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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. 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
2 -3 -5 -7
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

2. Prime Numbers:4x
1.4
41 -43 -47
PERFECT CUBES
15

3. v225=
A non-multiple of N.
33n = 3^{n+1}
A PERFECT SQUARE
15

4. If N is a divisor of x and y - then _______.
16
N is a divisor of x+y
41 -43 -47
PERFECT CUBES

5. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
11 -13 -17 -19
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.
A non-multiple of N.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

6. If the problem states/assumes that a number is an integer - check to see if you can use _______.
The average of an EVEN number of consecutive integers will NEVER be an integer.
The middle number
Prime factorization
2.5

7. Positive integers with only two factors must be ___.
In an evenly spaced set - the average and the median are equal.
Prime
The PRODUCT of n consecutive integers is divisible by n!.
The average of the set times the number of elements in the set

8. The two statements in a data sufficiency problem will _______________.
Prime factorization
2 -3 -5 -7
25
NEVER CONTRADICT ONE ANOTHER

9. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
The sum of any two primes will be even - unless one of the two primes is 2.
1.4
1. The smallest or largest element 2. The increment 3. The number of items in the set

10. N! is _____ of all integers from 1 to N.
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 MULTIPLE
ODD
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. For ODD ROOTS - the root has ______.
33n = 3^{n+1}
The same sign as the base
EVEN
14

12. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
The average of an ODD number of consecutive integers will ALWAYS be an integer.
16
71 -73 -79

13. 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.
ONLY the nonnegative root of the numberUNLIKE
2.5
The average of an ODD number of consecutive integers will ALWAYS be an integer.

14. v216 =
83 -89
EVEN
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2 3 = 6 - so v216 = v6 = 6

15. The sum of any two primes will be ____ - unless ______.
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 sum of any two primes will be even - unless one of the two primes is 2.
EVEN
61 -67

16. Prime Numbers:0x
71 -73 -79
2 -3 -5 -7
[(last - first) / increment] + 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.

17. Positive integers with more than two factors are ____.
31 -37
A PERFECT SQUARE
Never prime
In an evenly spaced set - the average and the median are equal.

18. Prime Numbers:7x
The middle number
23 -29
71 -73 -79
61 -67

19. Prime Numbers:8x
Prime factorization
83 -89
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.

20. The average of an ODD number of consecutive integers will ________ be an integer.
13
PERFECT CUBES
A MULTIPLE
The average of an ODD number of consecutive integers will ALWAYS be an integer.

21. v2
1.4
97
The average of the set times the number of elements in the set
16

22. In an evenly spaced set - the average can be found by finding ________.
The middle number
1. The smallest or largest element 2. The increment 3. The number of items in the set
A PERFECT SQUARE
FACTOR

23. In an evenly spaced set - the mean and median are equal to the _____ of _________.
83 -89
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
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

24. 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
53 -59
EVEN
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.
41 -43 -47

25. 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.
A MULTIPLE
If 2 cannot be one of the primes in the sum - the sum must be even.
The same sign as the base

26. Any integer with an EVEN number of total factors cannot be ______.
The same sign as the base
A PERFECT SQUARE
41 -43 -47
EVEN

27. v169=
[(last - first) / increment] + 1
41 -43 -47
The PRODUCT of n consecutive integers is divisible by n!.
13

28. The prime factorization of a perfect square contains only ______ powers of primes.
25
2 -3 -5 -7
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.

29. v625=
ODD
33n = 3^{n+1}
15
25

30. The formula for finding the number of consecutive multiples in a set is _______.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
83 -89
[(last - first) / increment] + 1
If 2 cannot be one of the primes in the sum - the sum must be even.

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
31 -37
EVEN
A PERFECT SQUARE

32. How to find the sum of consecutive integers:
97
Either a multiple of N or a non-multiple of N
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.
Never prime

33. Prime Numbers:9x
A MULTIPLE
A non-multiple of N.
97
ODD

34. 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
14
A non-multiple of N.
83 -89

35. Prime Numbers:2x
41 -43 -47
The same sign as the base
The average of an EVEN number of consecutive integers will NEVER be an integer.
23 -29

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

37. v256=
16
A PERFECT SQUARE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE

38. Prime Numbers:6x
61 -67
Prime factorization
N is a divisor of x+y
The average of the set times the number of elements in the set

39. v5
If 2 cannot be one of the primes in the sum - the sum must be even.
2.5
Either a multiple of N or a non-multiple of N
FACTOR

40. v3
The sum of any two primes will be even - unless one of the two primes is 2.
1. The smallest or largest element 2. The increment 3. The number of items in the set
1.7
Prime

41. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
15
53 -59
1. The smallest or largest element 2. The increment 3. The number of items in the set

42. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
16
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
The PRODUCT of n consecutive integers is divisible by n!.

43. 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.
1. The smallest or largest element 2. The increment 3. The number of items in the set
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.
1.4

44. Prime Numbers:5x
53 -59
1.7
41 -43 -47
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.

45. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
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.
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.
ONLY the nonnegative root of the numberUNLIKE

46. Prime Numbers:3x
ONLY the nonnegative root of the numberUNLIKE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A MULTIPLE
31 -37

47. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
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.
1.7
14

48. v196=
Either a multiple of N or a non-multiple of N
25
53 -59
14

49. Any integer with an ODD number of total factors must be _______.
1.4
The same sign as the base
53 -59
A PERFECT SQUARE

50. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
61 -67
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
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2 3 = 6 - so v216 = v6 = 6

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