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. v2˜
1.4
The average of an ODD number of consecutive integers will ALWAYS be an integer.
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.
15

2. v3˜
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 same sign as the base
The average of an EVEN number of consecutive integers will NEVER be an integer.
1.7

3. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
2.5
Prime factorization

4. v196=
Prime
The sum of any two primes will be even - unless one of the two primes is 2.
14
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

5. v625=
25
14
The middle number
13

6. v5˜
2.5
71 -73 -79
Put the coefficient under the radical to get a better approximation
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

7. Prime Numbers:8x
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
83 -89
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

8. If estimating a root with a coefficient - _____ .
ODD
Put the coefficient under the radical to get a better approximation
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
EVEN

9. In an evenly spaced set - the mean and median are equal to the _____ of _________.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Never prime
11 -13 -17 -19
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

10. 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?
A MULTIPLE
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.
A PERFECT SQUARE
1.4

11. Prime Numbers:0x
2 -3 -5 -7
97
The sum of any two primes will be even - unless one of the two primes is 2.
N is a divisor of x+y

12. Prime Numbers:3x
61 -67
The middle number
71 -73 -79
31 -37

13. For ODD ROOTS - the root has ______.
The PRODUCT of n consecutive integers is divisible by n!.
15
2 -3 -5 -7
The same sign as the base

14. The formula for finding the number of consecutive multiples in a set is _______.
16
1. The smallest or largest element 2. The increment 3. The number of items in the set
EVEN
[(last - first) / increment] + 1

15. If N is a divisor of x and y - then _______.
N is a divisor of x+y
13
The average of the set times the number of elements in the set
The average of an EVEN number of consecutive integers will NEVER be an integer.

16. In an evenly spaced set - the average can be found by finding ________.
The middle number
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE
N is a divisor of x+y

17. How to find the sum of consecutive integers:
71 -73 -79
23 -29
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.
A PERFECT SQUARE

18. 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

19. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
23 -29
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A PERFECT SQUARE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

20. 3n + 3n + 3n = _____ = ______
ODD
1. The smallest or largest element 2. The increment 3. The number of items in the set
3·3n = 3^{n+1}
Either a multiple of N or a non-multiple of N

21. 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
11 -13 -17 -19
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
13
N is a divisor of x+y

22. The two statements in a data sufficiency problem will _______________.
16
NEVER CONTRADICT ONE ANOTHER
Either a multiple of N or a non-multiple of N
A PERFECT SQUARE

23. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
If 2 cannot be one of the primes in the sum - the sum must be even.
A PERFECT SQUARE
11 -13 -17 -19
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

24. The prime factorization of a perfect square contains only ______ powers of primes.
A PERFECT SQUARE
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.
EVEN
13

25. Any integer with an EVEN number of total factors cannot be ______.
2 -3 -5 -7
11 -13 -17 -19
A PERFECT SQUARE
PERFECT CUBES

26. Prime Numbers:1x
97
EVEN
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
11 -13 -17 -19

27. Positive integers with only two factors must be ___.
Prime factorization
Prime
23 -29
Never prime

28. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
A non-multiple of N.
53 -59
Either a multiple of N or a non-multiple of N

29. Prime Numbers:2x
83 -89
A PERFECT SQUARE
23 -29
EVEN

30. v169=
The average of the set times the number of elements in the set
Prime
13
A PERFECT SQUARE

31. Prime Numbers:4x
A MULTIPLE
41 -43 -47
PERFECT CUBES
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

32. The average of an EVEN number of consecutive integers will ________ be an integer.
2.5
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 EVEN number of consecutive integers will NEVER be an integer.
15

33. The sum of any two primes will be ____ - unless ______.
If 2 cannot be one of the primes in the sum - the sum must be even.
The sum of any two primes will be even - unless one of the two primes is 2.
Never prime
[(last - first) / increment] + 1

34. 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
71 -73 -79
The sum of any two primes will be even - unless one of the two primes is 2.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Prime

35. Prime factors of _____ must come in pairs of three.
23 -29
PERFECT CUBES
Prime factorization
ONLY the nonnegative root of the numberUNLIKE

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

37. The average of an ODD number of consecutive integers will ________ be an integer.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
N is a divisor of x+y
The PRODUCT of n consecutive integers is divisible by n!.
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

38. Prime Numbers:9x
97
Prime
2.5
A non-multiple of N.

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.
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 same sign as the base
[(last - first) / increment] + 1

40. In an evenly spaced set - the ____ and the ____ are equal.
A PERFECT SQUARE
N is a divisor of x+y
In an evenly spaced set - the average and the median are equal.
Prime

41. ³v216 =
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
25
The average of an EVEN number of consecutive integers will NEVER be an integer.
EVEN

42. The prime factorization of __________ contains only EVEN powers of primes.
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
A PERFECT SQUARE
Put the coefficient under the radical to get a better approximation
1. The smallest or largest element 2. The increment 3. The number of items in the set

43. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
83 -89
If 2 cannot be one of the primes in the sum - the sum must be even.
1. The smallest or largest element 2. The increment 3. The number of items in the set
EVEN

44. N! is _____ of all integers from 1 to N.
A MULTIPLE
NEVER CONTRADICT ONE ANOTHER
41 -43 -47
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.

45. The PRODUCT of n consecutive integers is divisible by ____.
If 2 cannot be one of the primes in the sum - the sum must be even.
The PRODUCT of n consecutive integers is divisible by n!.
A PERFECT SQUARE
N is a divisor of x+y

46. v225=
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
ONLY the nonnegative root of the numberUNLIKE
15
53 -59

47. Let N be an integer. If you add two non-multiples of N - the result could be _______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Either a multiple of N or a non-multiple of N
15
EVEN

48. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
A PERFECT SQUARE
The sum of any two primes will be even - unless one of the two primes is 2.
FACTOR
Never prime

49. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
83 -89
15
FACTOR

50. Prime Numbers:5x
[(last - first) / increment] + 1
The PRODUCT of n consecutive integers is divisible by n!.
53 -59
2.5