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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. ³v216 =
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
2 -3 -5 -7
The same sign as the base
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

2. N! is _____ of all integers from 1 to N.
[(last - first) / increment] + 1
13
A MULTIPLE
23 -29

3. Prime Numbers:4x
41 -43 -47
In an evenly spaced set - the average and the median are equal.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Either a multiple of N or a non-multiple of N

4. 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.
16
The same sign as the base
61 -67

5. The sum of any two primes will be ____ - unless ______.
ODD
NEVER CONTRADICT ONE ANOTHER
25
The sum of any two primes will be even - unless one of the two primes is 2.

6. Prime Numbers:7x
Put the coefficient under the radical to get a better approximation
71 -73 -79
In an evenly spaced set - the average and the median are equal.
25

7. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
Never prime
The average of the set times the number of elements in the set
If 2 cannot be one of the primes in the sum - the sum must be even.
ONLY the nonnegative root of the numberUNLIKE

8. Positive integers with more than two factors are ____.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
1. The smallest or largest element 2. The increment 3. The number of items in the set
Never prime
The sum of any two primes will be even - unless one of the two primes is 2.

9. All perfect squares have a(n) _________ number of total factors.
ONLY the nonnegative root of the numberUNLIKE
If 2 cannot be one of the primes in the sum - the sum must be even.
ODD
EVEN

10. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
If 2 cannot be one of the primes in the sum - the sum must be even.
Prime
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 _______.
3·3n = 3^{n+1}
Either a multiple of N or a non-multiple of N
PERFECT CUBES
61 -67

12. Prime Numbers:3x
31 -37
NEVER CONTRADICT ONE ANOTHER
Never prime
61 -67

13. Prime factors of _____ must come in pairs of three.
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.
3·3n = 3^{n+1}
PERFECT CUBES
The average of the set times the number of elements in the set

14. Prime Numbers:6x
61 -67
N is a divisor of x+y
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

15. v2˜
2.5
A MULTIPLE
Never prime
1.4

16. v256=
16
A MULTIPLE
A PERFECT SQUARE
1.4

17. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
15
FACTOR
EVEN
61 -67

18. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
Prime
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
FACTOR

19. v5˜
[(last - first) / increment] + 1
41 -43 -47
The same sign as the base
2.5

20. 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?
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 the set times the number of elements in the set
31 -37
A PERFECT SQUARE

21. v625=
2 -3 -5 -7
1.4
25
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

22. Prime Numbers:9x
Either a multiple of N or a non-multiple of N
Prime factorization
97
2 -3 -5 -7

23. v169=
97
2 -3 -5 -7
13
61 -67

24. How to find the sum of consecutive integers:
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.
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 SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A non-multiple of N.

25. The average of an EVEN number of consecutive integers will ________ be an integer.
In an evenly spaced set - the average and the median are equal.
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.
2.5
The average of an EVEN number of consecutive integers will NEVER be an integer.

26. v225=
The average of an EVEN number of consecutive integers will NEVER be an integer.
15
31 -37
A PERFECT SQUARE

27. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
41 -43 -47
15

28. v3˜
1.7
97
14
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

29. Prime Numbers:1x
NEVER CONTRADICT ONE ANOTHER
11 -13 -17 -19
1.7
A non-multiple of N.

30. The PRODUCT of n consecutive integers is divisible by ____.
2.5
EVEN
23 -29
The PRODUCT of n consecutive integers is divisible by n!.

31. Prime Numbers:5x
53 -59
1.7
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The PRODUCT of n consecutive integers is divisible by n!.

32. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
13
11 -13 -17 -19
In an evenly spaced set - the average and the median are equal.

33. The average of an ODD number of consecutive integers will ________ be an integer.
97
In an evenly spaced set - the average and the median are equal.
A PERFECT SQUARE
The average of an ODD number of consecutive integers will ALWAYS be an integer.

34. Positive integers with only two factors must be ___.
41 -43 -47
Prime
FACTOR
The middle number

35. Prime Numbers:8x
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
FACTOR
2 -3 -5 -7
83 -89

36. Prime Numbers:0x
2 -3 -5 -7
97
Prime factorization
1.4

37. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
Put the coefficient under the radical to get a better approximation
The average of the set times the number of elements in the set
16

38. In an evenly spaced set - the average can be found by finding ________.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
2.5
The middle number
In an evenly spaced set - the average and the median are equal.

39. If the problem states/assumes that a number is an integer - check to see if you can use _______.
1.7
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 ODD number of consecutive integers will ALWAYS be an integer.
Prime factorization

40. In an evenly spaced set - the sum of the terms is equal to ____.
[(last - first) / increment] + 1
13
NEVER CONTRADICT ONE ANOTHER
The average of the set times the number of elements in the set

41. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
97
1. The smallest or largest element 2. The increment 3. The number of items in the set
2.5

42. 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
2 -3 -5 -7
[(last - first) / increment] + 1
71 -73 -79

43. 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

44. Prime Numbers:2x
83 -89
61 -67
23 -29
ODD

45. 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
2.5
14
A PERFECT SQUARE
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

46. Any integer with an EVEN number of total factors cannot be ______.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
13
A PERFECT SQUARE
11 -13 -17 -19

47. If 2 cannot be one of the primes in the sum - the sum must be _____.
The middle number
The PRODUCT of n consecutive integers is divisible by n!.
If 2 cannot be one of the primes in the sum - the sum must be even.
NEVER CONTRADICT ONE ANOTHER

48. The formula for finding the number of consecutive multiples in a set is _______.
The average of an EVEN number of consecutive integers will NEVER be an integer.
NEVER CONTRADICT ONE ANOTHER
[(last - first) / increment] + 1
13

49. For ODD ROOTS - the root has ______.
Either a multiple of N or a non-multiple of N
83 -89
The sum of any two primes will be even - unless one of the two primes is 2.
The same sign as the base

50. 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
EVEN
61 -67
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.