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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. 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.
The sum of any two primes will be even - unless one of the two primes is 2.
The middle number
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. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
PERFECT CUBES
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
31 -37

3. If 2 cannot be one of the primes in the sum - the sum must be _____.
2 -3 -5 -7
A non-multiple of N.
If 2 cannot be one of the primes in the sum - the sum must be even.
[(last - first) / increment] + 1

4. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
83 -89
A PERFECT SQUARE
N is a divisor of x+y
1. The smallest or largest element 2. The increment 3. The number of items in the set

5. The prime factorization of a perfect square contains only ______ powers of primes.
16
ONLY the nonnegative root of the numberUNLIKE
EVEN
The same sign as the base

6. v2˜
14
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.
1. The smallest or largest element 2. The increment 3. The number of items in the set

7. Prime Numbers:3x
31 -37
A PERFECT SQUARE
FACTOR
Either a multiple of N or a non-multiple of N

8. Any integer with an EVEN number of total factors cannot be ______.
15
If 2 cannot be one of the primes in the sum - the sum must be even.
A PERFECT SQUARE
41 -43 -47

9. v5˜
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.
2.5
1. The smallest or largest element 2. The increment 3. The number of items in the set

10. In an evenly spaced set - the ____ and the ____ are equal.
61 -67
In an evenly spaced set - the average and the median are equal.
13
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

11. Prime Numbers:6x
61 -67
ODD
16
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

12. Any integer with an ODD number of total factors must be _______.
11 -13 -17 -19
The same sign as the base
Prime factorization
A PERFECT SQUARE

13. Positive integers with only two factors must be ___.
Prime
2 -3 -5 -7
A PERFECT SQUARE
2.5

14. Prime Numbers:5x
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.
53 -59
FACTOR

15. Prime Numbers:0x
The PRODUCT of n consecutive integers is divisible by n!.
[(last - first) / increment] + 1
2 -3 -5 -7
41 -43 -47

16. v169=
ODD
Prime factorization
1.4
13

17. The PRODUCT of n consecutive integers is divisible by ____.
A non-multiple of N.
Either a multiple of N or a non-multiple of N
83 -89
The PRODUCT of n consecutive integers is divisible by n!.

18. v225=
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 same sign as the base
83 -89
15

19. Prime Numbers:7x
71 -73 -79
15
If 2 cannot be one of the primes in the sum - the sum must be 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

20. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
16
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.
61 -67
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

21. Prime Numbers:4x
The average of the set times the number of elements in the set
41 -43 -47
The average of an EVEN number of consecutive integers will NEVER be an integer.
11 -13 -17 -19

22. Prime Numbers:9x
The sum of any two primes will be even - unless one of the two primes is 2.
FACTOR
97
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

23. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
53 -59
If 2 cannot be one of the primes in the sum - the sum must be even.
The same sign as the base

24. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
The middle number
NEVER CONTRADICT ONE ANOTHER
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

25. The sum of any two primes will be ____ - unless ______.
61 -67
In an evenly spaced set - the average and the median are equal.
A PERFECT SQUARE
The sum of any two primes will be even - unless one of the two primes is 2.

26. Prime Numbers:2x
23 -29
97
ONLY the nonnegative root of the numberUNLIKE
Never prime

27. 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.
In an evenly spaced set - the average and the median are equal.
Prime
3·3n = 3^{n+1}

28. Positive integers with more than two factors are ____.
Never prime
The PRODUCT of n consecutive integers is divisible by n!.
2 -3 -5 -7
3·3n = 3^{n+1}

29. v3˜
N is a divisor of x+y
14
25
1.7

30. If N is a divisor of x and y - then _______.
The average of the set times the number of elements in the set
PERFECT CUBES
71 -73 -79
N is a divisor of x+y

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
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 average of an EVEN number of consecutive integers will NEVER be an integer.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
83 -89

32. How to find the sum of consecutive integers:
The middle number
1.7
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.
16

33. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
The sum of any two primes will be even - unless one of the two primes is 2.
A MULTIPLE
FACTOR
1.4

34. If the problem states/assumes that a number is an integer - check to see if you can use _______.
The PRODUCT of n consecutive integers is divisible by n!.
97
Prime factorization
53 -59

35. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
FACTOR
41 -43 -47
A PERFECT SQUARE
ONLY the nonnegative root of the numberUNLIKE

36. 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.
14
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
83 -89

37. 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.
[(last - first) / increment] + 1
The PRODUCT of n consecutive integers is divisible by n!.
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

38. Prime Numbers:1x
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.
11 -13 -17 -19
NEVER CONTRADICT ONE ANOTHER
The average of the set times the number of elements in the set

39. Let N be an integer. If you add two non-multiples of N - the result could be _______.
The average of the set times the number of elements in the set
Prime
The same sign as the base
Either a multiple of N or a non-multiple of N

40. All perfect squares have a(n) _________ number of total factors.
ODD
11 -13 -17 -19
3·3n = 3^{n+1}
Prime

41. The two statements in a data sufficiency problem will _______________.
Prime
In an evenly spaced set - the average and the median are equal.
NEVER CONTRADICT ONE ANOTHER
[(last - first) / increment] + 1

42. The formula for finding the number of consecutive multiples in a set is _______.
N is a divisor of x+y
[(last - first) / increment] + 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.
The average of an ODD number of consecutive integers will ALWAYS be an integer.

43. v625=
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
14
25
11 -13 -17 -19

44. In an evenly spaced set - the average can be found by finding ________.
If 2 cannot be one of the primes in the sum - the sum must be even.
The middle number
Put the coefficient under the radical to get a better approximation
NEVER CONTRADICT ONE ANOTHER

45. ³v216 =
A MULTIPLE
41 -43 -47
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The middle number

46. 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
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.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The sum of any two primes will be even - unless one of the two primes is 2.
[(last - first) / increment] + 1

47. v196=
The sum of any two primes will be even - unless one of the two primes is 2.
A MULTIPLE
14
Prime factorization

48. 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

49. Prime Numbers:8x
83 -89
Prime factorization
In an evenly spaced set - the average and the median are equal.
3·3n = 3^{n+1}

50. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
The PRODUCT of n consecutive integers is divisible by n!.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
23 -29