GMAT Math : Conceptual solving

Many times we don’t actually have to solve a Data Sufficiency question. A good conceptual understanding of the situation helps shortlist options.

Let’s look at an example :

Is the average of set x consisting of 9 positive numbers less than the average of set y consisting of 8 positive numbers

  1. Each of the numbers in set x is greater than each of the numbers in set y
  2. The sum of set x numbers is less than the sum of set y numbers

The first statement logically qualifies the question statement. If each of the numbers in one set is greater than each of the numbers of the other set, then the average (which will fall somewhere in between the range of the numbers) of the first set must be greater than the average of the second set.

The second statement is a bit trickier.

Let Sx denote the sum of the first set and Sy denote the sum of the second set.

Sx /8 is the average of the first set and Sy/9 is the average of the second set.

We are given

Sx  < Sy

Now it follows,

Sx/9  < Sy/8  (since a smaller number is being divided by a bigger denominator)

Hence, each statement alone is sufficient and we go with option (C)

Key learning: Good to have a ‘conceptual’ understanding of constructs like averages, medians and absolute values. Notice how we could rapidly process statement 1 without writing any intricate equations. Statement 2 could also be processed similarly. All done in 30 seconds!

Our hackbook has a comprehensive coverage of questions where you can practice this skill