About: GMAT, Maths, Numbers, Quantitative, Shortcuts
A short list of small time saving tricks my teacher has kindly tought me and I thought I would pass them along.
Those tricks are actually quite useful to know and the GMAT loves to ask those sorts of questions, looks terrifying on paper with huge calculations to do but actually if you know a few tricks they are easy.
Relations between Odd and Even Numbers
It seems that a lot of questions are about the relationship between odd and even. Generally the GMAT is only looking to check that you understand the relationships between Odd and Even numbers. Here are the simple ones:
Multiplication
- even × even = even
- even × odd = even
- odd × odd = odd
Addition and subtraction
- even ± even = even
- even ± odd = odd
- odd ± odd = even
Remember that the number 0 is considered an even number.
Multiplying big numbers by 11
Multiplications by 11? I tend to simply multiply by 10 and add the number to the result once. But this is apparently the slow way of doing it. Here is the fast and easy way:
For example:
11 x 35 = 385
How do you get that, simply take the digits you are multiplying by 11, in this case 3 & 5, add them up 3+5 = 8 and add , if you add that number in between the two digits you are multiplying by 11.
There is one other thing to remember, if you add up the numbers and get a number superior to 10 (such as 12 ) don’t forget to add the 1 to the first digit.
For Example:
11 x 68 = 748 (6+8 = 14) thus you need to transfer the 1 to the digit before (6+1 = 7)
For larger numbers, there is a system called adding the neighbour where you add each number by its neighbour. I have tried this a few times but find my method easiest for larger numbers.
Multiplying two numbers ending by “5” quickly
If you have two identical positive integers who end in 5 that need to be multiplied, its easy:
25 x 25 = 20 x 30 +25 = 85
55 x 55 = 50 x 60 + 25 = 3,025
105 x 105 = 100 x 110 + 25 = 11,025
Just remember to always add the 25! Doesn’t work for 5 x 5 (obviously)
Finding out if a number is divisible by 3, 6 or 9
Add all the digits in the number you are trying to find out together, and if they add up to a 3, 6 or 9 or a multiple of those, then yes that number is divisible by 3, 6 or 9.
For example:
47,382 = 4+7+3+8+2 = 24 which is therefore divisible by 3 (3×8) and also 6 (6×4) but not by 9.
532 = 5+3+2 = 10 which is not divisble entirely by 3, 6 or 9
4,653 = 4+6+5+3 = 18 which is divisible by 3 (3×6) 6 (6×3) and 9 (2×9)
Finding out if a number is divisible by 4 or 8 entirely:
On the GMAT you are often given questions with impossibly long numbers and they ask, is this number evenly divisible by 4 or 8? Instead of making long lists on paper to work out if that is the case, look at the last two digits of the number to find out if that number is divisible by 4 or 8. As a quick tip, if the last digit is not a multiple of 2 (an even number) than that is your answer (NO!)
For example:
Is 234,928 divisible by 4? 28 = 7×4 so yes
Is 1,204 divisible by 4? 04 = 1×4 so yes
Is 535 divisible by 4? 35 = 8,75 x 4 so no
Finding out if a number is divisible by 11 entirely:
Take a number you’d hate to divide out longhand: 1,358,024,668.
Add its first digit to its third to its fifth etc. till there are no more: 1 + 5 + 0 + 4 + 6 = 16.
Repeat with the even digits: 3 + 8 + 2 + 6 + 8 = 27.
Subtract the larger number from the smaller. If the result is 11 or 0, your number is divisible by eleven, otherwise not. In this case, 27 – 16 = 11, so 1,358,024,668 IS divisible by eleven.
Easy no?
About: GMAT, Maths, Numbers, Quantitative, Shortcuts
