GMAT Quant Shortcut Techniques

Quantitative reasoning of the GMAT exam is a difficult section. This is where your mathematics skills are tested and you are expected to solve many questions within a given period of time. Since this is a section where you have to do a lot of calculations, it could be time consuming. Hence, this is where GMAT quant shortcut techniques work. In this article, we will discuss some important shortcuts to solve GMAT quant questions.

Why Should You Learn GMAT Quant Shortcut Techniques?

Why do you have to learn shortcuts or approaches to solve aptitude questions? This is because the most important factor in any aptitude exam is time and this is no different for the GMAT exam. Besides, it’s even more important to learn shortcuts to solve questions in GMAT because you are not allowed to use any online or physical calculator.  

In the GMAT Quant section, there are a total of 31 questions, which you have to solve within 62 minutes. So, on an average, you would need two minutes per question. Having said that, this two minutes per question strategy doesn’t always work. This is because easy or medium level questions could be solved in under 1.5 minutes and difficult or extremely difficult questions might require 2.5 minutes to 3 minutes. Since time plays a crucial role here, hence, it is important to learn GMAT quant shortcut techniques or approaches to solve questions faster.

Moreover, if you are someone who doesn’t have a strong mathematical background or if you are professional and have lost touch with your studies, then these GMAT quant shortcut techniques are very handy. This will help save your time and effort to solve complex mathematical problems in the quant section of the GMAT exam.

Before we discuss the shortcuts or strategies, let’s give you some tips to speed up your mental calculations. 

Tips to Help You Speed up Mental Calculations for the GMAT Quant Section:

  • Make sure you memorize multiplication tables up to 30.
  • Learn to identify square, square roots, cube and cube roots of numbers up to 30. 
  • When you practice, never use a calculator! Do all your day-to-day calculations mentally. If you start using a calculator then you may become dependent on it. And, since  you are not allowed to use a calculator for the GMAT quant section, it’s ideal that you practice without it. 

Without further ado, let us dive into these simple mathematics shortcut techniques to help you overcome challenges in the quant section of the GMAT exam.

GMAT Quant Shortcut Techniques

There are a lot of shortcuts to solve questions in the Quantitative exam, let’s look at some of them. 

  1. Addition and Subtraction:

We are not going to learn any Vedic mathematics or any abacus methods to solve calculations faster. We are just going to learn simple methods to solve a complex calculation. 

We know that the numbers which are tens or multiples of tens are always easier to calculate. But, how do we  add or subtract numbers which aren’t multiples of ten or hundred? 

This is very simple, find its nearest tens number and then add or subtract. For example:

  1. 172 + 47

In case of 47, the nearest number with multiple of 10 is 50

Hence, the calculation can be done as

172 + (50-3) = 219

If you want to simplify it further, you can also find the nearest multiple of ten for 172.

170 + 2 + 50 -3 = 219. Bingo!

Now, let’s take a slightly bigger number this time.

  1. 2285 – 192

= 2285 – (200 – 8) 

= 2285 – 200 + 8 = 2093

OR
= 2300 – 15 – 200 +8 = 2093

  1. Multiply or Divide by 5:

To divide a number by 5, double the number (i.e., multiply the number with 2) and divide the result by 10. The simple and logical reasoning behind this trick is that it is easier to double a number and multiply or divide a number by 10.

Because 15=210  

For example:

  1. 93 divided by 5?

= 93*210

Again, at this stage, if you are comfortable with large numbers then don’t waste time by multiplying 93 with 2, rather use the above shortcut which we learnt, 

90 + 3 = 93

= (90+3) * 2 

= 180 + 6 = 186

Now, 18610

= 18.6

Hence, the desired result of 93 divided by 5 is 18.6.

Now, to multiply a number with 5, just do the reverse process.

Multiply with 10 and divide it by 2.

5=102

For example: 

  1. 88 * 5

= 88*102 

= 440.

You can extend this rule even to multiply or divide with 25.

We know that, 25=1004

Similarly, 125=4100

For example:

  1. 68 * 25

= 68*1004

= 17 * 100

= 1700.

  1. 1430 divided by 25.

= 1430*4100

= 1400+30*4100

= 5600+120100=5720100=57.2  

Now that we have learnt a couple of shortcuts to do the calculations faster. Let’s discuss the two strategies to solve the word problems faster. 

How to Solve GMAT Word Problems Faster?

  1. Alligation method to tackle the mixtures algebra questions and weighted average questions.
  2. Product constant rule for word problems.

