GMAT Math : Understanding the properties of integers
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Example Questions
Example Question #31 : Understanding The Properties Of Integers
Add the composite numbers between 81 and 90 inclusive.
The only prime numbers from 81 to 90 are 83 and 89, so we add:
Example Question #32 : Understanding The Properties Of Integers
Add the prime numbers between 60 and 90.
The prime numbers between 60 and 90 are:
Add them:
Example Question #33 : Understanding The Properties Of Integers
Add the factors of 29.
29 is a prime number and therefore has two factors, 1 and itself. The sum of the two is 30.
Example Question #34 : Understanding The Properties Of Integers
How many integers from 71 to 100 inclusive do not have 2, 3, or 5 as a factor?
The factors of 2 are exactly the integers that end in 2, 4, 6, 8, or 0, and the factors of 5 are exactly the integers that end in 5 or 0. Therefore, we will start with the integers that end in 1, 3, 7, and 9, and eliminate the multiples of 3:
Of these, 81, 87, 93, and 99 are the only multiples of 3. Remove them and we have the set
a set of eight elements.
Example Question #34 : Properties Of Integers
Which of these numbers is relatively prime with 45?
For a number to be relatively prime with 45, it cannot share any of its prime factors.
so a number is relatively prime with 45 if and only if neither 3 nor 5 is a factor.
57 and 63 are multiples of 3, so both of these can be eliminated. 65 and 115 are multiples of 5, so both of these can be eliminated.
But the prime factorization of 88 is 
Example Question #34 : Understanding The Properties Of Integers
What is the median of the prime numbers between 40 and 90?
The prime numbers between 40 and 90 are: 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89. Since there are twelve, the median is the mean of the sixth- and seventh-highest numbers:
Example Question #35 : Understanding The Properties Of Integers
To the nearest whole number, what is the mean of the prime numbers between 50 and 100?
The prime numbers between 50 and 100 are: 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. There are ten primes total, so add them and divide by 10:
This rounds to 73.
Example Question #36 : Understanding The Properties Of Integers
Which of the following values of 
For 
Since all of the choices are even, we test to see which one is divisible by 9. The easiest way to do this is to apply the divisibility test by finding each the sum of the digits in each number. If the sum of the digits is divisible by 9, then the number is divisible by 9 as well.
Of the five choices, only 19,836 has a digit sum divisible by 9.
Example Question #34 : Understanding The Properties Of Integers
A group of 
How many different arrangements can the single file line take?
To solve this problem we use factorials. This is a quicker way to find out the number of combination for this specific set of data.
The number of ways to arrange the 2 girls is 2! and the number of ways to arrange the 3 boys is 3!.
Therefore the number of possible file arrangements is:
Example Question #36 : Understanding The Properties Of Integers
What is the least common multiple of 
The multiples of 10 are: 10 , 20 , 30 , 40 , 50 , 60 , 70 and so on
The multiples of 12 are: 12 , 24 , 36 , 48 , 60 , 72 , 84 and so on
So the LCM (10 ; 12) = 60
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