GMAT Math: Calculation Shortcuts
The GMAT for many is not simply a test of your ability, but rather a test of how fast you can use your abilities. It's a race against time to find the right answer, where you have to use every trick you have to save your time.
By learning simple tricks to speed up regular calculations you can save yourself much needed time during the exam. These shortcuts will allow you to find solutions quickly, check answers faster and even make best guesses.
Here are two easy to learn tricks that can help you increase your speed during the challenging quantitative section of the exam.
Multiplying numbers the easy way:
Quite often during the GMAT you will have to multiply numbers together. You may be trying to find the total weight of objects within a box, or even calculating the distance on a map, but fundamentally they are all simply asking you to multiply numbers together.
Lets take the example of a common map based question:
On a map each centimetre is equivalent to 60km. The distance between two islands is 27cm on the map. What is the true distance in km?
This is a very basic question which simply asks you to multiply 27 and 60.
We could begin the process of long multiplication and find the answer, but there is a much easier method.
We begin by using 60 as our base. It's an easy number to work with, and we can work out most of its multiplications simply because it follows the 6 times table.
In the first step we break the remaining number, 27, into it's parts. We do this simply by separating the tens and unit digits so we have a 20 and we have a 7.
Instead of the long multiplication, we now have two much shorter expressions:
20 × 60
7 × 60
Remember, 27 × 60 simply means 27 lots of 60. (Or think about it as 27 boxes all containing 60 items each). It makes little difference whether we count them all together or in parts, as the answer will always be the same. In our example, instead of calculating 27 lots of 60 at once, we are going to count 20 lots first, then the remaining 7, but ultimately it will still give us the same answer.
So now we have two much easier expressions, which you can learn to solve in seconds.
What we do is simply take the zero of the end of 60 and leave it as a 6, making the equations even easier. We will simply add the zero back later.
This will give us:
20 × 6
7 × 6
Both are very easy calculations:
20 × 6 = 120
7 × 6 = 42
Remember, if 20 × 6 = 120, then 20 × 60 is simply going to be an extra zero on the end:
20 × 60 = 1200
7 × 60 = 420
So, 27 × 60 = 1620. Simple!
Once you learn the method you can do it in your head even without having to put pen to paper.
This method does rely however on your ability to multiply basic numbers. A very basic first step for which is, of course, learning your timetables up to 20 inclusive. This will save you a huge amount of time and allow you to speed up many mathematical calculations.
Let's try one more example:
70 × 33
We simply break 33 down into 30 and 3 respectively leaving us with:
70 × 3
70 × 30
Now we begin calculating:
70 × 3 = 210
70 × 30 = 2100
Adding them together gives us the total: 2310.
Quick and easy, saving you much needed time on the exam. The more you practice, the easier it will become.
Percentages the easy way:
Quite often on the GMAT exam you will be asked to calculate percentages. The traditional way involves multiplications and divisions to find the answer, but quite often we can simply use a little trick to get there faster.
It works on the principle of finding 10% of a number quickly and then deducing the corresponding 1%.
To find 10% of any number, we simply add a decimal place.
So for example, 10% of 70 is simply 7.0
10% of 543453 is 54345.3
The last example may not be the easiest to work with but it does prove that you can find 10% of any number fast. The next step is to find 1% of a number, which again is simply adding another decimal place to our 10%.
So 10% of 70 is 7.0 and 1% of 70 is 0.70
Now if you were asked to find 20% of 70, you could do it easily. You would firstly find 10% as above, and then multiply it by 2 to give you 20%:
10% of 70 is 7.0
20% of 70 = 2 × 10% = 14
You can use this trick to find almost any percentage. Let's make it harder and try to work out 42% of 70.
42% is simply 40% plus another 2%, so as we learnt earlier we simply split this into two different equations.
40% of 70 = 4 × 10% or 4 × 7.0 = 28
2% of 70 = 2 × 1% or 2 × 0.7 = 1.4
Adding them together gives us 42% of 70 or 29.4
Naturally these two methods will take a little practice initially, however you will quickly begin to see the power of these tools and you will start to notice a major increase in your speed of calculations, something that will help immensely in your race against time on the GMAT exam.
- GMAT Math:Picking Numbers
- GMAT Math: Backsolving
- GMAT Math: Comparing Fractions
- GMAT Math: Learn from Nature