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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 n consecutive integers is divisible by n if ____ - but not if ______.
FACTOR
61 -67
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

2. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
A PERFECT SQUARE
Either a multiple of N or a non-multiple of N
2.5

3. Any integer with an ODD number of total factors must be _______.
2 -3 -5 -7
71 -73 -79
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE

4. Prime Numbers:8x
83 -89
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
1.4
The same sign as the base

5. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
31 -37
ONLY the nonnegative root of the numberUNLIKE
71 -73 -79

6. How to find the sum of consecutive integers:
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set
Prime factorization
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.

7. v2˜
61 -67
1.7
1.4
1. The smallest or largest element 2. The increment 3. The number of items in the set

8. All perfect squares have a(n) _________ number of total factors.
53 -59
2 -3 -5 -7
ODD
15

9. 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

10. The sum of any two primes will be ____ - unless ______.
The PRODUCT of n consecutive integers is divisible by n!.
The sum of any two primes will be even - unless one of the two primes is 2.
Prime factorization
The average of an EVEN number of consecutive integers will NEVER be an integer.

11. Prime Numbers:7x
NEVER CONTRADICT ONE ANOTHER
23 -29
71 -73 -79
97

12. v3˜
1.7
25
Either a multiple of N or a non-multiple of N
The middle number

13. The average of an EVEN number of consecutive integers will ________ be an integer.
Put the coefficient under the radical to get a better approximation
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
The average of an EVEN number of consecutive integers will NEVER be an integer.

14. v625=
The same sign as the base
25
Prime factorization
61 -67

15. Positive integers with more than two factors are ____.
A non-multiple of N.
N is a divisor of x+y
In an evenly spaced set - the average and the median are equal.
Never prime

16. 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?
The sum of any two primes will be even - unless one of the two primes is 2.
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 mean and median are equal to the average of the first and the last number.
13

17. The prime factorization of a perfect square contains only ______ powers of primes.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Never prime
EVEN
71 -73 -79

18. 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.
97
The sum of any two primes will be even - unless one of the two primes is 2.
PERFECT CUBES

19. If N is a divisor of x and y - then _______.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The PRODUCT of n consecutive integers is divisible by n!.
N is a divisor of x+y
The average of an EVEN number of consecutive integers will NEVER be an integer.

20. The PRODUCT of n consecutive integers is divisible by ____.
PERFECT CUBES
1. The smallest or largest element 2. The increment 3. The number of items in the set
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The PRODUCT of n consecutive integers is divisible by n!.

21. The formula for finding the number of consecutive multiples in a set is _______.
The average of the set times the number of elements in the set
[(last - first) / increment] + 1
The PRODUCT of n consecutive integers is divisible by n!.
53 -59

22. Prime Numbers:6x
Prime factorization
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.
The average of an EVEN number of consecutive integers will NEVER be an integer.

23. For ODD ROOTS - the root has ______.
A PERFECT SQUARE
The PRODUCT of n consecutive integers is divisible by n!.
The same sign as the base
ODD

24. If the problem states/assumes that a number is an integer - check to see if you can use _______.
A PERFECT SQUARE
Prime factorization
71 -73 -79
83 -89

25. Prime Numbers:9x
11 -13 -17 -19
The middle number
97
A MULTIPLE

26. In an evenly spaced set - the mean and median are equal to the _____ of _________.
The sum of any two primes will be even - unless one of the two primes is 2.
[(last - first) / increment] + 1
2 -3 -5 -7
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

27. In an evenly spaced set - the average can be found by finding ________.
PERFECT CUBES
N is a divisor of x+y
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The middle number

28. The prime factorization of __________ contains only EVEN powers of primes.
Prime factorization
3·3n = 3^{n+1}
A PERFECT SQUARE
71 -73 -79

29. Let N be an integer. If you add two non-multiples of N - the result could be _______.
The sum of any two primes will be even - unless one of the two primes is 2.
61 -67
Either a multiple of N or a non-multiple of N
ONLY the nonnegative root of the numberUNLIKE

30. Positive integers with only two factors must be ___.
Put the coefficient under the radical to get a better approximation
Prime
A MULTIPLE
Prime factorization

31. 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
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.
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
PERFECT CUBES

32. Prime factors of _____ must come in pairs of three.
The sum of any two primes will be even - unless one of the two primes is 2.
PERFECT CUBES
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.

33. N! is _____ of all integers from 1 to N.
14
N is a divisor of x+y
A MULTIPLE
1. The smallest or largest element 2. The increment 3. The number of items in the set

34. Prime Numbers:2x
1.4
23 -29
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.

35. In an evenly spaced set - the ____ and the ____ are equal.
A non-multiple of N.
41 -43 -47
2 -3 -5 -7
In an evenly spaced set - the average and the median are equal.

36. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
15
Put the coefficient under the radical to get a better approximation
83 -89

37. If 2 cannot be one of the primes in the sum - the sum must be _____.
PERFECT CUBES
25
ODD
If 2 cannot be one of the primes in the sum - the sum must be even.

38. 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
23 -29
ODD
3·3n = 3^{n+1}
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

39. v225=
15
Prime
ODD
The middle number

40. The two statements in a data sufficiency problem will _______________.
In an evenly spaced set - the average and the median are equal.
FACTOR
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
NEVER CONTRADICT ONE ANOTHER

41. Prime Numbers:4x
31 -37
41 -43 -47
Prime factorization
Never prime

42. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
2 -3 -5 -7
[(last - first) / increment] + 1
FACTOR
Prime factorization

43. Prime Numbers:0x
N is a divisor of x+y
2 -3 -5 -7
11 -13 -17 -19
1. The smallest or largest element 2. The increment 3. The number of items in the set

44. If estimating a root with a coefficient - _____ .
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.
Put the coefficient under the radical to get a better approximation
1.7

45. Prime Numbers:1x
ONLY the nonnegative root of the numberUNLIKE
11 -13 -17 -19
A PERFECT SQUARE
53 -59

46. ³v216 =
N is a divisor of x+y
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The middle number
The average of an EVEN number of consecutive integers will NEVER be an integer.

47. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
41 -43 -47
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.
31 -37

48. v256=
2 -3 -5 -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.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
16

49. v196=
PERFECT CUBES
14
11 -13 -17 -19
97

50. Prime Numbers:5x
The same sign as the base
11 -13 -17 -19
The average of the set times the number of elements in the set
53 -59