Number Properties

by on September 8th, 2010

Number properties may sound scary, but they just constitute elementary mathematical principles. You probably know most of these principles by memory; if not, you could easily execute a calculation to ascertain them. The best option, though, is to study these principles enough that they seem intuitive. The GMAT Quantitative section is all about saving time; making number theory second nature will definitely save you some valuable seconds.

1. Odds and Evens

Addition

Even + Even = Even e.g., (12 + 14 = 36)

Odd+ Odd = Even e.g., (13 + 19 = 32)

Even + Odd =  Odd e.g., (8 + 11 = 19)

To more easily remember these, just think that a sum is only odd if you add an even and an odd.

Multiplication

Even x Even = Even e.g., (6 x 4 = 24)

Odd x Odd = Odd  e.g., (5 x 3 = 15)

Even x Odd = Even e.g., (6 x 5 = 30)

To more easily remember these, just think that a product is only odd if you multiply two odds.

Example Question

If r is even and t is odd, which of the following is odd?

A. rt
B. 5rt
C. 6(r^2)t
D. 5r + 6t
E. 6r + 5t

In this example, we could either plug in numbers for r and t, or we could use our knowledge of number theory to figure out the answer. We instantly know that rt, an odd times an even, is even. 5rt means we multiply an odd times that even product, which is even. C translates to an even (even^2) times an odd (t), which is even, times another even (6), so that’s even. D adds an even (odd times even) to an even (even times odd) , so that’s even. E adds an even (even times even) to an odd (odd times odd), which is finally odd. E is our answer.

2. Primes

Prime numbers are numbers whose only factors are themselves and one. 11, for example, is a prime because it can only be evenly divided by itself and 1. In some questions, you will have to identify less recognizable primes. Note that 1 is not a prime.

If you were asked to identify the primes between 40 and 60, for example, you should quickly narrow down the primes with a sequence of steps.

First, write down the numbers, and cross out all the even numbers (all even numbers greater than 2 can be divided by 2, and thus are not primes); alternatively, you can just write down the odd numbers in the set.

40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Then, cross out your multiples of 3; it may help you to recall that a number is divisible by 3 if its digits add up to 3.

40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Then, cross out multiples of 5 (those that end in 5 or 0)

40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

We are left with 41, 43, 47, 49, 53, and 59. Take one last look at your group, and you should notice that 49 is 7 squared. So we are now left with 41, 43, 47, 53, and 59.

The more you practice finding primes, the less often you’ll have to do this. But, in the beginning, it’s more important to be thorough than it is to be fast. Missing just one prime means missing the question, so be sure to watch out for those pesky composite numbers like 51 and 57. Remember, practice makes perfect, and Grockit makes great practice.

1 comment

  • thanks
    for
    earlier one...is there any better/simplier/faster way of doing thing rather than checking it one by one for each option...
    i normally check 2 and 3 but most of the time it is timeconfusing....as the option equations are more complicated

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