Six Process Skills in Quant
INTRODUCTIONI am going to start this article by making a statement, and I want you to tell me if you agree with it.
I am very confident that you would wholeheartedly agree with the above statement. After all, that is the way we have been learning all our lives. So why should GMAT Quant be any different!
Well, the truth is that the mantra described above not only is very inefficient but also does not always produce favorable results. And this is the reason why, at
e-GMAT, we follow a different mantra, which is woven into the very fabric of our verbal and quant courses.
Here is the
e-GMAT mantra marked up from the above one. Notice the highlighted changes.
As you can see, there are two main points of difference:
1. The e-GMAT mantra includes the mastery of process skills that are absolutely essential to solve GMAT questions.
2. Per the e-GMAT mantra, one does not need to solve as many questions as possible. On the contrary, one needs to solve only those many questions that are necessary to reach one’s target ability.
This article explores the first point of difference – the “process skills.” Our goal is to help you recognize the value of the process skills. And once you do understand the importance of these skills, we will guide you about how you can build these skills so that you reach your target score in Quant.
To summarize this section, we will mathematically present the
e-GMAT mantra to success in Quant.
PROCESS SKILLSIMPORTANCE OF PROCESS SKILLSBefore we go into the “what” of the process skills, let me explain the “how”- i.e., how do process skills help you reach your target score.
Let’s set some background - I think it will be fair to assume that all of us know the importance of learning the concepts. So, for the sake of this discussion, let’s assume that your conceptual knowledge is solid.
Now, I want you to ponder about these two questions:
1. Have you ever wondered why you make a mistake despite having the conceptual understanding?
2. Have you ever wondered why it is that you need to solve thousands of questions to master GMAT Quant?
Here are the answers:
1. You make a mistake not because you don’t know the concept, but because you do not know how to apply that concept.
2. Likewise, you need to solve so many questions to reach that level of ability despite knowing the concepts since you have not learned the method to apply those concepts to solve GMAT questions, and that is why you need to practice and practice with the hope that you will reach your target score. And you know by experience that this approach is a hit or a miss.
So how do you solve this problem of “application”?
This is where “process skills” come into the picture. To learn how to APPLY these concepts, you
need to learn these process skills. And as you master these process skills, your ability to answer GMAT questions improves.
After thousands of hours researching the official content, we have formulated six process skills that you need to master to solve difficult quant questions with ease and accuracy.
Here they are:
1. Infer
2. Translate
3. Simplify
4. Visualize
5. Consider all cases
6. Apply constraints
In this article, we will outline each of these skills, and then over the next few weeks, we will delve into each process skill in detail.
APPLICABILITY OF PROCESS SKILLSThese process skills are applicable across all sub-sections of Quant and both types of quant questions – PS and DS. So, as you master them in the context of one sub-section, you will notice that your proficiency in those skills will improve in the other sub-sections. To offer a simile, building these process skills is akin to building a muscle, as you build a muscle in the context of one sport say tennis, your performance also improves in other sports, such as racquetball or squash.
LEARNING PROCESS SKILLSBefore I explain each of the process skills, I want to make sure that you do not feel burdened by the prospect of learning something brand new. In fact, it’s quite the opposite. Mastering process skills is a very logical activity, one that focuses on re-channeling your existing resources – i.e., your conceptual knowledge - to maximize their output.
PROCESS SKILL 1 – INFER“INFER” DEFINITIONOne needs to continually infer or deduce throughout the solution – not just in the beginning, not only in the middle, and not just in the end. As you learn to apply this process skill, you learn to stay actively engaged while solving the questions. This, in turn, helps with the timing aspect of the test.
We will take an example to demonstrate this process skill to you. Solve this 700-level question. This question is from the Official GMAT Practice Exam.
QUESTIONAll boxes in a certain warehouse were arranged in stacks of 12 boxes each, with no boxes left over. After 60 additional boxes arrived and no boxes were removed, all the boxes in the warehouse were arranged in stacks of 14 boxes each, with no boxes left over. How many boxes were in the warehouse before the 60 additional boxes arrived?
1. There were fewer than 110 boxes in the warehouse before the 60 additional arrived.
2. There were fewer than 120 boxes in the warehouse after the 60 additional arrived.
Now review the solution of this question. If you prefer a video solution, you may view it
here.
SOLUTIONINFERENCE PROCESS SKILL AT PLAYObserve carefully what would have happened if you had not drawn the inference that x+5 is a multiple of 7. You would have still arrived at the fact that statement 1 is not sufficient, but you would have also considered that statement 2 is not sufficient since x could be 1, 2, 3, or 4. Even by combining the two statements, you would have concluded that the information is not sufficient, thereby selecting choice E as the correct answer.
Thus, drawing inference is the key to solving this question.
