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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. v256=
14
16
1.4
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.

2. N! is _____ of all integers from 1 to N.
A MULTIPLE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
ODD
Never prime

3. Prime Numbers:3x
The middle number
PERFECT CUBES
31 -37
[(last - first) / increment] + 1

4. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
1.7
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
13

5. In an evenly spaced set - the ____ and the ____ are equal.
Put the coefficient under the radical to get a better approximation
NEVER CONTRADICT ONE ANOTHER
In an evenly spaced set - the average and the median are equal.
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

6. If N is a divisor of x and y - then _______.
Prime
Never prime
14
N is a divisor of x+y

7. v225=
Prime
The PRODUCT of n consecutive integers is divisible by n!.
97
15

8. v169=
13
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
16
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

9. Prime Numbers:0x
2 -3 -5 -7
ODD
11 -13 -17 -19
2.5

10. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
23 -29
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
16
ONLY the nonnegative root of the numberUNLIKE

11. The average of an ODD number of consecutive integers will ________ be an integer.
The average of an EVEN number of consecutive integers will NEVER be an integer.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
13
A non-multiple of N.

12. All perfect squares have a(n) _________ number of total factors.
13
Never prime
ODD
A PERFECT SQUARE

13. 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 EVEN number of consecutive integers will NEVER be an integer.
If 2 cannot be one of the primes in the sum - the sum must be even.
31 -37

14. The prime factorization of a perfect square contains only ______ powers of primes.
14
Either a multiple of N or a non-multiple of N
EVEN
If 2 cannot be one of the primes in the sum - the sum must be even.

15. The average of an EVEN number of consecutive integers will ________ be an integer.
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.
Put the coefficient under the radical to get a better approximation

16. In an evenly spaced set - the sum of the terms is equal to ____.
The middle number
Put the coefficient under the radical to get a better approximation
Prime
The average of the set times the number of elements in the set

17. The two statements in a data sufficiency problem will _______________.
FACTOR
NEVER CONTRADICT ONE ANOTHER
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.

18. Positive integers with only two factors must be ___.
N is a divisor of x+y
1. The smallest or largest element 2. The increment 3. The number of items in the set
Prime
61 -67

19. In an evenly spaced set - the mean and median are equal to the _____ of _________.
Put the coefficient under the radical to get a better approximation
The average of the set times the number of elements in the set
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 mean and median are equal to the average of the first and the last number.

20. Prime Numbers:6x
2 -3 -5 -7
FACTOR
61 -67
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

21. v5˜
A MULTIPLE
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 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
2.5

22. For ODD ROOTS - the root has ______.
97
71 -73 -79
The same sign as the base
A PERFECT SQUARE

23. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
83 -89
25
A non-multiple of N.
NEVER CONTRADICT ONE ANOTHER

24. ³v216 =
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The average of the set times the number of elements in the set
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
23 -29

25. v2˜
NEVER CONTRADICT ONE ANOTHER
1.4
ONLY the nonnegative root of the numberUNLIKE
A non-multiple of N.

26. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
3·3n = 3^{n+1}
In an evenly spaced set - the average and the median are equal.
13

27. 3n + 3n + 3n = _____ = ______
The middle number
3·3n = 3^{n+1}
PERFECT CUBES
16

28. The formula for finding the number of consecutive multiples in a set is _______.
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.
16
[(last - first) / increment] + 1
3·3n = 3^{n+1}

29. Prime Numbers:1x
16
11 -13 -17 -19
A PERFECT SQUARE
1.7

30. v196=
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Prime
14
A PERFECT SQUARE

31. 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.
3·3n = 3^{n+1}
The sum of any two primes will be even - unless one of the two primes is 2.
83 -89

32. 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

33. v3˜
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.
1.7
71 -73 -79
The PRODUCT of n consecutive integers is divisible by n!.

34. Prime Numbers:9x
The average of an ODD number of consecutive integers will ALWAYS be an integer.
1.7
N is a divisor of x+y
97

35. Prime Numbers:4x
Put the coefficient under the radical to get a better approximation
83 -89
Either a multiple of N or a non-multiple of N
41 -43 -47

36. If the problem states/assumes that a number is an integer - check to see if you can use _______.
2.5
A PERFECT SQUARE
Prime factorization
FACTOR

37. Prime Numbers:5x
53 -59
If 2 cannot be one of the primes in the sum - the sum must be even.
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 non-multiple of N.

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

39. 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
31 -37
Never prime
14

40. 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.
The sum of any two primes will be even - unless one of the two primes is 2.
23 -29
3·3n = 3^{n+1}

41. The PRODUCT of n consecutive integers is divisible by ____.
EVEN
The PRODUCT of n consecutive integers is divisible by n!.
ODD
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

42. The sum of any two primes will be ____ - unless ______.
15
Either a multiple of N or a non-multiple of N
The sum of any two primes will be even - unless one of the two primes is 2.
A PERFECT SQUARE

43. In an evenly spaced set - the average can be found by finding ________.
Put the coefficient under the radical to get a better approximation
The same sign as the base
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The middle number

44. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
N is a divisor of x+y
[(last - first) / increment] + 1

45. Prime Numbers:7x
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.
71 -73 -79
Prime
23 -29

46. The prime factorization of __________ contains only EVEN powers of primes.
The average of an EVEN number of consecutive integers will NEVER be an integer.
83 -89
A PERFECT SQUARE
71 -73 -79

47. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
1.4
FACTOR
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.

48. Prime Numbers:8x
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
83 -89
NEVER CONTRADICT ONE ANOTHER
The middle number

49. v625=
The same sign as the base
61 -67
25
11 -13 -17 -19

50. 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.
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
FACTOR
53 -59