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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. If the problem states/assumes that a number is an integer - check to see if you can use _______.
If 2 cannot be one of the primes in the sum - the sum must be even.
Prime factorization
[(last - first) / increment] + 1
1.4

2. 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.
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
16

3. Positive integers with only two factors must be ___.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Prime
71 -73 -79
23 -29

4. Prime Numbers:3x
The same sign as the base
31 -37
Never prime
The average of an EVEN number of consecutive integers will NEVER be an integer.

5. Prime Numbers:4x
Prime
97
1. The smallest or largest element 2. The increment 3. The number of items in the set
41 -43 -47

6. 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?
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 -13 -17 -19
2.5
The average of the set times the number of elements in the set

7. For ODD ROOTS - the root has ______.
41 -43 -47
The same sign as the base
71 -73 -79
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

8. 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

9. If estimating a root with a coefficient - _____ .
A PERFECT SQUARE
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.
16

10. 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.
25
23 -29
A PERFECT SQUARE

11. 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.
EVEN
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
1.4

12. 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
N is a divisor of x+y
[(last - first) / increment] + 1

13. Prime Numbers:1x
3·3n = 3^{n+1}
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.
11 -13 -17 -19

14. v225=
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.
15
71 -73 -79

15. In an evenly spaced set - the mean and median are equal to the _____ of _________.
A PERFECT SQUARE
The average of an EVEN number of consecutive integers will NEVER 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.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

16. Prime Numbers:6x
61 -67
The average of the set times the number of elements in the set
The same sign as the base
16

17. Let N be an integer. If you add two non-multiples of N - the result could be _______.
The average of the set times the number of elements in the set
Either a multiple of N or a non-multiple of N
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.
If 2 cannot be one of the primes in the sum - the sum must be even.

18. In an evenly spaced set - the ____ and the ____ are equal.
15
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.
N is a divisor of x+y

19. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
1.7
ONLY the nonnegative root of the numberUNLIKE
2 -3 -5 -7
In an evenly spaced set - the average and the median are equal.

20. The average of an EVEN number of consecutive integers will ________ be an integer.
The average of an EVEN number of consecutive integers will NEVER be an integer.
The middle number
A PERFECT SQUARE
Prime factorization

21. Prime Numbers:5x
1.7
A PERFECT SQUARE
53 -59
16

22. v2˜
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
11 -13 -17 -19
[(last - first) / increment] + 1

23. The prime factorization of a perfect square contains only ______ powers of primes.
The sum of any two primes will be even - unless one of the two primes is 2.
83 -89
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
EVEN

24. Prime Numbers:7x
1.4
71 -73 -79
Prime
16

25. The formula for finding the number of consecutive multiples in a set is _______.
ONLY the nonnegative root of the numberUNLIKE
1.7
[(last - first) / increment] + 1
EVEN

26. In an evenly spaced set - the sum of the terms is equal to ____.
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 the set times the number of elements in the set
A PERFECT SQUARE
2 -3 -5 -7

27. The PRODUCT of n consecutive integers is divisible by ____.
EVEN
The PRODUCT of n consecutive integers is divisible by n!.
61 -67
A PERFECT SQUARE

28. All perfect squares have a(n) _________ number of total factors.
41 -43 -47
The average of an EVEN number of consecutive integers will NEVER be an integer.
ODD
The PRODUCT of n consecutive integers is divisible by n!.

29. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
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
Never prime
41 -43 -47

30. 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.
11 -13 -17 -19
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

31. Prime Numbers:0x
ONLY the nonnegative root of the numberUNLIKE
[(last - first) / increment] + 1
2 -3 -5 -7
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

32. 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
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.
A PERFECT SQUARE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

33. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
23 -29
1. The smallest or largest element 2. The increment 3. The number of items in the set
2 -3 -5 -7

34. If N is a divisor of x and y - then _______.
The same sign as the base
83 -89
Prime factorization
N is a divisor of x+y

35. In an evenly spaced set - the average can be found by finding ________.
The middle number
EVEN
53 -59
16

36. Prime Numbers:9x
The PRODUCT of n consecutive integers is divisible by n!.
2.5
97
EVEN

37. The two statements in a data sufficiency problem will _______________.
1. The smallest or largest element 2. The increment 3. The number of items in the set
NEVER CONTRADICT ONE ANOTHER
EVEN
Prime factorization

38. v169=
NEVER CONTRADICT ONE ANOTHER
The PRODUCT of n consecutive integers is divisible by n!.
Never prime
13

39. 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.
11 -13 -17 -19
ODD
FACTOR

40. Prime factors of _____ must come in pairs of three.
Either a multiple of N or a non-multiple of N
1. The smallest or largest element 2. The increment 3. The number of items in the set
PERFECT CUBES
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.

41. v256=
Put the coefficient under the radical to get a better approximation
16
N is a divisor of x+y
The PRODUCT of n consecutive integers is divisible by n!.

42. The prime factorization of __________ contains only EVEN powers of primes.
PERFECT CUBES
83 -89
A PERFECT SQUARE
If 2 cannot be one of the primes in the sum - the sum must be even.

43. v3˜
EVEN
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
1.7
A PERFECT SQUARE

44. Prime Numbers:2x
11 -13 -17 -19
23 -29
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Prime

45. v5˜
11 -13 -17 -19
FACTOR
2.5
The PRODUCT of n consecutive integers is divisible by n!.

46. 3n + 3n + 3n = _____ = ______
[(last - first) / increment] + 1
ONLY the nonnegative root of the numberUNLIKE
The sum of any two primes will be even - unless one of the two primes is 2.
3·3n = 3^{n+1}

47. v196=
14
3·3n = 3^{n+1}
13
FACTOR

48. Positive integers with more than two factors are ____.
PERFECT CUBES
Never prime
EVEN
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

49. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
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.
41 -43 -47
13

50. Any integer with an ODD number of total factors must be _______.
13
1. The smallest or largest element 2. The increment 3. The number of items in the set
Prime
A PERFECT SQUARE