Everyone feels charmed about their lucky number. They take all pains to add up the digits in their date of birth and get to their licky number. A tiny mathematical trick is quite useful here. In the context of GMAT, I use it extensively to attack remainder problems when large numbers are involved. Say when I have to find out if 3 is one of the prime factors, I use this trick.
This post is deliberately being left out of the Remainders post which is more elaborate and covers more prime numbers than the explanation below entails.
Whenever I have to find the remainder divided by 9, I merely add all the digits and take the sum. I subject the sum to the same trick again and this process goes on repeatedly until I have a single digit. That single digit is the remainder when the number is divided by 9. For example, consider the following number:
The first sum would be: 7 + 2 + 3 + ... + 2 = 38
Repeating on 38, I get a 11 and repeat on 11, the final sum will be 2 which means that the number leaves a remainder of 2 when divided by 9. This also means that the number is not divisible by 3 and leaves a remainder of 2.
What does this mean to GMAT math questions? If you want to quickly find out whether 3 is a prime factor, use this trick and if 3 or 6 is the lucky number, then bingo. 3 is a prime factor involved.
Deciding about 2 and 5 needs no explanations. I am not sensing that the GMAT will test you on higher primes anyway.
NB: As a further shorter cut, do not add 9 if it appears somewhere in the digits. And even drop those numbers that add up to 9. You'd not need a calculator. So in the above number, the result is easy to see even as you glance at the number.
This also has a mathematical proof. So feel safe and exploit the trick