A lot of mathematics exams nowadays, e.g. GMAT, SAT, etc, are either completely multiple choice or they have multiple-choice components. These exams required students to solve a stipulated large number of questions within a small amount of time. Students break a lot of sweat over solving these questions, by trying to solve them completely like other questions, and not utilizing the information that is in front of them.
One of the basic difference between multiple-choice questions and other questions is that for multiple-choice ones you have to just figure out the answer, and for achieving this objective, you need not necessarily solve the question completely, as the answer is right in front of you, among the 4-5 choices that have been provided.
Ball-park, or possible range strategy, is one such very effective method to quickly solve a multiple-choice question in arithmetic. In order to use it, you first make a quick guess of what the possible range of your answer will be. Once, you have made such a guess, you can easily eliminate all the other answers, which don’t fall in that range, and so can be ruled out as a choice for the possible answer. You are now left with just 1 or 2 choices, which you can just plug-in to confirm which one is the correct answer.
This strategy doesn’t work well if all the choices are in the possible range, and it is particularly useful when the answers are scattered over a large range, as in the following example:
If 0.303z = 2,727, then z =
We can notice that the range of answers is too large, so we can use ball parking to solve this question. .303 is very close to 1/3, which means 1/3 of z = 2,727, then what answer could be possibly correct. You don’t even have to do the math. 2,727 is about 1/3 of 9,000; therefore, the answer must be 9,000, according to the Ballpark Strategy (note that there are no other answers even in the 9,000 range.
If you don’t use the ballpark strategy, you could multiply both sides by 1000 to eliminate the decimal points, and then divide 2,727,000 by 303 and get the same answer, although after spending much more time.
Another important use of this strategy is to double-check your answer. Once you have solved a multiple-choice arithmetic question, you should confirm whether the answer lies in the ballpark of what the answer could be.
So, invest sometime in learning and practicing to use ball-parking. This will allow you to solve the arithmetic questions much faster and will save you precious time, enabling you to score much higher.
LazyMaths.com focuses on this strategy and has hundreds of examples to show how and where one can use ballparking. Visit the Smart Math section of the site to know more about it and check out the free examples.