The GMAT is an exam largely focused on numbers and numerical data. And while doing math on the GMAT should be avoided sometimes it is inevitable. True, the test-taker is given a calculator for the duration of the Integrated Reasoning section but the same cannot be said for the Quantitative Reasoning Section.
This article is going to provide some smart calculation shortcuts and mental math tips to help you go through some arithmetical questions without losing too much time and help you get a higher score on the GMAT Quant.
The Basics
Before explaining any methods for dividing and multiplying with ease, let’s make sure we have revised a few simple rules:
- Numbers with an even last digit are divisible by 2 – 576 is and 943 is not;
- Numbers with a sum of digits divisible by 3 are also divisible by 3 – 3,465 for example (3+4+6+5=18);
- If the last 2 digits of a number a divisible by 4, the number itself is divisible by 4 – 5,624 for example (because 24/4=6);
- Numbers with last digit 0 or 5 are divisible by 5;
- Numbers that can be divided by both 2 and 3 can be divided by 6;
- Similar to numbers divisible by 3, numbers divisible by 9 must have a sum of digits divisible by 9 – 6,453 for example;
- If the last digit of a number is 0 it is divisible by 10;
With that out of the way, we can move onto some more advanced mental math techniques.
Avoid division at all costs
Don’t divide unless there is no other option. And that is especially true with long division. The reason why long division is so perilous is that it is very easy to make a careless mistake as there are usually several steps included in the calculation, it takes too much time, and to be honest, few people are comfortable doing it.
Fortunately, the GMAT doesn’t test the candidates’ human-calculator skills but rather their capacity to think outside the box and show creativity in their solution paths, especially when under pressure – exactly what business schools look for.
However, sometimes you cannot avoid division, and when that is the case remember: Factoring is your best friend. Always simplify fractions especially if you’ll need to turn them into decimals. For example, if you have 234/26 don’t start immediately trying to calculate the result. Instead, factor them little by little until you receive something like 18/2 which is a lot easier to calculate.
A tip for factoring is to always start with smaller numbers as they are easier to use (2 is easier to use compared to 4, 6, or 8) and also look for nearby round numbers.
If you have to calculate 256/4 it would be far less tedious and time-consuming to represent 256 as 240+16 and calculate 240/4+16/4=60+4=64. Another example is 441/3. If we express it like 450-9 it is far easier to calculate 450/3-9/3=150-3=147.
Dividing and Multiplying by 5
Sometimes when you have to divide and multiply by 5 (you’ll have to do it a lot) it would be easier to substitute the number with 10/2. It might not always be suitable for your situation but more often than not it can be utilized in order to save some time.
Using 9s
With most problems, you could safely substitute 9 with 10-1. For example, if you have to calculate 46(9) you can express it as 46(10 – 1) which is a lot more straightforward to compute as 46(10) – 46(1) = 460 – 46 = 414
You can also use the same method for other numbers such as 11, 8, 15, 100, etc:
18(11) = 18(10 + 1) = 180 + 18 = 198
28(8) = 28(10 – 2) = 280 – 56 = 224
22(15) = 22(10 + 5) = 220 + 110 = 330
26(99) = 26(100 – 1) = 2600 – 26 = 2574
Dividing by 7
The easiest way to check if a number is divisible by 7 is to find the nearest number you know is divisible by 7. For instance, if you want to check if you can divide 98 by 7 you should look for the nearest multiple of 7. In this instance either 70, 77, or 84. Start adding 7 until you reach the number: 70 + 7 = 77 + 7 = 84 + 7 = 91 + 7 = 98. The answer is yes, 98 is divisible by 7 and it equals 14
Squaring
When you have to find the square of a double-digit number it might be easier to break the number into components. For example, 22^2 would be calculated like this:
22^2
= (20 + 2)(20 + 2)
= 400 + 40 + 40 + 4
= 484
Similarly, if you have to find the square of 39 instead of calculating (30 + 9)(30 +9) you could express it like this:
39^2
= (40 – 1)(40 – 1)
= 1600 – 40 – 40 + 1
= 1521
You can use the same approach when multiplying almost any double-digit numbers, not only squaring. For example 37 times 73:
(40 – 3)(70 + 3)
= 2800 + 120 – 210 – 9
= 2701
Conclusion
This ends the list of mental math tips and tricks you can utilize to make the Quant section a bit less laborious. Keep in mind that no strategy or shortcut would be able to compensate for the lack of proper prep so it all comes down not only to practicing but doing so the right way.
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