eduGMAT® mini-test 1: Arithmetic Exercises

Numbers
Numbers are classified according to their type. The first type is the one you have known since elementary school:
Natural numbers (whole positive numbers) – are the numbers used for counting: 1, 2, 3, 4, 5, … Adding 0 and the negatives of the naturals, we obtain
Integers – numbers from the set {…, -2, -1, 0, 1, 2, 3, 4, 5, … }
Note: The integer 0 is neither positive nor negative. 
1. The value of -3 – (-10) is how much greater than the value of -10 – (-3)?
2.

Properties of even/odd integers
even × even = even
even × odd = even
odd × odd = odd
even +/− even = even
odd +/− odd = even
odd +/− even = odd
even/odd = even or not integer
even/even = even or odd or not integer
odd/odd = odd or not integer

3. If n is a member of the set {33, 36, 38, 39, 41, 42}, what is the value of n?
(1) n is even
(2) n is a multiple of 3
4. If positive integers x and y are not both odd, which of the following must be even?
5. If n is a positive integer, is n odd?
(1) 3n is odd
(2) n + 3 is even
The numbers –2, –1, 0, 1, 2, 3, 4, 5 are consecutive integers. Consecutive integers can be represented by n, n + 1, n + 2, n + 3, . . . , where n is an integer.
The numbers 0, 2, 4, 6, 8 are consecutive even integers. Consecutive even integers can be represented by 2n, 2n + 2, 2n + 4, . . . , where n is an integer.
The numbers 1, 3, 5, 7, 9 are consecutive odd integers. Consecutive odd integers can be represented by 2n + 1, 2n + 3, 2n + 5, . . . , where n is an integer.
Note: if the numbers are given in the problem in a raw like a, b, c it does not mean that a<b<c.
Properties:

    • for every two consecutive integers n and n + 1 product n ∙ (n + 1) is divisible by 2;
    • for every three consecutive integers n, n + 1, n + 2 product n ∙ (n + l) ∙ (n + 2) is divisible by 3 and by 2;
    • for every k consecutive integers their product is divisible by all numbers from 1 to k.
6. The set consists of five consecutive integers. If the first member of this set is a, find the sum of all its members in terms of a.
7. If n is a positive integer, then n(n +1)(n + 2) is
8. If a, b, and с are consecutive positive integers and a < b < c, which of the following must be true?
I. c - a = 2
II.abc is an even integer
III.(a + b + c)/3 is an integer
9. If x, y, and z are three integers, are they consecutive integers?
(1) z – x = 2
(2) x < y < z
A prime number is a positive integer that has exactly two different positive divisors: 1 and itself.
For example, 2, 3, 5 are prime numbers, but 15 is not, since 15 has four different positive divisors, 1, 3, 5, and 15.
First prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47…
Note: If the number less than 100 is not divisible by 2, 3, 5, 7, it is prime.
Note: The number 1 is not a prime number since it has only one positive divisor.
Note: 2 is the only even prime. Indeed, if a prime greater than 2 were even, it would have at least three different divisors: 1, itself and 2.
10. The sum of prime numbers that are greater than 60 but less than 70 is
11. Is the positive integer y a prime number?
(1) 80 < y < 95
(2) y = 3x +1, where x is a positive integer