| INTRODUCTION | | | | world of GMAT and GRE, the category of |
| | | | miscellaneous problems is called Word |
| What is a standardized test? | | | | Problems. The key to dowell in this section |
| | | | is two-fold: (1) Know the basics of |
| Standardized tests (e.g., SAT,ACT, GRE, GMAT | | | | Arithmetic, Algebra, and Geometry; (2) Apply |
| etc.) are aptitude tests to assess the | | | | common sense to translate the given |
| proficiency of studentsfor a given course of | | | | information and thequestion in the form of |
| study. The scores obtained in standardized | | | | mathematical equations. |
| tests aresupposed to predict individual | | | | |
| success in job or profession after | | | | FORMATOF MATH PROBLEMS |
| completingthe course. For example, research | | | | |
| shows that the Graduate Management Admission | | | | Math problems in standardized tests are |
| Test (GMAT) is a valid predictor of students' | | | | almost always in the objective multiple |
| performance in the MBA program. Studies also | | | | choice question form. The Grid-in questions |
| support the proposition of post-MBA career | | | | in the SAT exam are an exception.The usual |
| successes with GMAT test scores. | | | | format includes a description of problem with |
| | | | one or more usefulpiece of information. A |
| Most standardized tests consist ofsome form | | | | question statement follows the given |
| of evaluation for two subjects: English and | | | | information. Then the problem is followed by |
| Math. The first part of English, often called | | | | 4 or 5 answer choices. |
| verbal ability test, assesses test-takers | | | | |
| ability to readand write grammatically | | | | Students taking the test are required to |
| correct English. Several years of reading | | | | utilize the given information in answering |
| text-books,writing papers, speaking in front | | | | the question statement. The answer thus found |
| of the class at elementary and high schools | | | | is one among many options. There is no single |
| allows standardized test takers to score well | | | | strategy to solve a multiple-choice math |
| without much effort. | | | | problem. Experts usuallyrecommend one or more |
| | | | of the following methods, |
| Math in Standardized Tests | | | | |
| | | | - Plugging numbers: Helps avoid complex |
| The standardized test on Math, onthe other | | | | algebraic calculations |
| hand, is not as natural or easy as the | | | | |
| English part. Students often receiveless than | | | | - Back solving: Taking the help of answer |
| satisfactory training in developing their | | | | choices to eliminate wrongoptions |
| mathematical abilities and the format of the | | | | |
| questions does not helpeither. For example, | | | | - Eye-balling &approximating: Helpful |
| how often does one have to figure out the | | | | in simple geometrical problems |
| probability of anumber to be odd when a | | | | |
| two-digit number is chosen at random. Or what | | | | - Intelligentguessing: Eliminating unlikely |
| is average speed of Jack in total, when Jack | | | | answers todecrease options. |
| drove one way at rate of 40 mph, andreturned | | | | |
| at rate of 50 mph? | | | | The strategies described above work best when |
| | | | test-takers are equipped with basic concepts |
| The standardized exam may becomposed of its | | | | of Arithmetic, Algebra, & Geometry, and |
| own format of math questions. The Math | | | | invest time & effort in practicing sample |
| section, sometimescalled Quantitative | | | | questions in actual exam like format. |
| section, can have questions of the following | | | | |
| types: ProblemSolving, Data Sufficiency, Data | | | | Other formats of Math problems (e.g., Data |
| Comparison, Graphical Problems, and | | | | sufficiency in GMAT, Grid-in in SAT, Graphin |
| Grid-Ins.Despite quantitative problems | | | | GRE & SAT) form a small percentage of all |
| appearing in numerous forms, they test a | | | | questions in the test.Students are advised to |
| limited number of concepts. The concepts can | | | | develop their own strategy for such |
| be categorized in 3 broad sections of Math: | | | | questions. Once again, knowing the basics and |
| Arithmetic, Algebra, and Geometry. | | | | practicing with such problems is the key for |
| | | | doing well in such problems. |
| - Arithmetic section | | | | |
| | | | SampleExample Problems: |
| Most standardized testsgive considerable | | | | |
| importance to the arithmetic concepts such as | | | | - After 20% discount,due to Christmas sale, |
| Percent, Ratio,Average, and Numbers. The | | | | the price of a book is $40. What is the total |
| arithmetic section often makes for 50% or | | | | saving than usual price, for Jim, when he |
| over partof the Quantitative section of the | | | | purchases two volumes of the book indiscount |
| test. The number of arithmetic problems inthe | | | | sale? |
| GMAT or GRE Math is about 55% to 60% of the | | | | |
| total number of questions. Inthe SAT and ACT | | | | A. 100 |
| exam, the arithmetic portion of the Math | | | | |
| section is about 50%. | | | | B. 50 |
| | | | |
| - Algebra section | | | | C. 40 |
| | | | |
| In terms of the number ofquestions asked in | | | | D. 20 |
| the test, Algebra is not as important. The | | | | |
| areas tested inthe Algebra are: Solving | | | | E. 10 |
| Simple Equations, Binomial Theorem & | | | | |
| QuadraticEquations, and Advance Algebra with | | | | Ans: D |
| Inequalities. About 15% to 25% of problems | | | | |
| are from Algebra section of Math. The | | | | - In the year 2000, Marywas twice as old as |
| percentage distribution may vary for | | | | her sister Sally. In the year 2008, Mary will |
| different exams. | | | | be 5 yeasolder than Sally. What is the age of |
| | | | Mary now (in year 2007)? |
| - Geometry section | | | | |
| | | | A. 6 |
| Test-makers prefer to make questions in | | | | |
| Geometry in many different forms and flavors. | | | | B. 10 |
| The basic concepts tested in this area come | | | | |
| from: Angles & Triangles, Squares & | | | | C. 17 |
| Rectangles, Circles, Co-ordinate, and Solid | | | | |
| Geometry. Even though advance questions | | | | D. 18 |
| require knowledge and practice with important | | | | |
| concepts, the easier problems are often | | | | E. 20 |
| intuitive and aptitude based. In any given | | | | |
| standardized Math test, about 20% to 40% of | | | | Ans: C |
| all questions are from the Geometry section. | | | | |
| In SATexam, about 35% pf questions are from | | | | - The numerical value ofthe ratio of area |
| the Geometry. In the GMAT exam only 20%of all | | | | and circumference of a circle is 2. What is |
| questions are Geometry problems. | | | | the diameter ofthe circle? |
| MiscellaneousProblems | | | | |
| | | | A. 4 |
| Makers of standardized tests have a special | | | | |
| liking for oddball questions. Thesequestions | | | | B. 8 |
| are derived from concepts of more than one | | | | |
| topic and often requirecommon sense besides | | | | C. 16 |
| basic section concepts. It is not uncommon to | | | | |
| find a problem on a geometrical figure, which | | | | D. 18 |
| can be resolved into an algebraic expression | | | | |
| with some simple common sense method. In the | | | | E. |