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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
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
11 -13 -17 -19
1. The smallest or largest element 2. The increment 3. The number of items in the set
1.7

2. The PRODUCT of n consecutive integers is divisible by ____.
97
N is a divisor of x+y
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.
The PRODUCT of n consecutive integers is divisible by n!.

3. Prime Numbers:6x
61 -67
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
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

4. The average of an ODD number of consecutive integers will ________ be an integer.
ONLY the nonnegative root of the numberUNLIKE
61 -67
The average of an ODD number of consecutive integers will ALWAYS be an integer.
25

5. v625=
Prime factorization
The sum of any two primes will be even - unless one of the two primes is 2.
25
A MULTIPLE

6. Prime Numbers:3x
In an evenly spaced set - the average and the median are equal.
[(last - first) / increment] + 1
31 -37
NEVER CONTRADICT ONE ANOTHER

7. 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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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.
2.5
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

8. v256=
23 -29
71 -73 -79
The middle number
16

9. The two statements in a data sufficiency problem will _______________.
NEVER CONTRADICT ONE ANOTHER
31 -37
A MULTIPLE
25

10. Positive integers with more than two factors are ____.
25
Never prime
The average of an EVEN number of consecutive integers will NEVER be an integer.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

11. If estimating a root with a coefficient - _____ .
The PRODUCT of n consecutive integers is divisible by n!.
A non-multiple of N.
A MULTIPLE
Put the coefficient under the radical to get a better approximation

12. The prime factorization of a perfect square contains only ______ powers of primes.
2 -3 -5 -7
If 2 cannot be one of the primes in the sum - the sum must be even.
EVEN
A PERFECT SQUARE

13. Prime Numbers:5x
The same sign as the base
53 -59
The average of an ODD number of consecutive integers will ALWAYS be an integer.
83 -89

14. Any integer with an EVEN number of total factors cannot be ______.
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE
The same sign as the base
FACTOR

15. If the problem states/assumes that a number is an integer - check to see if you can use _______.
1. The smallest or largest element 2. The increment 3. The number of items in the set
In an evenly spaced set - the average and the median are equal.
Prime factorization
EVEN

16. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
3·3n = 3^{n+1}
The average of an ODD number of consecutive integers will ALWAYS be an integer.
In an evenly spaced set - the average and the median are equal.

17. In an evenly spaced set - the ____ and the ____ are equal.
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.
1. The smallest or largest element 2. The increment 3. The number of items in the set
In an evenly spaced set - the average and the median are equal.

18. Prime Numbers:4x
83 -89
ONLY the nonnegative root of the numberUNLIKE
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.

19. The sum of any two primes will be ____ - unless ______.
14
Prime
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.

20. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
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 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

21. Prime factors of _____ must come in pairs of three.
If 2 cannot be one of the primes in the sum - the sum must be even.
PERFECT CUBES
2.5
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.

22. v2˜
1.4
EVEN
13
2 -3 -5 -7

23. Positive integers with only two factors must be ___.
A MULTIPLE
1.7
11 -13 -17 -19
Prime

24. The formula for finding the number of consecutive multiples in a set is _______.
The PRODUCT of n consecutive integers is divisible by n!.
13
1. The smallest or largest element 2. The increment 3. The number of items in the set
[(last - first) / increment] + 1

25. The prime factorization of __________ contains only EVEN powers of primes.
1.4
A PERFECT SQUARE
PERFECT CUBES
The average of an EVEN number of consecutive integers will NEVER be an integer.

26. 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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27. Prime Numbers:2x
97
23 -29
[(last - first) / increment] + 1
The sum of any two primes will be even - unless one of the two primes is 2.

28. 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
71 -73 -79
The average of an ODD number of consecutive integers will ALWAYS be an integer.

29. v5˜
A non-multiple of N.
EVEN
2.5
FACTOR

30. N! is _____ of all integers from 1 to N.
A MULTIPLE
ONLY the nonnegative root of the numberUNLIKE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Prime factorization

31. Prime Numbers:8x
83 -89
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
In an evenly spaced set - the average and the median are equal.
FACTOR

32. Prime Numbers:0x
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
2 -3 -5 -7
31 -37
Prime factorization

33. 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
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Never prime
71 -73 -79

34. Prime Numbers:9x
97
Never prime
N is a divisor of x+y
A non-multiple of N.

35. v169=
71 -73 -79
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.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
13

36. 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.
13
25
11 -13 -17 -19

37. Let N be an integer. If you add two non-multiples of N - the result could be _______.
1. The smallest or largest element 2. The increment 3. The number of items in the set
Prime factorization
Either a multiple of N or a non-multiple of N
FACTOR

38. 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?
ODD
97
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.
ONLY the nonnegative root of the numberUNLIKE

39. For ODD ROOTS - the root has ______.
The same sign as the base
14
A MULTIPLE
13

40. In an evenly spaced set - the average can be found by finding ________.
The sum of any two primes will be even - unless one of the two primes is 2.
2 -3 -5 -7
The middle number
N is a divisor of x+y

41. v196=
FACTOR
Never prime
41 -43 -47
14

42. In an evenly spaced set - the sum of the terms is equal to ____.
The average of an EVEN number of consecutive integers will NEVER be an integer.
1.4
Either a multiple of N or a non-multiple of N
The average of the set times the number of elements in the set

43. Prime Numbers:7x
The middle number
A PERFECT SQUARE
71 -73 -79
FACTOR

44. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Put the coefficient under the radical to get a better approximation
41 -43 -47
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

45. In an evenly spaced set - the mean and median are equal to the _____ of _________.
NEVER CONTRADICT ONE ANOTHER
If 2 cannot be one of the primes in the sum - the sum must be even.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
FACTOR

46. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
14
A non-multiple of N.
Prime
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

47. All perfect squares have a(n) _________ number of total factors.
2 -3 -5 -7
ODD
NEVER CONTRADICT ONE ANOTHER
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

48. v225=
41 -43 -47
16
15
2 -3 -5 -7

49. ³v216 =
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
2 -3 -5 -7
The sum of any two primes will be even - unless one of the two primes is 2.
15

50. 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.
13
The average of the set times the number of elements in the set
1.4

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GMAT Number Properties

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