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GMAT quant section and the high school maths syllabus are synonymous. It is stated that a student will be scoring pretty high in the quant section if they were proficient during their high school days. But, despite the syllabus being the same, the difficulty level of the quant section of GMAT is somewhat intense. It is quite expected for the test makers to put an ample amount of confusion mingled with nervousness to make the student feel the same. But, if proper preparation tips for GMAT are followed then non-maths students can also be scoring high in this exam.
The average is a topic that students have been dealing with for a long time now. Few had it during their high school days and some had even during their graduation if they were into science programs. In GMAT, one will come across certain distinct types of sums which will make the students go dizzy at first but what we are going to uncover today will guide them throughout the preparation.
The weighted average is the hardest one as stated by many students out there and it is this type of sums which are counted as problems. Let us discuss this today.
The situation of weighted averages occurs when we consider a combination of different groups and sizes. For instance, in a school, there are plenty of students with a combination of boys and girls. Now, if we are told to count the average of the scores they have received we have to count the number of boys and then girls. It is very unlikely for the GMAT quant section to provide a similar number of boys and girls because that way it is going to tremendously easy to decode the outcome. Here, the numbers provided will very contrast to each other thereby making it tough. Then we will have to combine the gender averages to receive the total average for all students – that is what a weighted average is.
Now when we know how the weighted average is dealt with, we can jump to the ways of solving it. Solving weighted averages in the GMAT quant section can be divided into three ways.
The first one being –
The average term is an umbrella one and has certain ways of solving it. Ordinary average questions can often be solved easily when dealt with the sum’s viewpoint. It is true that we cannot add or deduct anything from the average of the average in general but we can always perform that step with the sums. This is a very trusted way of solving the weighted average problem. Like we discussed in the above example about the groups, it is to be noted that the exam will display even more groups and can even rise to four in number – thus making it quite a challenging one. But here, if we add each individual group and come up with the sums, we can readily add up these sums and the outcome will be the sum of the whole group. Alternatively, if the size of the total group and the average of everyone are mentioned – we can calculate the sum for everyone and then deduct the sum of the individual groups to find out the result.
To ace it up, certain GMAT quant questions come up with percentages instead of actual counts of the individual groups. In this case, what we can do to solve it relatively easily is – assume the percentages to be numbered and then moving on. For instance, group A has 20%, and B and C both have 30% each. We can assume group A to be 3 and group B and C to be 4+4 so the total is 3+4+4= 11. This number will help solve the problem.
There are times when the information about the sizes of the groups are not given in absolute numbers but in percentages or proportions. In fact, in the above examples to we will notice that one is asking for a percentage and the other one is giving out percentages but not actual counts. It is possible to go for the first way but there is even a better one.
In this approach, we will multiply each group average with the percentage of the populations which is displayed as a decimal that group occupies. And when we club all these together, the outcome is the total average for everyone. Let us take, for instance, there are three groups – J, K, and L.
This has to be presented in a decimal form so –
pJ + pK + pL = 1
Then, the total average is placed by –
(pJ)(AJ) + (pK)(AJ) + (pL)(AL) = total average.
Before we start with this method for the GMAT preparation tips, the students need to know that this approach is applicable only when there are two groups and no more.
Now, let us again consider our previous example. We have two groups – 1 and 2. Let us assume, group 1 has a bigger number but a lesser group average. Whereas, group 2 has a lesser number but bigger group average. Now, it is quite obvious if we combine the two groups’ average then the result will be between two individual group averages. Also, as group 1 is bigger the average received will be nearer to that particular group.
In this line, we can notice that the d1 is the distance from the average group 1 to the combined average and the d2 is the distance from the average group 2 to the combined average. Now, the ratio of the two distances is equivalent to the ratio of the size of two individual groups. Here as group 1 is the bigger one, so, it will have more effect on the combined average and thereby nearer to the combined average. Therefore, the ratio of the distances must equalize the reciprocal of the same ratio of the sizes of the groups:
D1/D2 = N2/N1
Let’s assume, group 1 is 3 times bigger than group 2. This indicates d2, the distance from group 2’s average to the combined average, will have to be 3 times bigger than d1, the distance from group 1’s average to the combined average. If the latter is x, then the former is 3x, and the total distance measured is 4x. If we are aware of the averages of the two groups independently, we would precisely have to divide the distinction between those group averages by 4: the combined average would be one part away from group 1’s average, or three parts away from group 2’s average.
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