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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. Prime Numbers:1x
15
Prime factorization
11 -13 -17 -19
53 -59

2. v225=
25
15
ONLY the nonnegative root of the numberUNLIKE
If 2 cannot be one of the primes in the sum - the sum must be even.

3. 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
Either a multiple of N or a non-multiple of N
EVEN
A MULTIPLE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

4. Prime Numbers:6x
61 -67
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
97

5. The average of an EVEN number of consecutive integers will ________ be an integer.
97
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
2.5
The average of an EVEN number of consecutive integers will NEVER be an integer.

6. How to find the sum of consecutive integers:
71 -73 -79
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.
11 -13 -17 -19
A PERFECT SQUARE

7. Prime Numbers:4x
41 -43 -47
31 -37
1.4
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.

8. Prime Numbers:0x
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.
2 -3 -5 -7
41 -43 -47

9. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
Prime factorization
1. The smallest or largest element 2. The increment 3. The number of items in the set
NEVER CONTRADICT ONE ANOTHER

10. In an evenly spaced set - the ____ and the ____ are equal.
1.4
The PRODUCT of n consecutive integers is divisible by n!.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
In an evenly spaced set - the average and the median are equal.

11. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The average of an EVEN number of consecutive integers will NEVER be an integer.
The sum of any two primes will be even - unless one of the two primes is 2.

12. The formula for finding the number of consecutive multiples in a set is _______.
61 -67
[(last - first) / increment] + 1
2.5
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

13. Prime Numbers:5x
N is a divisor of x+y
The PRODUCT of n consecutive integers is divisible by n!.
53 -59
Put the coefficient under the radical to get a better approximation

14. v5˜
NEVER CONTRADICT ONE ANOTHER
ODD
Put the coefficient under the radical to get a better approximation
2.5

15. 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
14
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
EVEN

16. In an evenly spaced set - the mean and median are equal to the _____ of _________.
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.
25
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
A PERFECT SQUARE

17. All perfect squares have a(n) _________ number of total factors.
A PERFECT SQUARE
ODD
In an evenly spaced set - the average and the median are equal.
A PERFECT SQUARE

18. v169=
A PERFECT SQUARE
13
Prime factorization
Either a multiple of N or a non-multiple of N

19. Prime Numbers:9x
41 -43 -47
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE
97

20. 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

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21. In an evenly spaced set - the average can be found by finding ________.
1. The smallest or largest element 2. The increment 3. The number of items in the set
14
53 -59
The middle number

22. v3˜
71 -73 -79
31 -37
53 -59
1.7

23. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
2.5
61 -67
15

24. v625=
61 -67
A non-multiple of N.
3·3n = 3^{n+1}
25

25. N! is _____ of all integers from 1 to N.
A MULTIPLE
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.
2 -3 -5 -7

26. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The average of an EVEN number of consecutive integers will NEVER be an integer.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
ONLY the nonnegative root of the numberUNLIKE

27. Prime Numbers:3x
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
31 -37

28. In an evenly spaced set - the sum of the terms is equal to ____.
3·3n = 3^{n+1}
25
The average of the set times the number of elements in the set
A PERFECT SQUARE

29. The PRODUCT of n consecutive integers is divisible by ____.
71 -73 -79
The PRODUCT of n consecutive integers is divisible by n!.
16
PERFECT CUBES

30. 3n + 3n + 3n = _____ = ______
N is a divisor of x+y
3·3n = 3^{n+1}
11 -13 -17 -19
Never prime

31. If N is a divisor of x and y - then _______.
Never prime
41 -43 -47
N is a divisor of x+y
A PERFECT SQUARE

32. Prime Numbers:7x
61 -67
N is a divisor of x+y
71 -73 -79
25

33. The sum of any two primes will be ____ - unless ______.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
97
A PERFECT SQUARE
The sum of any two primes will be even - unless one of the two primes is 2.

34. ³v216 =
Prime
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Never prime
Put the coefficient under the radical to get a better approximation

35. Prime Numbers:8x
2 -3 -5 -7
83 -89
15
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.

36. 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?
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.
25
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 non-multiple of N.

37. Positive integers with more than two factors are ____.
Never prime
83 -89
A PERFECT SQUARE
3·3n = 3^{n+1}

38. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
1.4
ODD
15

39. The two statements in a data sufficiency problem will _______________.
The same sign as the base
83 -89
NEVER CONTRADICT ONE ANOTHER
ODD

40. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
ODD
EVEN
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
61 -67

41. The average of an ODD number of consecutive integers will ________ be an integer.
16
Either a multiple of N or a non-multiple of N
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.

42. Let N be an integer. If you add two non-multiples of N - the result could be _______.
15
Either a multiple of N or a non-multiple of N
A PERFECT SQUARE
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.

43. v256=
16
Put the coefficient under the radical to get a better approximation
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The average of an ODD number of consecutive integers will ALWAYS be an integer.

44. Prime Numbers:2x
The average of an EVEN number of consecutive integers will NEVER be an integer.
Put the coefficient under the radical to get a better approximation
23 -29
A non-multiple of N.

45. If estimating a root with a coefficient - _____ .
2 -3 -5 -7
Put the coefficient under the radical to get a better approximation
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.
14

46. If 2 cannot be one of the primes in the sum - the sum 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.
The average of the set times the number of elements in the set
Put the coefficient under the radical to get a better approximation
If 2 cannot be one of the primes in the sum - the sum must be even.

47. Positive integers with only two factors must be ___.
N is a divisor of x+y
If 2 cannot be one of the primes in the sum - the sum must be even.
The average of the set times the number of elements in the set
Prime

48. For ODD ROOTS - the root has ______.
The same sign as the base
The average of the set times the number of elements in the set
97
Never prime

49. v196=
Put the coefficient under the radical to get a better approximation
ODD
14
83 -89

50. The prime factorization of __________ contains only EVEN powers of primes.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
31 -37
A PERFECT SQUARE
If 2 cannot be one of the primes in the sum - the sum must be even.