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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:3x
1.4
16
31 -37
PERFECT CUBES

2. If 2 cannot be one of the primes in the sum - the sum must be _____.
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 average of an ODD number of consecutive integers will ALWAYS be an integer.
83 -89

3. Prime Numbers:6x
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Never prime
ONLY the nonnegative root of the numberUNLIKE
61 -67

4. 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?
A PERFECT SQUARE
23 -29
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.

5. v625=
25
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Never prime
N is a divisor of x+y

6. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
A PERFECT SQUARE
53 -59
ONLY the nonnegative root of the numberUNLIKE
1.7

7. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
71 -73 -79
The PRODUCT of n consecutive integers is divisible by n!.
41 -43 -47

8. The sum of any two primes will be ____ - unless ______.
16
3·3n = 3^{n+1}
The sum of any two primes will be even - unless one of the two primes is 2.
Prime

9. Positive integers with more than two factors are ____.
97
15
Prime
Never prime

10. The average of an ODD number of consecutive integers will ________ be an integer.
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.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Prime

11. Positive integers with only two factors must be ___.
Never prime
13
A non-multiple of N.
Prime

12. 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
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
14
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

13. 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
41 -43 -47
31 -37
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.

14. In an evenly spaced set - the mean and median are equal to the _____ of _________.
A PERFECT SQUARE
11 -13 -17 -19
14
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

15. The prime factorization of a perfect square contains only ______ powers of primes.
ODD
EVEN
1.7
A PERFECT SQUARE

16. 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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17. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
3·3n = 3^{n+1}
FACTOR
25
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

18. 3n + 3n + 3n = _____ = ______
11 -13 -17 -19
The PRODUCT of n consecutive integers is divisible by n!.
The same sign as the base
3·3n = 3^{n+1}

19. Prime Numbers:9x
1. The smallest or largest element 2. The increment 3. The number of items in the set
25
97
Prime factorization

20. For ODD ROOTS - the root has ______.
Put the coefficient under the radical to get a better approximation
The same sign as the base
The sum of any two primes will be even - unless one of the two primes is 2.
A PERFECT SQUARE

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
[(last - first) / increment] + 1
13
83 -89

22. Prime Numbers:4x
41 -43 -47
31 -37
15
ONLY the nonnegative root of the numberUNLIKE

23. In an evenly spaced set - the average can be found by finding ________.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The middle number
ONLY the nonnegative root of the numberUNLIKE
FACTOR

24. 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.
NEVER CONTRADICT ONE ANOTHER
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.
53 -59

25. v3˜
14
1.7
Prime
NEVER CONTRADICT ONE ANOTHER

26. Prime Numbers:5x
EVEN
The sum of any two primes will be even - unless one of the two primes is 2.
53 -59
61 -67

27. Prime Numbers:2x
Never prime
A MULTIPLE
The middle number
23 -29

28. If N is a divisor of x and y - then _______.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
FACTOR
N is a divisor of x+y
A MULTIPLE

29. Prime Numbers:8x
25
The PRODUCT of n consecutive integers is divisible by n!.
83 -89
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

30. N! is _____ of all integers from 1 to 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
A MULTIPLE
2.5
97

31. v2˜
Either a multiple of N or a non-multiple of N
3·3n = 3^{n+1}
1.4
Prime

32. Prime factors of _____ must come in pairs of three.
EVEN
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.
PERFECT CUBES
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

33. How to find the sum of consecutive integers:
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
1. The smallest or largest element 2. The increment 3. The number of items in the set
2 -3 -5 -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.

34. Prime Numbers:0x
The sum of any two primes will be even - unless one of the two primes is 2.
97
3·3n = 3^{n+1}
2 -3 -5 -7

35. Let N be an integer. If you add two non-multiples of N - the result could be _______.
Either a multiple of N or a non-multiple of N
97
If 2 cannot be one of the primes in the sum - the sum must be even.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

36. In an evenly spaced set - the ____ and the ____ are equal.
2 -3 -5 -7
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
In an evenly spaced set - the average and the median are equal.

37. 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
31 -37
14
[(last - first) / increment] + 1

38. All perfect squares have a(n) _________ number of total factors.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
ODD
53 -59
41 -43 -47

39. Prime Numbers:7x
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.
In an evenly spaced set - the average and the median are equal.
The average of an EVEN number of consecutive integers will NEVER be an integer.
71 -73 -79

40. The average of an EVEN number of consecutive integers will ________ be an integer.
14
The average of an EVEN number of consecutive integers will NEVER be an integer.
71 -73 -79
2 -3 -5 -7

41. If estimating a root with a coefficient - _____ .
A PERFECT SQUARE
23 -29
FACTOR
Put the coefficient under the radical to get a better approximation

42. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set
1.7
15

43. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
3·3n = 3^{n+1}
Prime factorization
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

44. If the problem states/assumes that a number is an integer - check to see if you can use _______.
PERFECT CUBES
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Prime factorization
23 -29

45. v256=
16
Put the coefficient under the radical to get a better approximation
The sum of any two primes will be even - unless one of the two primes is 2.
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.

46. Any integer with an ODD number of total factors must be _______.
A non-multiple of N.
N is a divisor of x+y
A PERFECT SQUARE
The middle number

47. ³v216 =
PERFECT CUBES
Prime factorization
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
53 -59

48. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
2.5
Put the coefficient under the radical to get a better approximation
In an evenly spaced set - the average and the median are equal.

49. Prime Numbers:1x
FACTOR
11 -13 -17 -19
3·3n = 3^{n+1}
Never prime

50. v5˜
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 average of an EVEN number of consecutive integers will NEVER be an integer.
2.5
In an evenly spaced set - the average and the median are equal.