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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:9x
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.
97
13
The same sign as the base

2. In an evenly spaced set - the average can be found by finding ________.
The same sign as the base
97
The middle number
23 -29

3. The average of an ODD number of consecutive integers will ________ be an integer.
41 -43 -47
The average of an ODD number of consecutive integers will ALWAYS 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.
The middle number

4. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
A PERFECT SQUARE
FACTOR
14
In an evenly spaced set - the average and the median are equal.

5. In an evenly spaced set - the sum of the terms is equal to ____.
31 -37
A PERFECT SQUARE
The average of the set times the number of elements in the set
Put the coefficient under the radical to get a better approximation

6. For ODD ROOTS - the root has ______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The same sign as the base
The PRODUCT of n consecutive integers is divisible by n!.
ODD

7. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
3·3n = 3^{n+1}
The average of an ODD number of consecutive integers will ALWAYS be an integer.
In an evenly spaced set - the average and the median are equal.

8. v2˜
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. The smallest or largest element 2. The increment 3. The number of items in the set
1.4
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

9. v196=
1.4
FACTOR
14
[(last - first) / increment] + 1

10. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
3·3n = 3^{n+1}
[(last - first) / increment] + 1
The average of an ODD number of consecutive integers will ALWAYS be an integer.

11. Prime Numbers:1x
The average of an EVEN number of consecutive integers will NEVER be an integer.
11 -13 -17 -19
13
Either a multiple of N or a non-multiple of N

12. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
A MULTIPLE
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.
EVEN

13. Positive integers with more than two factors are ____.
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
Never prime
The same sign as the base
ONLY the nonnegative root of the numberUNLIKE

14. If the problem states/assumes that a number is an integer - check to see if you can use _______.
14
N is a divisor of x+y
Prime factorization
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.

15. Prime Numbers:2x
NEVER CONTRADICT ONE ANOTHER
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.
23 -29

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?
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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.
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.

17. Prime Numbers:0x
ODD
2 -3 -5 -7
PERFECT CUBES
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

18. The average of an EVEN number of consecutive integers will ________ be an integer.
[(last - first) / increment] + 1
The average of an EVEN number of consecutive integers will NEVER be an integer.
PERFECT CUBES
A non-multiple of N.

19. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
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
A non-multiple of N.
The PRODUCT of n consecutive integers is divisible by n!.

20. Prime Numbers:4x
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Never prime
41 -43 -47
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

21. All perfect squares have a(n) _________ number of total factors.
Put the coefficient under the radical to get a better approximation
ODD
If 2 cannot be one of the primes in the sum - the sum must be even.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

22. 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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23. v5˜
Prime factorization
83 -89
11 -13 -17 -19
2.5

24. How to find the sum of consecutive integers:
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.
53 -59
13

25. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
2.5
A PERFECT SQUARE
N is a divisor of x+y
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

26. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
2 -3 -5 -7
A MULTIPLE

27. ³v216 =
PERFECT CUBES
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Either a multiple of N or a non-multiple of N
The middle number

28. v169=
If 2 cannot be one of the primes in the sum - the sum must be even.
[(last - first) / increment] + 1
13
The average of an ODD number of consecutive integers will ALWAYS be an integer.

29. Any integer with an ODD number of total factors must be _______.
97
A PERFECT SQUARE
ONLY the nonnegative root of the numberUNLIKE
2.5

30. The sum of any two primes will be ____ - unless ______.
3·3n = 3^{n+1}
97
A MULTIPLE
The sum of any two primes will be even - unless one of the two primes is 2.

31. The prime factorization of __________ contains only EVEN powers of primes.
In an evenly spaced set - the average and the median are equal.
A PERFECT SQUARE
FACTOR
Prime

32. 3n + 3n + 3n = _____ = ______
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.
In an evenly spaced set - the average and the median are equal.
71 -73 -79

33. The prime factorization of a perfect square contains only ______ powers of primes.
A non-multiple of N.
14
In an evenly spaced set - the average and the median are equal.
EVEN

34. N! is _____ of all integers from 1 to N.
Never prime
A MULTIPLE
23 -29
The same sign as the base

35. v256=
2.5
The PRODUCT of n consecutive integers is divisible by n!.
83 -89
16

36. The two statements in a data sufficiency problem will _______________.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A non-multiple of N.
NEVER CONTRADICT ONE ANOTHER
2.5

37. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
15
41 -43 -47
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.
1. The smallest or largest element 2. The increment 3. The number of items in the set

38. If N is a divisor of x and y - then _______.
EVEN
A PERFECT SQUARE
Never prime
N is a divisor of x+y

39. If 2 cannot be one of the primes in the sum - the sum must be _____.
61 -67
A MULTIPLE
PERFECT CUBES
If 2 cannot be one of the primes in the sum - the sum must be even.

40. Prime Numbers:3x
2.5
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
1.4
31 -37

41. v225=
15
The same sign as the base
Either a multiple of N or a non-multiple of N
PERFECT CUBES

42. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
15
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
In an evenly spaced set - the average and the median are equal.

43. Prime Numbers:8x
N is a divisor of x+y
If 2 cannot be one of the primes in the sum - the sum must be even.
83 -89
The middle number

44. Prime Numbers:5x
The sum of any two primes will be even - unless one of the two primes is 2.
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
The average of an EVEN number of consecutive integers will NEVER be an integer.

45. Prime factors of _____ must come in pairs of three.
41 -43 -47
Put the coefficient under the radical to get a better approximation
[(last - first) / increment] + 1
PERFECT CUBES

46. v3˜
1.7
71 -73 -79
EVEN
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.

47. Prime Numbers:6x
13
The average of the set times the number of elements in the set
Prime
61 -67

48. Prime Numbers:7x
71 -73 -79
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.
25
23 -29

49. 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
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.
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

50. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
1. The smallest or largest element 2. The increment 3. The number of items in the set
PERFECT CUBES
EVEN