Now let’s look at how we arrived at the inference.
1. Information from the processing of the question statement.
2. Required Conceptual Knowledge
a. 6 is not a multiple of 7.
b. Understanding of product of two numbers.
3. Inference
a. Since 6 is not a multiple of 7, given the relationship, (x+5) has to be a multiple of 7.
We will discuss this skill in further detail in the subsequent articles that follow.
For now, review the definition of “Infer” once again.
PROCESS SKILL 2 – TRANSLATE “TRANSLATE” DEFINITIONPrimary function of GMAT Quant questions is to test your quantitative ability. But they
also test your understanding of English language in the context of how comfortably you can convert English to Math and Math to English.
Naturally, given the nature of this process skill, it is applied usually in the beginning of the solution to convert the English to Math or towards the end of the solution to convert the Math to English.
We will take an example to demonstrate this process skill to you. Solve this 700-level question. This question is from
the Official Guide Advanced book.
QUESTIONIf x is a positive integer, how many positive integers less than x are divisors of x?
1. \(x^2\) is divisible by exactly 4 positive integers less than \(x^2\).
2. 2x is divisible by exactly 3 positive integers less than 2x.
Now review the solution of this question. If you prefer a video solution, you may view it
here.
SOLUTIONTRANSLATION PROCESS SKILL AT PLAYObserve the solution and notice how we read the question statement to determine what the question is asking us. For your kind perusal, we have presented the details of how we did the translation.
___________________________________________________________________________________________________
If x is a positive integer, how many positive integers less than x are divisors of x?• If x is a positive integer,
• how many positive integers less than x
o need the number of integers
• are divisors of x?
o These integers are factors of x
• We need the number of factors of x but these factors should be less than x.
o Total number of factors of x – 1
since the total number of factors of x also include the number x itself
• Notice that you are using your conceptual understanding of “the total number of factors”.
____________________________________________________________________________________________________
We want to draw your attention to the following points:
1. Notice how we strategically paused to translate. We split this short question statement into 3 parts. This is very important so that you don’t miss out on any critical information.
2. Notice how we brought in our conceptual understanding of the total number of factors of a number.
3. Notice how this translation is helped us arrive at the mathematical form of what the question is asking us. In the absence of this step, we would have been completely lost in the question statement. And the individual statements would not have helped at all.
We will discuss this skill in further detail in the subsequent articles that follow. But for now, we want you to actively start translating information by reading the question statement by strategically pausing.
For now, review the definition of “Translate” once again.
PROCESS SKILL 3 – SIMPLIFY “SIMPLIFY” DEFINITIONSolving a question in methodical manner requires that we convert complex looking expressions into simpler forms and that is why mastering this skill is very important. In fact, this is a key skill to succeed in life as well. Breaking down complex situations or problems into simpler small problems facilitates effective solutions!
We will take an example to demonstrate this process skill to you. Solve this 700-level question. This question is from
the Official Guide Advanced book.
QUESTIONFor each positive integer k, let \(a_k = (1+{\frac{1}{k+1}})\) . Is the product \(a_1 a_2 … a_n\) an integer?
1) n + 1 is a multiple of 3.
2) n is a multiple of 2.
Now review the solution of this question. If you prefer a video solution, you may view it
here.
SOLUTION SIMPLIFY PROCESS SKILL AT PLAYObserve the solution and notice how while analyzing the question statement, we have taken such a complicated looking expression and very comfortably we simplified it into such a simple form – is \(\frac{n+2}{2}\) an integer?
This is the process skill of “simplify” in action.
We want you to realize this fact - difficult GMAT Quant questions often contain complicated looking expressions. And we also want you to understand that the test maker will not throw anything at you that you cannot handle. The way you do not have to be a grammarian to answer SC questions correctly, you do not need to be a mathematician to answer difficult quant questions correctly.
And this the reason for the importance of “simplify” process skill. Whenever you see something scary and complicated, remind yourself that you have everything in your arsenal to tackle that complicated expression. And you utilize the process skill of simplify.
At this point, I want to ask you a question – Look at the part where we simplify the question statement. And tell me – is there any conceptual knowledge required to do this simplification? The answer is no. All that is needed is the comfort level in applying the process skill of “simplify”.
We will discuss this skill in further detail in the subsequent articles that follow. But for now, we want you to not get scared of complex expressions but take them up head-on with the confidence that you will simplify them.
For now, review the definition of “Simplify” once again.
PROCESS SKILL 4 – VISUALIZE “VISUALIZE” DEFINITIONThis skill is very essential, especially when the given information appears to be an overload on our mental faculties. In some way, we are ‘simplifying’ the complex information in a visual form so that we can make better sense of that information.
