Test your basic knowledge |

GMAT Number Properties

Subjects : gmat, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. Positive integers with only two factors must be ___.
Prime
11 -13 -17 -19
Either a multiple of N or a non-multiple of N
ONLY the nonnegative root of the numberUNLIKE

2. v2˜
1.4
The sum of any two primes will be even - unless one of the two primes is 2.
NEVER CONTRADICT ONE ANOTHER
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

3. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
Look at the numbers from 1 to 30 - inclusive - that have at least one factor of 3 and count up how many each has: 3-1; 6-1; 9-2; 12-1; 15-1; 18-2; 21-1; 24-1; 27-3; 30-1 - The answer is 14.
NEVER CONTRADICT ONE ANOTHER
A non-multiple of N.
2 -3 -5 -7

4. The average of an ODD number of consecutive integers will ________ be an integer.
14
1. Average the first and last to find the mean. 2. Count the number of terms. 3. Multiply the mean by the number of terms.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
1. The smallest or largest element 2. The increment 3. The number of items in the set

5. How to solve: If p is the product of the integers from 1 to 30 - inclusive - what is the greatest integer n for which 3n is a factor of p?
In an evenly spaced set - the average and the median are equal.
1. The smallest or largest element 2. The increment 3. The number of items in the set
Look at the numbers from 1 to 30 - inclusive - that have at least one factor of 3 and count up how many each has: 3-1; 6-1; 9-2; 12-1; 15-1; 18-2; 21-1; 24-1; 27-3; 30-1 - The answer is 14.
The average of an ODD number of consecutive integers will ALWAYS be an integer.

6. v196=
14
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
A MULTIPLE
61 -67

7. If N is a divisor of x and y - then _______.
Express as 2k + 3m = t. 1. If k is a multiple of 3 - then so is t and we have a yes. => S 2. If m is a multiple of 3 - we don't know. => I A/1 Alone.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Look at the numbers from 1 to 30 - inclusive - that have at least one factor of 3 and count up how many each has: 3-1; 6-1; 9-2; 12-1; 15-1; 18-2; 21-1; 24-1; 27-3; 30-1 - The answer is 14.
N is a divisor of x+y

8. v3˜
1. The smallest or largest element 2. The increment 3. The number of items in the set
1.7
25
Put the coefficient under the radical to get a better approximation

9. Prime factors of _____ must come in pairs of three.
The average of the set times the number of elements in the set
The same sign as the base
A PERFECT SQUARE
PERFECT CUBES

10. In an evenly spaced set - the average can be found by finding ________.
The middle number
The average of the set times the number of elements in the set
13
Look at the numbers from 1 to 30 - inclusive - that have at least one factor of 3 and count up how many each has: 3-1; 6-1; 9-2; 12-1; 15-1; 18-2; 21-1; 24-1; 27-3; 30-1 - The answer is 14.

11. 3n + 3n + 3n = _____ = ______
The average of the set times the number of elements in the set
3·3n = 3^{n+1}
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.

12. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
1.7
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The same sign as the base

13. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Put the coefficient under the radical to get a better approximation
The sum of any two primes will be even - unless one of the two primes is 2.
The sum of EVEN INTEGERS between 99 and 301 is the sum of EVEN INTEGERS between 100 and 300 - or the sum of the 50th EVEN INTEGER through the 150th EVEN INTEGER.To get this sum: -Find the sum of the FIRST 150 even integers (ie 2 times the sum of the
Prime factorization

14. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The same sign as the base
Never prime

15. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
Express as 2k + 3m = t. 1. If k is a multiple of 3 - then so is t and we have a yes. => S 2. If m is a multiple of 3 - we don't know. => I A/1 Alone.
Look at the numbers from 1 to 30 - inclusive - that have at least one factor of 3 and count up how many each has: 3-1; 6-1; 9-2; 12-1; 15-1; 18-2; 21-1; 24-1; 27-3; 30-1 - The answer is 14.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
ONLY the nonnegative root of the numberUNLIKE

16. In an evenly spaced set - the sum of the terms is equal to ____.
16
The average of the set times the number of elements in the set
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
1. The smallest or largest element 2. The increment 3. The number of items in the set

17. Any integer with an ODD number of total factors must be _______.
A non-multiple of N.
A PERFECT SQUARE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
25

18. Prime Numbers:2x
23 -29
1.7
PERFECT CUBES
In an evenly spaced set - the average and the median are equal.

19. Prime Numbers:8x
A PERFECT SQUARE
83 -89
A non-multiple of N.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

20. In an evenly spaced set - the mean and median are equal to the _____ of _________.
13
1. Average the first and last to find the mean. 2. Count the number of terms. 3. Multiply the mean by the number of terms.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
71 -73 -79

21. Positive integers with more than two factors are ____.
The sum of any two primes will be even - unless one of the two primes is 2.
61 -67
Never prime
25

22. Prime Numbers:6x
The PRODUCT of n consecutive integers is divisible by n!.
In an evenly spaced set - the average and the median are equal.
61 -67
Never prime

23. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Never prime
FACTOR
1. Average the first and last to find the mean. 2. Count the number of terms. 3. Multiply the mean by the number of terms.

