Number Properties is the most important topic on the Quant section because it underlies all of the other sections. Most *Problem Solving* questions include at the very least some multiplication or division, so the more familiar you can become with numbers, the better. The numbers to get to grips with are the numbers up to 100, for starters, and then from 101-200. You don’t often need to go much further. Here, then, are some drills that you can do to speed that process:

**Doubling and halving**: Pick small numbers at random and double them. Now pick bigger numbers and double them. Then pick small even numbers and halve them. Then bigger even numbers. Then small odd numbers, then bigger odd numbers (halving still). Finally, start with n.5 and double it. And if you want an extension to this task, try tripling and thirding or quadrupling and quartering.

**Factor pairs and factor trees**: You should know what a factor tree is. If you don’t, find out. You need to be able to do a factor tree, quickly, for any number up to 100.

Factor pairs involves listing all of the factors of a number in pairs, like so (using 12 as an example):

1 2 3 4 6 12 (you can even draw little rainbows here to show which pairs multiply to give 12)

or

1 12

2 6

3 4

**Unusual times table****s**: You probably know your times tables from 1-10, or 1-12, depending on your schooling. It’s really useful to go through the following as well:

13, 14, 15, 16, 17, 18, 19

1.5, 2.5, 3.5, 7.5

20, 25, 30, 40, 50, 60, 75, 125

18 is especially important as the numbers appear regularly in geometry questions. 2, 3, 5 and 7 are crucial for prime factorisation: of these, 7 is the least intuitive and is worth going over if you’re not absolutely sure.

**Closest multiple of x to y**: What’s the closest multiple of 6 to 100? How about 7? 8? By changing x and y, you can make this exercise more or less difficult. (The same principle applies to all of these exercises ~ start with easy numbers and go from there.)

**Count backwards**: Can you count backwards in 3s from 30? From 40? From 50? How about counting backwards in 7s from 50? Again, manipulate the numbers to change the difficulty level of the exercise.

**Approximate the square root**: What’s the square root of 50? Well, the square root of 49 is 7; the square root of 64 is 8; and 50 is much closer to 49 than to 64 on the number line, so the square root of 50 is approximately 7.1. Each time you’ll be testing two square numbers, one above and one below, as well as recognising where numbers lie in relation to each other on the number line.

**Powers of 2 and 3**: Run through these two powers until you get up to about 1000. Simple. You could also run through all of the squares up to 25 squared if you feel so inclined.

**Pairs of primes**: Multiply all the possible pairs of primes from 2 to 19. Some of these products are numbers that look like primes but aren’t.