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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:0x
A non-multiple of N.
PERFECT CUBES
2 -3 -5 -7
The same sign as the base

2. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
61 -67
The same sign as the base
1.4

3. Prime Numbers:6x
15
Never prime
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
61 -67

4. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
15
Either a multiple of N or a non-multiple of N
Never prime

5. The prime factorization of __________ contains only EVEN powers of primes.
The same sign as the base
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
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 PERFECT SQUARE

6. If N is a divisor of x and y - then _______.
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
83 -89
N is a divisor of x+y
EVEN

7. N! is _____ of all integers from 1 to N.
23 -29
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 MULTIPLE
N is a divisor of x+y

8. Let N be an integer. If you add two non-multiples of N - the result could be _______.
Prime
Either a multiple of N or a non-multiple of N
61 -67
1.4

9. The prime factorization of a perfect square contains only ______ powers of primes.
In an evenly spaced set - the average and the median are equal.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
11 -13 -17 -19
EVEN

10. In an evenly spaced set - the sum of the terms is equal to ____.
25
The average of the set times the number of elements in the set
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

11. 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
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
25
The sum of any two primes will be even - unless one of the two primes is 2.

12. In an evenly spaced set - the average can be found by finding ________.
The middle number
The average of an ODD number of consecutive integers will ALWAYS be an integer.
15
The average of an EVEN number of consecutive integers will NEVER be an integer.

13. v256=
53 -59
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.
ODD
16

14. The two statements in a data sufficiency problem will _______________.
71 -73 -79
NEVER CONTRADICT ONE ANOTHER
13
97

15. Prime Numbers:1x
ONLY the nonnegative root of the numberUNLIKE
11 -13 -17 -19
EVEN
1. The smallest or largest element 2. The increment 3. The number of items in the set

16. Prime Numbers:5x
23 -29
A MULTIPLE
53 -59
The average of an EVEN number of consecutive integers will NEVER be an integer.

17. Prime Numbers:2x
97
Put the coefficient under the radical to get a better approximation
FACTOR
23 -29

18. In an evenly spaced set - the mean and median are equal to the _____ of _________.
NEVER CONTRADICT ONE ANOTHER
In an evenly spaced set - the average and the median are equal.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

19. Prime Numbers:7x
A non-multiple of N.
71 -73 -79
A PERFECT SQUARE
The sum of any two primes will be even - unless one of the two primes is 2.

20. 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?
31 -37
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.
A PERFECT SQUARE
2.5

21. v2˜
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
[(last - first) / increment] + 1
1.4
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

22. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
23 -29
FACTOR
13
Put the coefficient under the radical to get a better approximation

23. Positive integers with only two factors must be ___.
Prime
The PRODUCT of n consecutive integers is divisible by n!.
The average of an EVEN number of consecutive integers will NEVER be an integer.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

24. Positive integers with more than two factors are ____.
The average of the set times the number of elements in the set
A PERFECT SQUARE
ODD
Never prime

25. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
41 -43 -47
16
[(last - first) / increment] + 1

26. 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
11 -13 -17 -19
EVEN

27. Prime Numbers:4x
83 -89
The same sign as the base
16
41 -43 -47

28. v169=
31 -37
1.4
13
A PERFECT SQUARE

29. The PRODUCT of n consecutive integers is divisible by ____.
The middle number
71 -73 -79
The PRODUCT of n consecutive integers is divisible by n!.
3·3n = 3^{n+1}

30. v225=
25
The sum of any two primes will be even - unless one of the two primes is 2.
23 -29
15

31. v5˜
2.5
1.4
ODD
The same sign as the base

32. Any integer with an ODD number of total factors must be _______.
11 -13 -17 -19
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.
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE

33. Any integer with an EVEN number of total factors cannot be ______.
31 -37
A MULTIPLE
The middle number
A PERFECT SQUARE

34. If estimating a root with a coefficient - _____ .
A non-multiple of N.
A PERFECT SQUARE
Put the coefficient under the radical to get a better approximation
A MULTIPLE

35. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
83 -89
53 -59
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

36. 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
FACTOR
The average of an EVEN number of consecutive integers will NEVER 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
53 -59

37. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
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.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The sum of any two primes will be even - unless one of the two primes is 2.

38. 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.
2 -3 -5 -7
PERFECT CUBES
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

39. Prime Numbers:3x
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.
A PERFECT SQUARE
31 -37
FACTOR

40. 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.
1.7
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.

41. 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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42. How to find the sum of consecutive integers:
15
23 -29
The average of an EVEN number of consecutive integers will NEVER be an integer.
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.

43. All perfect squares have a(n) _________ number of total factors.
A MULTIPLE
16
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
ODD

44. v625=
The PRODUCT of n consecutive integers is divisible by n!.
2.5
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.
25

45. Prime Numbers:9x
A MULTIPLE
53 -59
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.

46. v3˜
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE
1.7

47. Prime Numbers:8x
83 -89
Prime factorization
N is a divisor of x+y
The sum of any two primes will be even - unless one of the two primes is 2.

48. v196=
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
[(last - first) / increment] + 1
14
11 -13 -17 -19

49. If the problem states/assumes that a number is an integer - check to see if you can use _______.
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. The smallest or largest element 2. The increment 3. The number of items in the set
Prime factorization
Prime

50. ³v216 =
ONLY the nonnegative root of the numberUNLIKE
15
13
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6