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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
Prime
23 -29
N is a divisor of x+y
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

2. Prime Numbers:6x
61 -67
ODD
The middle number
In an evenly spaced set - the average and the median are equal.

3. For ODD ROOTS - the root has ______.
1.7
61 -67
The same sign as the base
23 -29

4. 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
In an evenly spaced set - the average and the median are equal.
The PRODUCT of n consecutive integers is divisible by n!.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

5. Prime factors of _____ must come in pairs of three.
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.
PERFECT CUBES
The same sign as the base

6. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
11 -13 -17 -19
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

7. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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.
15

8. Prime Numbers:4x
97
41 -43 -47
1.7
The sum of any two primes will be even - unless one of the two primes is 2.

9. In an evenly spaced set - the sum of the terms is equal to ____.
Either a multiple of N or a non-multiple of N
15
The average of the set times the number of elements in the set
83 -89

10. v196=
14
2 -3 -5 -7
16
1.7

11. The average of an ODD number of consecutive integers will ________ be an integer.
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.
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

12. If 2 cannot be one of the primes in the sum - the sum must 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.
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.
Put the coefficient under the radical to get a better approximation
If 2 cannot be one of the primes in the sum - the sum must be even.

13. All perfect squares have a(n) _________ number of total factors.
A PERFECT SQUARE
A PERFECT SQUARE
1.4
ODD

14. Prime Numbers:0x
Prime factorization
3·3n = 3^{n+1}
2 -3 -5 -7
The PRODUCT of n consecutive integers is divisible by n!.

15. Let N be an integer. If you add two non-multiples of N - the result could be _______.
71 -73 -79
ONLY the nonnegative root of the numberUNLIKE
Either a multiple of N or a non-multiple of N
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.

16. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
11 -13 -17 -19
If 2 cannot be one of the primes in the sum - the sum must be even.
The PRODUCT of n consecutive integers is divisible by n!.

17. In an evenly spaced set - the average can be found by finding ________.
The middle number
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
1.4

18. ³v216 =
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 mean and median are equal to the average of the first and the last number.
FACTOR
41 -43 -47

19. The two statements in a data sufficiency problem will _______________.
61 -67
83 -89
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
NEVER CONTRADICT ONE ANOTHER

20. Prime Numbers:8x
11 -13 -17 -19
83 -89
53 -59
Never prime

21. v3˜
1.4
A PERFECT SQUARE
1.7
A MULTIPLE

22. Positive integers with only two factors must be ___.
Either a multiple of N or a non-multiple of N
The sum of any two primes will be even - unless one of the two primes is 2.
The average of an EVEN number of consecutive integers will NEVER be an integer.
Prime

23. Positive integers with more than two factors are ____.
NEVER CONTRADICT ONE ANOTHER
Never prime
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
23 -29

24. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
EVEN
The middle number
11 -13 -17 -19
FACTOR

25. Prime Numbers:7x
71 -73 -79
97
13
The same sign as the base

26. v625=
25
23 -29
A PERFECT SQUARE
PERFECT CUBES

27. 3n + 3n + 3n = _____ = ______
31 -37
Prime
3·3n = 3^{n+1}
In an evenly spaced set - the average and the median are equal.

28. Prime Numbers:5x
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
53 -59
23 -29

29. Prime Numbers:3x
A PERFECT SQUARE
2.5
31 -37
1.7

30. If N is a divisor of x and y - then _______.
The sum of any two primes will be even - unless one of the two primes is 2.
N is a divisor of x+y
2.5
Either a multiple of N or a non-multiple of N

31. Prime Numbers:1x
The middle number
16
11 -13 -17 -19
Never prime

32. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
The middle number
FACTOR
71 -73 -79
1. The smallest or largest element 2. The increment 3. The number of items in the set

33. N! is _____ of all integers from 1 to N.
Never prime
The average of an ODD number of consecutive integers will ALWAYS be an integer.
EVEN
A MULTIPLE

34. Prime Numbers:9x
1. The smallest or largest element 2. The increment 3. The number of items in the set
97
The middle number
41 -43 -47

35. v5˜
2.5
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The middle number
14

36. The sum of any two primes will be ____ - unless ______.
The sum of any two primes will be even - unless one of the two primes is 2.
97
ONLY the nonnegative root of the numberUNLIKE
1.7

37. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Never prime
The average of the set times the number of elements in the set
Prime factorization
ODD

38. 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
EVEN
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The sum of any two primes will be even - unless one of the two primes is 2.

39. The formula for finding the number of consecutive multiples in a set 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.
25
[(last - first) / increment] + 1
A MULTIPLE

40. The average of an EVEN number of consecutive integers will ________ be an integer.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
61 -67
The average of an EVEN number of consecutive integers will NEVER be an integer.
Prime factorization

41. The prime factorization of a perfect square contains only ______ powers of primes.
1. The smallest or largest element 2. The increment 3. The number of items in the set
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.
11 -13 -17 -19

42. v169=
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
23 -29
13
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

43. v2˜
N is a divisor of x+y
[(last - first) / increment] + 1
1.4
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

44. Prime Numbers:2x
23 -29
Either a multiple of N or a non-multiple of 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.
83 -89

45. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
1.4
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
2 -3 -5 -7

46. v256=
41 -43 -47
16
PERFECT CUBES
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

47. 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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48. In an evenly spaced set - the mean and median are equal to the _____ of _________.
13
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
97
FACTOR

49. The PRODUCT of n consecutive integers is divisible by ____.
23 -29
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 sum of any two primes will be even - unless one of the two primes is 2.
The PRODUCT of n consecutive integers is divisible by n!.

50. 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?
PERFECT CUBES
Either a multiple of N or a non-multiple of N
16
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.