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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. 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.
53 -59
The middle number
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

2. v2˜
A PERFECT SQUARE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
1.4
23 -29

3. 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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4. 3n + 3n + 3n = _____ = ______
The middle number
3·3n = 3^{n+1}
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.

5. The sum of any two primes will be ____ - unless ______.
41 -43 -47
Never prime
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.

6. ³v216 =
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
11 -13 -17 -19
NEVER CONTRADICT ONE ANOTHER
23 -29

7. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
14
Prime
A PERFECT SQUARE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

8. How to find the sum of consecutive integers:
31 -37
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.
1.7
The average of an EVEN number of consecutive integers will NEVER be an integer.

9. If the problem states/assumes that a number is an integer - check to see if you can use _______.
FACTOR
Prime factorization
1.7
The PRODUCT of n consecutive integers is divisible by n!.

10. The two statements in a data sufficiency problem will _______________.
97
NEVER CONTRADICT ONE ANOTHER
The middle number
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. Let N be an integer. If you add two non-multiples of N - the result could be _______.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
NEVER CONTRADICT ONE ANOTHER
83 -89
Either a multiple of N or a non-multiple of N

12. The PRODUCT of n consecutive integers is divisible by ____.
14
NEVER CONTRADICT ONE ANOTHER
3·3n = 3^{n+1}
The PRODUCT of n consecutive integers is divisible by n!.

13. Prime Numbers:8x
PERFECT CUBES
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.
83 -89
The PRODUCT of n consecutive integers is divisible by n!.

14. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
The average of an ODD number of consecutive integers will ALWAYS be 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.
11 -13 -17 -19

15. v625=
ODD
25
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE

16. The average of an EVEN number of consecutive integers will ________ be an integer.
83 -89
The PRODUCT of n consecutive integers is divisible by n!.
The same sign as the base
The average of an EVEN number of consecutive integers will NEVER be an integer.

17. Any integer with an EVEN number of total factors cannot be ______.
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
ONLY the nonnegative root of the numberUNLIKE
Either a multiple of N or a non-multiple of N

18. Prime Numbers:2x
A PERFECT SQUARE
23 -29
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.
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.

19. v225=
14
EVEN
The same sign as the base
15

20. Prime Numbers:7x
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The PRODUCT of n consecutive integers is divisible by n!.
ODD
71 -73 -79

21. In an evenly spaced set - the sum of the terms is equal to ____.
The average of the set times the number of elements in the set
ONLY the nonnegative root of the numberUNLIKE
The same sign as the base
Never prime

22. The average of an ODD number of consecutive integers will ________ be an integer.
The same sign as the base
A PERFECT SQUARE
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A MULTIPLE

23. In an evenly spaced set - the mean and median are equal to the _____ of _________.
FACTOR
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
1.7
11 -13 -17 -19

24. In an evenly spaced set - the ____ and the ____ are equal.
1. The smallest or largest element 2. The increment 3. The number of items in the set
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.
The middle number

25. For ODD ROOTS - the root has ______.
The same sign as the base
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
2 -3 -5 -7
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

26. The prime factorization of a perfect square contains only ______ powers of primes.
Put the coefficient under the radical to get a better approximation
The same sign as the base
53 -59
EVEN

27. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
In an evenly spaced set - the average and the median are equal.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
FACTOR
2 -3 -5 -7

28. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
61 -67
Prime factorization
N is a divisor of x+y

29. The formula for finding the number of consecutive multiples in a set is _______.
N is a divisor of x+y
61 -67
[(last - first) / increment] + 1
Put the coefficient under the radical to get a better approximation

30. v3˜
Prime
2.5
1.7
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

31. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
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.
The same sign as the base
1. The smallest or largest element 2. The increment 3. The number of items in the set

32. Prime Numbers:3x
ODD
1. The smallest or largest element 2. The increment 3. The number of items in the set
31 -37
13

33. v196=
A PERFECT SQUARE
14
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
15

34. In an evenly spaced set - the average can be found by finding ________.
53 -59
14
The middle number
A PERFECT SQUARE

35. Prime Numbers:5x
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.
1.7
53 -59

36. If N is a divisor of x and y - then _______.
13
A PERFECT SQUARE
N is a divisor of x+y
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

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?
NEVER CONTRADICT ONE ANOTHER
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 2 cannot be one of the primes in the sum - the sum must be even.
71 -73 -79

38. Prime Numbers:4x
16
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
41 -43 -47
2 -3 -5 -7

39. 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
13
61 -67
The average of the set times the number of elements in the set
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

40. Positive integers with only two factors must be ___.
A MULTIPLE
Prime factorization
Prime
A PERFECT SQUARE

41. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
The sum of any two primes will be even - unless one of the two primes is 2.
71 -73 -79
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
ONLY the nonnegative root of the numberUNLIKE

42. Prime factors of _____ must come in pairs of three.
23 -29
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
PERFECT CUBES
In an evenly spaced set - the average and the median are equal.

43. v169=
The same sign as the base
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.
13

44. Prime Numbers:0x
2 -3 -5 -7
Prime
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.
1.4

45. Prime Numbers:6x
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
61 -67
A PERFECT SQUARE
25

46. All perfect squares have a(n) _________ number of total factors.
53 -59
The sum of any two primes will be even - unless one of the two primes is 2.
41 -43 -47
ODD

47. v256=
2 -3 -5 -7
The sum of any two primes will be even - unless one of the two primes is 2.
31 -37
16

48. Prime Numbers:1x
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.
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.

49. Prime Numbers:9x
Prime
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
NEVER CONTRADICT ONE ANOTHER
97

50. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
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.
53 -59
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
ONLY the nonnegative root of the numberUNLIKE