GMAT number system, GMAT QUant, GMAT solvingThought it might be quite obvious to most of you that the goal of any GMAT question is to get the answer right, what may not be so obvious is that ‘GMAT is less about “doing math” than approaching a problem strategically’. The value of any strategic approach resides in its ability to let you get to the answer quickly and accurately than traditional classroom math does. At the core of every strategic approach is pattern recognition, which let’s us determine the strategy a question is testing and the strategic approach necessary to help us get to the right answer quickly.

Today we’ll talk about one such strategic approach (one of our favourites at Kaplan-LogIQuest): Picking Numbers. This approach is quite effective since it ensures that we stay open to possibilities that may not occur to us immediately (or even eventually). Picking Numbers works best in situations in which a question asks “what must be, could be, or cannot be true”. On these questions, we can pick our numbers and plug them in each answer choice or pick different numbers for each answer choice trying to eliminate them.

Let’s see this at work with a GMAT like Quantitative reasoning question:

If integers a and b are distinct factors of 30, which of the following CANNOT be a factor of 30?

  1. ab+b2
  2. (a+b)2
  3. a+b
  1. I only
  2. II only
  3. III only
  4. I and II only
  5. I,II and III

Here we’re asked which of the following cannot be a factor of 30: this means that we are looking to eliminate anything that could be a factor of 30. In order for us to eliminate a Roman numeral here, it’s not that it must be a factor of 30. It’s simply that it could be a factor of 30. We are told that integers a and b are distinct factors of 30. This means that we need to figure out what they could be. A factor chart is a great tool to make use to ensure that we’ve accounted for all the possible factors of a given number.

Here’s the factor chart for 30 which says that a and b could equal to 1, 2, 3, 5, 6, 10, 15, or 30. Any one of those are possibilities, but we know the two variables have to be different from one another. Let’s pick some agreeable numbers and then go to the Roman numerals to see what we can eliminate by proving that it could be a factor of 30.

Let’s start by picking 2 and 3 respectively for a and b. These numbers are good because they are small easy to calculate numbers that will work with the problem. Now, let’s attack this by starting with the Roman numeral statement that appears most frequently in the answer choices, Roman numeral I. If we can get rid of that one, we can eliminate numerous answer choices at once and improve our chances of getting the right answer. With a equals 2 and b equals 3, we know that a times b is 6 and b squared is 9; add those together and we get 15, which is definitely a factor of 30.

We can eliminate Roman numeral I and any answer choice in which it appears: (A), (D), and (E). Looking at the remaining answer choices, we know that only one of the two Roman numerals left will work. If we try plugging in 2 and 3 to each of the remaining Roman numerals starting with II, we have 2 plus 3 squared and that ’s 25, which is not a factor of 30. Thus, we can’t eliminate anything else at this point. In Roman numeral III, we have 2 plus 3, or 5, which is clearly a factor of 30. That means we can eliminate any answer choice that has Roman numeral III in it. Get rid of (C).

That leaves us with only answer choice (B), which means we don’t need to pick another set of numbers to see if Roman numeral II would yield a different result. We know it won’t, because (B) is the only answer choice we have left.

And that’s how simple these questions can get if approached methodically with the appropriate strategy.


Thirsty for more GMAT Quant strategies? This blog on Patterns on GMAT Quant should help quench that thirst!