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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. 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

2. Prime Numbers:6x
61 -67
PERFECT CUBES
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
2.5

3. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
Never prime
14
1.7
1. The smallest or largest element 2. The increment 3. The number of items in the set

4. N! is _____ of all integers from 1 to N.
A MULTIPLE
14
[(last - first) / increment] + 1
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

5. ³v216 =
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.
A PERFECT SQUARE

6. The prime factorization of a perfect square contains only ______ powers of primes.
Either a multiple of N or a non-multiple of N
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
EVEN
If 2 cannot be one of the primes in the sum - the sum must be even.

7. Let N be an integer. If you add two non-multiples of N - the result could be _______.
A PERFECT SQUARE
23 -29
Either a multiple of N or a non-multiple of N
N is a divisor of x+y

8. Prime Numbers:7x
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
13
71 -73 -79

9. v5˜
13
23 -29
2.5
FACTOR

10. In an evenly spaced set - the mean and median are equal to the _____ of _________.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
53 -59
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The same sign as the base

11. Positive integers with only two factors must be ___.
15
Prime
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
N is a divisor of x+y

12. Prime Numbers:0x
2 -3 -5 -7
A MULTIPLE
23 -29
PERFECT CUBES

13. If the problem states/assumes that a number is an integer - check to see if you can use _______.
25
The middle number
Prime factorization
16

14. v169=
13
41 -43 -47
The same sign as the base
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

15. The sum of any two primes will be ____ - unless ______.
A non-multiple of N.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The sum of any two primes will be even - unless one of the two primes is 2.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

16. 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.
ONLY the nonnegative root of the numberUNLIKE
31 -37
Either a multiple of N or a non-multiple of N

17. In an evenly spaced set - the average can be found by finding ________.
25
The middle number
A PERFECT SQUARE
13

18. Prime Numbers:4x
ODD
The average of an EVEN number of consecutive integers will NEVER be an integer.
41 -43 -47
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

19. The prime factorization of __________ contains only EVEN powers of primes.
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.
23 -29
EVEN

20. Prime Numbers:3x
97
11 -13 -17 -19
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
31 -37

21. For ODD ROOTS - the root has ______.
The same sign as the base
In an evenly spaced set - the average and the median are equal.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A PERFECT SQUARE

22. 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.
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.
The average of the set times the number of elements in the set

23. Positive integers with more than two factors are ____.
71 -73 -79
Never prime
Put the coefficient under the radical to get a better approximation
61 -67

24. Prime Numbers:5x
53 -59
31 -37
3·3n = 3^{n+1}
The middle number

25. v256=
The sum of any two primes will be even - unless one of the two primes is 2.
16
FACTOR
The average of an ODD number of consecutive integers will ALWAYS be an integer.

26. The formula for finding the number of consecutive multiples in a set is _______.
ODD
[(last - first) / increment] + 1
53 -59
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.

27. 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?
15
1.7
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.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

28. Prime Numbers:8x
83 -89
25
A PERFECT SQUARE
EVEN

29. Prime Numbers:1x
11 -13 -17 -19
97
2 -3 -5 -7
The average of the set times the number of elements in the set

30. If estimating a root with a coefficient - _____ .
Either a multiple of N or a non-multiple of N
The middle number
2 -3 -5 -7
Put the coefficient under the radical to get a better approximation

31. v196=
14
15
1.4
[(last - first) / increment] + 1

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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
13
PERFECT CUBES
83 -89

33. 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.
A PERFECT SQUARE
Prime
The average of an EVEN number of consecutive integers will NEVER be an integer.

34. If N is a divisor of x and y - then _______.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
N is a divisor of x+y
2.5
The middle number

35. 3n + 3n + 3n = _____ = ______
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The same sign as the base
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
3·3n = 3^{n+1}

36. v2˜
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The middle number
1.4
EVEN

37. 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.
61 -67
Either a multiple of N or a non-multiple of N
ONLY the nonnegative root of the numberUNLIKE

38. In an evenly spaced set - the ____ and the ____ are equal.
The sum of any two primes will be even - unless one of the two primes is 2.
2 -3 -5 -7
In an evenly spaced set - the average and the median are equal.
14

39. Prime Numbers:2x
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
13
A non-multiple of N.
23 -29

40. Any integer with an EVEN number of total factors cannot be ______.
2 -3 -5 -7
ONLY the nonnegative root of the numberUNLIKE
The PRODUCT of n consecutive integers is divisible by n!.
A PERFECT SQUARE

41. Prime Numbers:9x
25
[(last - first) / increment] + 1
97
1. The smallest or largest element 2. The increment 3. The number of items in the set

42. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
25
ONLY the nonnegative root of the numberUNLIKE
The average of an ODD number of consecutive integers will ALWAYS be an integer.
97

43. v3˜
15
1.7
31 -37
2.5

44. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
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.
53 -59
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

45. 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
ODD
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

46. How to solve: For any positive integer n - the sum of the 1st n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 301? (A) 10 -100 (B) 20 -200 (C) 22 -650 (D) 40 -200 (E) 45 -150
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
41 -43 -47
A PERFECT SQUARE
EVEN

47. The average of an ODD number of consecutive integers will ________ be an integer.
Never prime
The average of an ODD number of consecutive integers will ALWAYS be an integer.
41 -43 -47
ODD

48. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
[(last - first) / increment] + 1
PERFECT CUBES
ODD

49. All perfect squares have a(n) _________ number of total factors.
[(last - first) / increment] + 1
71 -73 -79
ODD
Put the coefficient under the radical to get a better approximation

50. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
EVEN
A PERFECT SQUARE
FACTOR
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