Both these concepts are based on a simple application of ratios. Assuming that you already know the ratio and proportion concepts. If you don’t, get started with familiarizing yourself with it. 

Let’s discuss these two strategies elaborately. Here are two ways to solve GMAT word problems faster.

Strategy Number -1 – Alligation:

  • Alligation in Mixtures:

Alligation is the simple concept of deriving ratios from the weighted average.

So, what is the weighted average?

The weighted average is similar to simple average, except that instead of each of the data points contributing equally to the final average, only some data points contribute more than others.

For example, if there are two points 70 and 80 and both accounted once, then the average of 70 and 80 is 70+802=75. But if there are two 70’s and one 80 i.e., 70, 70 and 80, then average is 70*2+803=2203 ~73.33 

When some values get more weight than others, the central point (the mean) can change:

So, how to write the formula then,

If “n” is the weight of a data point “x” and “m” is the weight of a data point “y”, then the weighted average 

A=n*x+m*yn+m

Similarly, we can extend this to the average of two different objects.

If “n” objects have an average of A1 and “m” objects has an average of A2, then the weighted average = 

A= n*A1+m*A2n+m

Now, what is Alligation?

Let’s solve the above equation to understand this better.

An+m= n*A1+m*A2

A*n+A*m= n*A1+m*A2

A*n-n*A1=m*A2-A*m

nA-A1=mA2-A

So, nm=A-A1A2-A

So, the above ratio is the weights of the data points.

Whenever there are different data points given and the weighted average is provided, we can find the ratio of the weights of the two data points. Let’s see how to solve this using the short-cut Alligation.

Write in the form below:

Data point-1                  Data point-2 

         A1                    :               A2                

                   Weighted Average(A)                  

A2-A               :              A-A1 

Data point-1Data point-2=nm=|A2-A||A-A1|

Fox example: 

  1. If the average height of girls is 160 cm and that of boys is 175 cm, if the average height of all the class is 165 cm, can we calculate the ratio of boys and girls in the class?

      Boys                                Girls 

       160                    :             175                

                           165                 

175-165=10    :              165-160=5 

BoysGirls=105=21

That’s it. Bingo!. This might hardly take 30 seconds or less to solve.

So, you can use this method not only to calculate the average, but also whenever there are two mixed data points and when the weighted average (resultant) is given.Using these Alligation techniques will help you in finding out what ratio they are mixed within a short span of time and most importantly without using algebraic methods.

We can also use it in mixtures, profit and loss, interest questions, etc.

Now let’s see the second strategy.

  1. Product of Parameters:

The second shortcut we are going to learn about is when the two parameters are inversely proportional to each other, their product is constant. This is a very important technique to solve word problems pertaining to ratios.

If A is inversely proportional to B, that is, A∝1B then

A*B=C where C is constant

Let’s take a look at the scenarios where this relation is applicable,

  1. Speed and Time

Speed is inversely proportional to time, as speed increases time will decrease and vice-versa, where the distance is constant.

S∝1T

S*T=Distance

If “a” and “b” are different speeds for the fixed distance, then the respective time taken will be in the ratio of  ba

S1S2=ab then T1T2=ba

Let’s take a look at an example

  1. A man walked from his house to the office at 5mph and got 20 minutes late. If he had travelled at 7.5 mph, then he would have reached 12 minutes early. What is the distance between his home and work?
  • 2
  • 4
  • 6
  • 8
  • 12      

Original Speed(S1)Increased Speed(S2)=57.5

Since, speed and time are inversely proportional

Original Time(T1) Reduced Time(T2)=7.55

We know the difference in time.

T1T2=7.5x5x

Given the difference in the times = 20 + 12 = 32 minutes

7.5x-5x=32mins

2.5x = 32 mins

and original time T1= 7.5x = 96 mins

converting minutes to hours, 9660

So, distance from his home to office

Distance = Speed * time taken = S1*T1=5*9660=8

Hence the answer is D.

There are a lot of such techniques and shortcuts to solve word problems in Algebra Arithmetic, Geometry and Statistics. 

Only knowing or understanding the following GMAT quant shortcut techniques will not guarantee you success in the GMAT quant section. You should have a systematic approach to solve a GMAT quant question and most importantly you should have a good knowledge of the basic mathematics concepts. 

Hope this article was helpful and you will be able to solve certain questions in the quant section faster. All the best for your preparations!

Talk to an expert?

Leave a Reply

Your email address will not be published. Required fields are marked *