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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. N! is _____ of all integers from 1 to N.
71 -73 -79
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
A MULTIPLE
A PERFECT SQUARE

2. In an evenly spaced set - the sum of the terms is equal to ____.
11 -13 -17 -19
31 -37
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

3. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
The same sign as the base
FACTOR
1.4
2.5

4. If the problem states/assumes that a number is an integer - check to see if you can use _______.
97
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.
Prime factorization
The average of an EVEN number of consecutive integers will NEVER be an integer.

5. 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
PERFECT CUBES
2.5
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.

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

7. If N is a divisor of x and y - then _______.
53 -59
23 -29
Prime factorization
N is a divisor of x+y

8. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
Either a multiple of N or a non-multiple of N
Put the coefficient under the radical to get a better approximation
A MULTIPLE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

9. Prime Numbers:9x
EVEN
A non-multiple of N.
The sum of any two primes will be even - unless one of the two primes is 2.
97

10. How to find the sum of consecutive integers:
61 -67
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.
EVEN
11 -13 -17 -19

11. Any integer with an EVEN number of total factors cannot be ______.
14
A PERFECT SQUARE
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

12. Positive integers with only two factors must be ___.
The PRODUCT of n consecutive integers is divisible by n!.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The average of an EVEN number of consecutive integers will NEVER be an integer.
Prime

13. Prime Numbers:4x
41 -43 -47
ONLY the nonnegative root of the numberUNLIKE
Never prime
71 -73 -79

14. The average of an EVEN number of consecutive integers will ________ be an integer.
13
If 2 cannot be one of the primes in the sum - the sum must be even.
The average of an EVEN number of consecutive integers will NEVER be an integer.
PERFECT CUBES

15. In an evenly spaced set - the ____ and the ____ are equal.
1.4
In an evenly spaced set - the average and the median are equal.
61 -67
The same sign as the base

16. Prime Numbers:3x
1.4
31 -37
A PERFECT SQUARE
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.

17. The formula for finding the number of consecutive multiples in a set is _______.
23 -29
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
[(last - first) / increment] + 1
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

18. 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
Put the coefficient under the radical to get a better approximation
31 -37
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
41 -43 -47

19. v196=
14
ODD
83 -89
[(last - first) / increment] + 1

20. v169=
53 -59
Never prime
13
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.

21. If estimating a root with a coefficient - _____ .
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.
Put the coefficient under the radical to get a better approximation
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
25

22. Prime Numbers:5x
2 -3 -5 -7
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
53 -59

23. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
23 -29
N is a divisor of x+y
[(last - first) / increment] + 1
A non-multiple of N.

24. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
In an evenly spaced set - the average and the median are equal.
Either a multiple of N or a non-multiple of N
1. The smallest or largest element 2. The increment 3. The number of items in the set
Put the coefficient under the radical to get a better approximation

25. v625=
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
25
EVEN
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.

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. Let N be an integer. If you add two non-multiples of N - the result could be _______.
31 -37
1. The smallest or largest element 2. The increment 3. The number of items in the set
15
Either a multiple of N or a non-multiple of N

28. The two statements in a data sufficiency problem will _______________.
15
The sum of any two primes will be even - unless one of the two primes is 2.
NEVER CONTRADICT ONE ANOTHER
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

29. Prime Numbers:0x
2 -3 -5 -7
3·3n = 3^{n+1}
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.
23 -29

30. v225=
15
In an evenly spaced set - the average and the median are equal.
A non-multiple of N.
Prime factorization

31. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
83 -89
A PERFECT SQUARE

32. Prime factors of _____ must come in pairs of three.
The same sign as the base
PERFECT CUBES
1. The smallest or largest element 2. The increment 3. The number of items in the set
The sum of any two primes will be even - unless one of the two primes is 2.

33. Prime Numbers:7x
A MULTIPLE
EVEN
97
71 -73 -79

34. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
PERFECT CUBES
71 -73 -79
1.7

35. v256=
11 -13 -17 -19
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Prime factorization
16

36. v2˜
1.4
A PERFECT SQUARE
[(last - first) / increment] + 1
The average of an ODD number of consecutive integers will ALWAYS be an integer.

37. 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?
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
83 -89
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.
61 -67

38. v5˜
71 -73 -79
The sum of any two primes will be even - unless one of the two primes is 2.
23 -29
2.5

39. v3˜
ODD
71 -73 -79
1.7
EVEN

40. The average of an ODD number of consecutive integers will ________ be an integer.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
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. For ODD ROOTS - the root has ______.
14
A PERFECT SQUARE
NEVER CONTRADICT ONE ANOTHER
The same sign as the base

42. Positive integers with more than two factors are ____.
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.
Never prime
2 -3 -5 -7
A PERFECT SQUARE

43. All perfect squares have a(n) _________ number of total factors.
A non-multiple of N.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
ODD
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

44. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
NEVER CONTRADICT ONE ANOTHER
83 -89
EVEN

45. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
PERFECT CUBES
13
83 -89

46. Prime Numbers:1x
FACTOR
Prime factorization
11 -13 -17 -19
13

47. 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.
41 -43 -47
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.

48. Prime Numbers:6x
In an evenly spaced set - the average and the median are equal.
1. The smallest or largest element 2. The increment 3. The number of items in the set
61 -67
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

49. Any integer with an ODD number of total factors must be _______.
Either a multiple of N or a non-multiple of N
A PERFECT SQUARE
2.5
ONLY the nonnegative root of the numberUNLIKE

50. In an evenly spaced set - the average can be found by finding ________.
A non-multiple of N.
The middle number
1.4
A PERFECT SQUARE