INSIGHT - How the TEST MAKERS work.
Most test prep companies concentrate on what you, the test TAKER, have to do to answer the questions. But there is another dimension to this: consider what the test MAKER has to do in order to DESIGN the question in the first place?
How does a GMAT question get written?
The GMAT test maker receives very specific instructions for question preparation. For instance, a question might be specified as:
"You are required to write a question that would normally be solved, using straight math, by the solution of simultaneous equations of two variables, y and z. However, only one equation will be specified, making the solution apparently impossible. It will be possible to solve the equation by factoring it and realizing that the combination of y and z appears in such a way as to make two equations unneccessary. There should also be an alternative solution method involving the properties of numbers, which allows the question to be solved more rapidly."
An EXAMPLE of what we mean:
Let's assume I am a test maker. I decide to write a question that should be solvable by a candidate with skills at the 65th percentile by a simple method, taking perhaps 1 minute and 45 seconds, but that a more advanced candidate should be able to solve, using a different (smarter) method, in just 30 seconds or less. This is the core of the GMAT problem solving area for Quant:
SMART CANDIDATES NOT ONLY ANSWER THE QUESTION CORRECTLY, THEY DO IT IN A FRACTION OF THE TIME TAKEN BY LESS-SMART CANDIDATES.
The question:
Which is greater and by how much: 55,000 x 55,002 or 55,001 x 55,001 ?
(Obviously this is not written in GMAT form since there are only two possibilities, and the test maker would in reality design the question either for multiple-choice or data-equivalency format, but it will serve to demonstrate what we mean by 'think smart'.)
Method 1: Use long multiplication to multiply each pair of numbers and find the correct answer.
You might like to try it for yourself, and find out how long it takes. (When I tried it, it took me 1 min. 35 sec. and was useless anyway because I made an error in long multiplication. How did you do?)
Evidently this is not a 'smart' method.
Method 2: Use algebra.
Principle behind the method: we can represent any number by a variable, no matter how big the number. This allows us to use algebra as a method of defeating GMAT questions that have really large numbers:
Let n = 55,000. Then 55,002 can be represented by x+2. The first multiplication then becomes:
(x)(x+2) which simplifies to x2 + 2x
The second pair of numbers becomes (x+1)(x+1) which - as you should know if you are a serious GMAT candidate, without having to use FOIL - simplifies to x2 + 2x + 1
Now it becomes immediately obvious that the second expression is larger, by 1.
How long does it take to use the smart method instead of long multiplication? How much less likely is it that you will make a calculation error? Isn't it simply more elegant, more satisfying?
This is the way we teach GMAT at CitiTutors. We teach our candidates to out-think the test makers. And we have ways of doing it with the VERBAL sections, too!
The example above is just one example of one method of solving a quant. There are many, many 'smart' methods for quant.
How did the test maker really design that question?
Do you think that a test maker would design the question above by thinking of a pair of numbers and then figuring out ways to solve it that are faster than long mult? I doubt it! Much more likely is that the test maker first thought: "I'm going to set an algebra problem but I am going to disguise it by converting the two expressions into pairs of numbers".
THINK SMART!
