 20 pounds
Nuts in the mixture = 28 -20 = 8 pounds
After adding 2 pounds of nuts to this mixture
The mixture has 20 pounds of beans and 10 pounds of nuts.
Therefore, the ratio of beans and nuts in new mixture = 20:10 = 2:1 (Answer 3)
Question 2:
An airplane travels distances of 2500 miles, 1200 miles, and 500 miles at the rate of 500mph, 400mph, and 250 mph respectively. What was the average speed for the entire journey?
385 mph400 mph415 mph420 mph516 mph
Solution 2:
Total distance = (2500 + 1200 + 500) miles = 4200 miles
Total time taken = (2500/500) + (1200/400) + (500/250) = 5 + 3 + 2 = 10 hours
Therefore Average speed = (Total distance / Total time) = (4200/10) mph = 420 mph (Answer 4)
Question 3:
Andrew can finish a job in 12 days while Betty can do it in 15 days. If both work at the job together, what time will they take to do the work?
20/3 days10/3 days3/20 days3/10 daysNone of the above
Solution:
Andrew's 1 days job = 1/12
Betty's 1 day job = 1/15
Therefore Andrew + Betty's 1 day job = (1/12) + (1/15) = 9/60 = 3/20
Finally, time taken by both to finish the work = 20/3 days (Answer 1)
Question 4:
The dimensions of a rectangular park are in the ratio of 3:2 and the area is 15,000 sq feet. Find the width of the park?
50100150200250
Solution 4:
Let the length and width of the park be 3x and 2x.
Then the area = (3x) (2x) = 15,000
Or, 6 (x)(x) = 15000
Or, (x)(x) = 15000/6 = 2500
Or, x = square root (2500) = 50
Therefore length = 3 (50) = 150 and width = 2 (50) = 100 (i.e., Answer 2)
Question 5:
Three cubes of sides 8 cm, 6 cm, and 1 cm are melted to form a new cube. What is the surface area of the new cube?
9 cm36 cm81 cm324 cm486 cm
Solution 5:
Volume of new cube = sum of volumes of three cubes
= (8)(8)(8) + (6)(6)(6) + (1)(1)(1) = 729
Edge or side of the new cube = cubic root of (729) = 9 cm
Therefore surface area of this new cube = 6 (side)(side)
= 6(9)(9) = 486 (i.e., Answer 5)
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