24. Prime Numbers:5x
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
61 -67
53 -59

25. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
1. The smallest or largest element 2. The increment 3. The number of items in the set
PERFECT CUBES
25
The middle number

26. v256=
61 -67
Prime factorization
[(last - first) / increment] + 1
16

27. The two statements in a data sufficiency problem will _______________.
[(last - first) / increment] + 1
Prime factorization
NEVER CONTRADICT ONE ANOTHER
Either a multiple of N or a non-multiple of N

28. The formula for finding the number of consecutive multiples in a set is _______.
Prime factorization
EVEN
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
[(last - first) / increment] + 1

29. How to find the sum of consecutive integers:
1. Average the first and last to find the mean. 2. Count the number of terms. 3. Multiply the mean by the number of terms.
The same sign as the base
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
31 -37

30. In an evenly spaced set - the ____ and the ____ are equal.
FACTOR
25
83 -89
In an evenly spaced set - the average and the median are equal.

31. N! is _____ of all integers from 1 to N.
A non-multiple of N.
FACTOR
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
A MULTIPLE

32. If estimating a root with a coefficient - _____ .
13
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Put the coefficient under the radical to get a better approximation
In an evenly spaced set - the average and the median are equal.

33. v225=
FACTOR
A non-multiple of N.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
15

34. The PRODUCT of n consecutive integers is divisible by ____.
EVEN
In an evenly spaced set - the average and the median are equal.
11 -13 -17 -19
The PRODUCT of n consecutive integers is divisible by n!.

35. How to test for sufficiency: If p is an integer - is p/n an integer? (1) k1p/n is an integer(2) k2p/n is an integer
3·3n = 3^{n+1}
The average of an ODD number of consecutive integers will ALWAYS be an integer.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
23 -29

36. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
31 -37
Express as 2k + 3m = t. 1. If k is a multiple of 3 - then so is t and we have a yes. => S 2. If m is a multiple of 3 - we don't know. => I A/1 Alone.
1. Average the first and last to find the mean. 2. Count the number of terms. 3. Multiply the mean by the number of terms.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

37. All perfect squares have a(n) _________ number of total factors.
FACTOR
In an evenly spaced set - the average and the median are equal.
ODD
97

38. Prime Numbers:9x
97
NEVER CONTRADICT ONE ANOTHER
71 -73 -79
The sum of EVEN INTEGERS between 99 and 301 is the sum of EVEN INTEGERS between 100 and 300 - or the sum of the 50th EVEN INTEGER through the 150th EVEN INTEGER.To get this sum: -Find the sum of the FIRST 150 even integers (ie 2 times the sum of the

39. If 2 cannot be one of the primes in the sum - the sum must be _____.
If 2 cannot be one of the primes in the sum - the sum must be even.
23 -29
[(last - first) / increment] + 1
31 -37

40. Prime Numbers:7x
The average of the set times the number of elements in the set
Look at the numbers from 1 to 30 - inclusive - that have at least one factor of 3 and count up how many each has: 3-1; 6-1; 9-2; 12-1; 15-1; 18-2; 21-1; 24-1; 27-3; 30-1 - The answer is 14.
71 -73 -79
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

41. The average of an EVEN number of consecutive integers will ________ be an integer.
In an evenly spaced set - the average and the median are equal.
The average of an EVEN number of consecutive integers will NEVER be an integer.
The sum of EVEN INTEGERS between 99 and 301 is the sum of EVEN INTEGERS between 100 and 300 - or the sum of the 50th EVEN INTEGER through the 150th EVEN INTEGER.To get this sum: -Find the sum of the FIRST 150 even integers (ie 2 times the sum of the
If 2 cannot be one of the primes in the sum - the sum must be even.

42. The prime factorization of __________ contains only EVEN powers of primes.
ONLY the nonnegative root of the numberUNLIKE
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A PERFECT SQUARE
83 -89

43. Prime Numbers:3x
FACTOR
The sum of EVEN INTEGERS between 99 and 301 is the sum of EVEN INTEGERS between 100 and 300 - or the sum of the 50th EVEN INTEGER through the 150th EVEN INTEGER.To get this sum: -Find the sum of the FIRST 150 even integers (ie 2 times the sum of the
31 -37
Prime factorization

44. v625=
FACTOR
If 2 cannot be one of the primes in the sum - the sum must be even.
25
ODD

45. How to solve: For any positive integer n - the sum of the 1st n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 301? (A) 10 -100 (B) 20 -200 (C) 22 -650 (D) 40 -200 (E) 45 -150
16
The sum of EVEN INTEGERS between 99 and 301 is the sum of EVEN INTEGERS between 100 and 300 - or the sum of the 50th EVEN INTEGER through the 150th EVEN INTEGER.To get this sum: -Find the sum of the FIRST 150 even integers (ie 2 times the sum of the
The same sign as the base
If 2 cannot be one of the primes in the sum - the sum must be even.

46. Prime Numbers:0x
2 -3 -5 -7
1. Average the first and last to find the mean. 2. Count the number of terms. 3. Multiply the mean by the number of terms.
Prime factorization
The sum of any two primes will be even - unless one of the two primes is 2.

47. Let N be an integer. If you add two non-multiples of N - the result could be _______.
Either a multiple of N or a non-multiple of N
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
[(last - first) / increment] + 1
The average of the set times the number of elements in the set

48. Any integer with an EVEN number of total factors cannot be ______.
97
The same sign as the base
The average of the set times the number of elements in the set
A PERFECT SQUARE

49. How to solve: If k - m - and t are positive integers and k/6 + m/4 = t/12 - do t and 12 have a common factor greater than 1? 1. k is a multiple of 3 2. m is a multiple of 3

50. The sum of any two primes will be ____ - unless ______.
The sum of any two primes will be even - unless one of the two primes is 2.
1. Average the first and last to find the mean. 2. Count the number of terms. 3. Multiply the mean by the number of terms.
ODD
Put the coefficient under the radical to get a better approximation