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. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
1. The smallest or largest element 2. The increment 3. The number of items in the set
NEVER CONTRADICT ONE ANOTHER
97

2. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
14
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A MULTIPLE
53 -59

3. The prime factorization of __________ contains only EVEN powers of primes.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A non-multiple of N.
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.

4. In an evenly spaced set - the ____ and the ____ are equal.
The sum of any two primes will be even - unless one of the two primes is 2.
The same sign as the base
2 -3 -5 -7
In an evenly spaced set - the average and the median are equal.

5. If the problem states/assumes that a number is an integer - check to see if you can use _______.
25
Prime factorization
1.4
A MULTIPLE

6. Prime Numbers:7x
A MULTIPLE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
71 -73 -79
The average of an EVEN number of consecutive integers will NEVER be an integer.

7. If estimating a root with a coefficient - _____ .
13
2 -3 -5 -7
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Put the coefficient under the radical to get a better approximation

8. N! is _____ of all integers from 1 to N.
13
The middle number
53 -59
A MULTIPLE

9. 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
14
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The average of the set times the number of elements in the set
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

10. The average of an EVEN number of consecutive integers will ________ be an integer.
14
The average of an EVEN number of consecutive integers will NEVER be an integer.
N is a divisor of x+y
71 -73 -79

11. Any integer with an EVEN number of total factors cannot be ______.
13
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE
The average of an ODD number of consecutive integers will ALWAYS be an integer.

12. Prime Numbers:2x
23 -29
2.5
The same sign as the base
Either a multiple of N or a non-multiple of N

13. Prime Numbers:6x
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
61 -67
FACTOR

14. v169=
NEVER CONTRADICT ONE ANOTHER
Prime factorization
13
61 -67

15. All perfect squares have a(n) _________ number of total factors.
Either a multiple of N or a non-multiple of N
A non-multiple of N.
The same sign as the base
ODD

16. 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
ODD
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
83 -89
The average of an EVEN number of consecutive integers will NEVER be an integer.

17. v256=
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.
16
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.
Prime factorization

18. v196=
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.
ODD
15

19. The formula for finding the number of consecutive multiples in a set is _______.
61 -67
[(last - first) / increment] + 1
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
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

20. The average of an ODD number of consecutive integers will ________ be an integer.
A PERFECT SQUARE
2.5
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A PERFECT SQUARE

21. Positive integers with more than two factors are ____.
If 2 cannot be one of the primes in the sum - the sum must be even.
Never prime
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
23 -29

22. 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
N is a divisor of x+y
If 2 cannot be one of the primes in the sum - the sum must be even.
A MULTIPLE

23. Let N be an integer. If you add two non-multiples of N - the result could be _______.
ODD
EVEN
The same sign as the base
Either a multiple of N or a non-multiple of N

24. 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?
The PRODUCT of n consecutive integers is divisible by n!.
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.
1.4
In an evenly spaced set - the average and the median are equal.

25. The sum of any two primes will be ____ - unless ______.
NEVER CONTRADICT ONE ANOTHER
2 -3 -5 -7
The sum of any two primes will be even - unless one of the two primes is 2.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

26. v2˜
71 -73 -79
Prime
The average of the set times the number of elements in the set
1.4

27. v625=
25
53 -59
1.7
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

28. In an evenly spaced set - the average can be found by finding ________.
31 -37
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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 middle number

29. How to find the sum of consecutive integers:
ODD
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.
97
A PERFECT SQUARE

30. 3n + 3n + 3n = _____ = ______
The middle number
3·3n = 3^{n+1}
1.7
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.

31. Prime Numbers:0x
[(last - first) / increment] + 1
The middle number
2 -3 -5 -7
A MULTIPLE

32. Prime factors of _____ must come in pairs of three.
3·3n = 3^{n+1}
31 -37
A non-multiple of N.
PERFECT CUBES

33. 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.
41 -43 -47
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.

34. Positive integers with only two factors must be ___.
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.
Prime
1.4
The average of an EVEN number of consecutive integers will NEVER be an integer.

35. v225=
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
15
A PERFECT SQUARE

36. Prime Numbers:5x
15
71 -73 -79
In an evenly spaced set - the average and the median are equal.
53 -59

37. Prime Numbers:4x
N is a divisor of x+y
The middle number
41 -43 -47
Either a multiple of N or a non-multiple of N

38. ³v216 =
ODD
Prime factorization
Either a multiple of N or 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

39. Prime Numbers:1x
11 -13 -17 -19
41 -43 -47
If 2 cannot be one of the primes in the sum - the sum must be even.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

40. For ODD ROOTS - the root has ______.
The sum of any two primes will be even - unless one of the two primes is 2.
The same sign as the base
A non-multiple of N.
ODD

41. 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

42. v3˜
A MULTIPLE
1.7
In an evenly spaced set - the average and the median are equal.
1.4

43. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
A non-multiple of N.
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE
25

44. In an evenly spaced set - the mean and median are equal to the _____ of _________.
53 -59
Put the coefficient under the radical to get a better approximation
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
2.5

45. Prime Numbers:3x
The sum of any two primes will be even - unless one of the two primes is 2.
31 -37
The average of an ODD number of consecutive integers will ALWAYS be an integer.
[(last - first) / increment] + 1

46. Prime Numbers:8x
83 -89
ODD
The PRODUCT of n consecutive integers is divisible by n!.
13

47. The PRODUCT of n consecutive integers is divisible by ____.
A PERFECT SQUARE
The PRODUCT of n consecutive integers is divisible by n!.
EVEN
Never prime

48. The prime factorization of a perfect square contains only ______ powers of primes.
The average of the set times the number of elements in the set
61 -67
EVEN
15

49. v5˜
Prime factorization
If 2 cannot be one of the primes in the sum - the sum must be even.
2.5
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

50. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
1. The smallest or largest element 2. The increment 3. The number of items in the set
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
41 -43 -47