We will take an example to demonstrate this process skill to you. Solve this 700-level question. This question is from
the Official Guide.
QUESTIONA border of uniform width is placed around a rectangular photograph that measures 8 inches by 10 inches. If the area of the border is 144 square inches, what is the width of the border, in inches?
Now review the solution of this question. If you prefer a video solution, you may view it
here.
SOLUTIONVISUALIZE PROCESS SKILL AT PLAYIt is very important to understand the question statement and convert it into a visual form so that we get more comfortable with the information provided. Such visual aids enhance the clarity in our mind and help us get closer to the solution of the question.
So never give into your laziness. At the same time never feel overconfident that you can do it all in your mind. Use your mind to do the processing and utilize these visual aids to make that processing more effective.
We will discuss this skill in further detail in the subsequent articles that follow. But for now, we want you to consciously draw such diagrams and/or tables so that you get the level of clarity that you need to solve the question correctly.
For now, review the definition of “Visualize” once again.
PROCESS SKILL 5 – CONSIDER ALL CASES “CONSIDER ALL CASES” DEFINITIONThis skill is very essential while solving both PS and DS questions.
We will take an example to demonstrate this process skill to you. Solve this 700-level question. This question is from
Official Guide Advanced book.
QUESTIONEach entry in the multiplication table above is an integer that is either positive, negative, or zero. What is the value of a ?
Now review the solution of this question. If you prefer a video solution, you may view it
here.
SOLUTION“CONSIDER ALL CASES” PROCESS SKILL AT PLAYThere are three things that I want to highlight, now that you have gone through the solution.
Critical process skill:I want to draw your attention to the analysis of statement 2. You would agree with me that if you failed to consider the case in which c = f = 0, then you would arrive at incorrect answer choice.
Consider all cases is a very critical process skill that is often overlooked. In fact, the test maker while framing difficult questions, relies on you not applying this process skill.
So, every test taker should work on building this process skill.
Conceptual understanding:Application of this skill has little to do with your conceptual understanding. Its more about being aware of the confines that you are working with.
Feedback:Review the solution one more time and tell me – if you had made that mistake, what remedial action would you have taken?
Majority of students would have stated this mistake as a silly mistake and hence from learning perspective, you would have lost an amazing opportunity to learn from this question.
On the contrary, if you started applying these process skills and you made this mistake, this
e-GMAT solution would have pointed it out that you faltered here because you failed to apply the process skill of “consider all cases”. Such precise feedback is what you need to improve as you solve next set of questions.
This is the “magic” of applying process skills. It not only helps improve your accuracy for medium and hard questions, it also helps with improvement in ability as you incorporate such feedback.
We will discuss this skill in further detail in the subsequent articles that follow. Next, we will talk about our last and definitely a very important process skill – Apply Constraints.
For now, review the definition of “Consider all Cases” once again.
PROCESS SKILL 6 – APPLY CONSTRAINTS “APPLY CONSTRAINTSThere are two kinds of constraints that one needs to be cognizant of.
• Constraints per the information in the question statement.
• Constraints per the conceptual understanding such as square of a number is always a non-negative number.
We will take an example to demonstrate this process skill to you. Solve this 700-level question. This question is from
the Official Guide.
QUESTIONHow many integers that satisfy the inequality \(\frac{(x + 2)(x + 3)}{(x - 2)} ≥ 0\) are less than 5?
Now review the solution of this question. If you prefer a video solution, you may view it
here.
SOLUTION“APPLY CONSTRAINTS” PROCESS SKILL AT PLAYNotice carefully how we first simplified the inequality, and we brought it in a familiar form. That was essential for the solution of the question. At the same time, it was essential to note the constraints imposed on the system by the question statement. The given inequality holds. And this inequality has (x-2) in the denominator, so x cannot be 2 since the denominator cannot be zero. You may wonder – how do I know when to do such analysis. And the straightforward answer is that you do such analysis automatically when you start to apply the process skill of “apply constraints consciously”.
We will discuss this skill in further detail in the subsequent articles that follow.
For now, review the definition of “Apply Constraints” once again.
CONCLUDING REMARKS You would have now gotten a flavor of these process skills. Over the next few weeks, we will publish articles so that you get more accustomed to each of these skills.
In fact, you can start applying these process skills starting today – I recommend taking a printout of this attachment and stick it in your study area so that you consciously remind yourself to apply these skills. As you start applying them, these skills will become second nature to you, and you will realize that mastering these process skills is a matter of developing good habits. Also, do a thorough strategic review of solutions and make an explicit mapping of the mistake to one of these process skills and/or conceptual gaps. Such analysis will take you to that next ability level in your preparation.
And with focused content that helps you master these skills, in no time you will be on your way to conquering GMAT Quant.
So, get on the journey to master these process skills. _________________