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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. The sum of any two primes will be ____ - unless ______.
Prime
[(last - first) / increment] + 1
The sum of any two primes will be even - unless one of the two primes is 2.
15

2. v5˜
ONLY the nonnegative root of the numberUNLIKE
2.5
The same sign as the base
FACTOR

3. 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.
11 -13 -17 -19
14
25

4. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
EVEN
A PERFECT SQUARE
A PERFECT SQUARE

5. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
Either a multiple of N or a non-multiple of N
14
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
1.7

6. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
71 -73 -79
2 -3 -5 -7
61 -67

7. In an evenly spaced set - the mean and median are equal to the _____ of _________.
Prime factorization
A PERFECT SQUARE
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.

8. If the problem states/assumes that a number is an integer - check to see if you can use _______.
31 -37
Prime factorization
The average of the set times the number of elements in the set
Never prime

9. v169=
The PRODUCT of n consecutive integers is divisible by n!.
13
FACTOR
25

10. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The middle number
N is a divisor of x+y

11. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
83 -89
N is a divisor of x+y
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.

12. Prime Numbers:8x
83 -89
The average of the set times the number of elements in the set
If 2 cannot be one of the primes in the sum - the sum must be even.
31 -37

13. The two statements in a data sufficiency problem will _______________.
NEVER CONTRADICT ONE ANOTHER
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.
N is a divisor of x+y
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

14. In an evenly spaced set - the average can be found by finding ________.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The middle number
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
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.

15. v625=
ONLY the nonnegative root of the numberUNLIKE
ODD
25
A PERFECT SQUARE

16. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
The average of an EVEN number of consecutive integers will NEVER be an integer.
14
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Never prime

17. Prime Numbers:0x
Either a multiple of N or a non-multiple of N
1.4
The same sign as the base
2 -3 -5 -7

18. ³v216 =
23 -29
2 -3 -5 -7
83 -89
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

19. Prime Numbers:2x
11 -13 -17 -19
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.
23 -29

20. Prime Numbers:4x
41 -43 -47
[(last - first) / increment] + 1
83 -89
23 -29

21. N! is _____ of all integers from 1 to N.
A MULTIPLE
11 -13 -17 -19
PERFECT CUBES
ODD

22. All perfect squares have a(n) _________ number of total factors.
[(last - first) / increment] + 1
ODD
Never prime
25

23. How to find the sum of consecutive integers:
N is a divisor of x+y
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.
83 -89
A PERFECT SQUARE

24. 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.
83 -89
1. The smallest or largest element 2. The increment 3. The number of items in the set
The PRODUCT of n consecutive integers is divisible by n!.

25. v2˜
The average of an EVEN number of consecutive integers will NEVER be an integer.
A MULTIPLE
61 -67
1.4

26. 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?
61 -67
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.
In an evenly spaced set - the average and the median are equal.
FACTOR

27. Prime Numbers:9x
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
NEVER CONTRADICT ONE ANOTHER
97

28. The formula for finding the number of consecutive multiples in a set is _______.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
[(last - first) / increment] + 1
Prime
If 2 cannot be one of the primes in the sum - the sum must be even.

29. If estimating a root with a coefficient - _____ .
In an evenly spaced set - the average and the median are equal.
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
Never prime

30. Prime Numbers:6x
61 -67
1.4
In an evenly spaced set - the average and the median are equal.
N is a divisor of x+y

31. v256=
The middle number
PERFECT CUBES
The average of the set times the number of elements in the set
16

32. Prime Numbers:7x
2 -3 -5 -7
1.7
71 -73 -79
The same sign as the base

33. If N is a divisor of x and y - then _______.
N is a divisor of x+y
The average of an ODD number of consecutive integers will ALWAYS 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
53 -59

34. Any integer with an EVEN number of total factors cannot be ______.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
NEVER CONTRADICT ONE ANOTHER
53 -59
A PERFECT SQUARE

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
1.7
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Put the coefficient under the radical to get a better approximation
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

36. If 2 cannot be one of the primes in the sum - the sum must be _____.
PERFECT CUBES
1. The smallest or largest element 2. The increment 3. The number of items in the set
Either a multiple of N or a non-multiple of N
If 2 cannot be one of the primes in the sum - the sum must be even.

37. v3˜
1.7
25
ODD
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

38. Prime Numbers:1x
11 -13 -17 -19
The PRODUCT of n consecutive integers is divisible by n!.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
2 -3 -5 -7

39. 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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40. Prime Numbers:3x
A MULTIPLE
2 -3 -5 -7
31 -37
ONLY the nonnegative root of the numberUNLIKE

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

42. Positive integers with only two factors must be ___.
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.
Prime
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

43. 3n + 3n + 3n = _____ = ______
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
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
3·3n = 3^{n+1}

44. Prime Numbers:5x
ONLY the nonnegative root of the numberUNLIKE
The average of the set times the number of elements in the set
53 -59
Prime factorization

45. Prime factors of _____ must come in pairs of three.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
15
PERFECT CUBES
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

46. The average of an EVEN number of consecutive integers will ________ be an integer.
NEVER CONTRADICT ONE ANOTHER
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The average of an EVEN number of consecutive integers will NEVER be an integer.
53 -59

47. Positive integers with more than two factors are ____.
A MULTIPLE
Never prime
Prime
The same sign as the base

48. The prime factorization of __________ contains only EVEN powers of primes.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Prime factorization
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE

49. v225=
23 -29
16
NEVER CONTRADICT ONE ANOTHER
15

50. v196=
14
25
31 -37
Prime factorization