Let me put down our framework again as a refresher for you.

1. Identify
2. Read
3. Reflect and Write
4. Organize and Solve

This time, we are going to apply in on a Data Sufficiency problem.

Here is our sample problem:

Question:

If m is an integer, is m odd?

Statement 1:  is not an even integer.

Statement 2: m-3 is an even integer.

1. Let us start by following our algorithm. The first step is to IDENTIFY the type of the problem

Identified the Problem as DS. Next.

2. The second step asks us to READ the problem

Reading the problem simply means glancing through the problem and keeping in mind what information has been given to us and what information has been asked.

In this problem, we have been asked to determine if “m” is even or odd

Statement 1 and Statement 2 give us some information about m.

3. Here we will club the next two steps: REFLECT and WRITE

This is where you decide on how to solve the problem, which information given to you is relevant and what formulas do you need to solve this problem.

• M is even if it is of the form 2k and odd if it is of the form 2k+1
• Statement 1 says is not an even integer.
• Statement 2 says m-3 is an even integer.

Formulas to be used:

• There are no formulas required for this problem

What is asked?

• Is m even or odd?

 

4. At this point, again we will club the next two steps: ORGANIZE and SOLVE

Organize simply means having a clear idea of what information has to be used at what step in solving the problem.

Once you have figured that out in your mind, start writing down things and come to the SOLVING part.

On the DS problems, make sure that you take one statement at a time only. You should never carry information from one statement to other in the first step.

The best way to start solving is write the headings for each statement.

Statement 1:

• ≠ even
• Let us consider values of m here

M	m/2	M = Even/odd
6	3	Even
7	3.5	Odd

• As we can see, M can assume any value, hence we cannot deduce anything about m.

NOT SUFFICIENT

Statement 2:

• m-3 is an even integer.
• We can rewrite this as
• m-3 = 2k
• Hence M = 2k+3.

So, we can identify that m is an odd integer.

SUFFICIENT.

Now, you may be thinking, “I am not at all going to follow this step. This will cause a lot of wastage of time.”

Well, after looking here you might think that I have to perform so many steps, but if you do not perform these steps and randomly start solving the problem from the word go, there is a high possibility that you might actually end up solving something else that is not asked in the problem.

Whereas if you dive in the problem without a plan, the solution will be much faster than in the case in which you are trying to solve a problem without a plan.

What if you can’t reflect and organize things and come up with a clear plan? The best thing to do in such case is to not to waste much time on the problem, make an educated guess and move on to the next one.

Key Takeaways for Every Problem You Will Ever Do:

1) First, understand what’s in front of you. Identify and Read the problem to pick up any clues, complexity, and strategies available. As you Read, Write down the given information.

(2) Next, Reflect on what you’ve been given and Organize your thoughts on your scratchpad. You might need to go back and forth between Reflect and Solve a couple of times. When you have to decide what work you need to do and whether you have enough to go ahead and solve the problem.

(3) Finally, solve the problem, back to Reflect and Organize, whenever needed. By going through the previous, now you must have understood the problem and would have a plan to solve it. If not, then make an educated guess when possible (estimate, for example) or just pick your favorite letter and move on.