Two crucial Gmat quant skills I recommend you begin to develop early in your gmat preparation is rephrasing and deconstructing questions into their individual components. Deconstruction will help you realize the steps you need to take to solve the problem. Rephrasing, when possible, can help you think of the problem in a simpler, more straightforward format.
One may argue that this is how we solve problems in everyday life anyways, so how is this advice new or important?
It is new and important if we remember the following:
- Once we learn how to solve a particular problem, the process we use to solve becomes a habit with repetition. Some processes are better than others, and if you are not aware of how you arrive at a particular solution, you cannot discover, practice and develop a better process. Maybe you remember a specific way to solve rate problems from highschool, but it may not be the best approach.
- Breaking a problem into its components is different from rephrasing it, and rephrasing is not as common in everyday life. Being aware that it is a helpful tool early on in your preparation means that you are more likely to practice doing it.
Lets consider two examples to illustrate the value of these two gmat quant skills.
Gmat Quant skills : Deconstruction
“The mean of a set of n integers, were n is divisible by 7!, is 21. Is the sum of the set of integers even?”
At first glance, this may seem like a difficult question. First you need to recognize all the different components that make up this question:
- Odd/even theory
- How to calculate the mean of a set of numbers
- What the factorial notation “!” means
- Divisibility of one number by another
All these concepts are implicit in this question.
First, start with the end in mind. “is the sum of the integers even?”.
so you ask: is the sum divisible by 2.
Second. it is mentioned that that the mean of the n integers is divisible by 7!. So, I can represent the mean as:
mean = 7! x K
where K is an integer. This means that the mean is either 7! or 7! x 2 or 7! x 3 etc..
To calculate the mean, I know the formula is:
mean = (Sum of integers) / (Number of integers)
In other words,
Sum of integers = (mean) x ( Number of integers).
So now, I now that
Sum = 7! x k x n.
Third, I know from the factorial notation, that 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1.
Laying out the number 7! brings to my attention that 7!, like any factorial greater than or equal to 2!, will always be even, because it contains at least one factor of 2.
Hence, I now know that
Sum = 7! x n , must be even.
Gmat Quant skills : Rephrasing
Is the integer P + 1 odd?
(1) P has 9 factors.
(2) P + 2 = 2n + 1, where n is a positive integer.
This may or may not be a difficult question. But, the first to recognize is that you can rephrase the question to make it simpler. Asking whether P + 1 is odd is the same as asking whether P is even. The latter is clearly simpler to deal with.
From statement (1), I know that P is a perfect square, nothing more.
From statement (2), and with simpler algebra, I can see that P = 2n – 1, meaning that P is odd.
It is hard to give due time in solving questions and to review every answer, right or wrong. However, if you have a particular weakness, or a inefficient process in problem solving, you may not improve even if you practice for a long time. This is a common reason as to why many people do a lot of practice, retake the Gmat, and don’t improve.
I recommend that you take your time in your preparation to review your correct answers in addition to the incorrect ones. Paying attention to how you solve a particular question, and not only to whether or not your answer was correct, will pay off in the end because you will become more efficient at problem solving.