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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
A PERFECT SQUARE
2.5
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
EVEN

2. The PRODUCT of n consecutive integers is divisible by ____.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
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.
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.

3. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
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.
Never prime
The sum of any two primes will be even - unless one of the two primes is 2.

4. N! is _____ of all integers from 1 to N.
A MULTIPLE
61 -67
N is a divisor of x+y
Never prime

5. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
If 2 cannot be one of the primes in the sum - the sum must be even.
In an evenly spaced set - the average and the median are equal.

6. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
Prime
A non-multiple of N.
Prime factorization

7. v256=
A PERFECT SQUARE
31 -37
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
16

8. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.
83 -89

9. For ODD ROOTS - the root has ______.
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 same sign as the base
3·3n = 3^{n+1}
1.4

10. Any integer with an EVEN number of total factors cannot be ______.
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 same sign as the base
A PERFECT SQUARE
Prime factorization

11. 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 PRODUCT of n consecutive integers is divisible by n!.
97
ODD

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
Prime
NEVER CONTRADICT ONE ANOTHER
14

13. Let N be an integer. If you add two non-multiples of N - the result could be _______.
71 -73 -79
31 -37
Either a multiple of N or a non-multiple of N
PERFECT CUBES

14. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
2.5
PERFECT CUBES
1.4

15. Prime Numbers:2x
23 -29
83 -89
NEVER CONTRADICT ONE ANOTHER
Put the coefficient under the radical to get a better approximation

16. If the problem states/assumes that a number is an integer - check to see if you can use _______.
A PERFECT SQUARE
Prime factorization
A non-multiple of N.
EVEN

17. Prime Numbers:3x
In an evenly spaced set - the average and the median are equal.
1. The smallest or largest element 2. The increment 3. The number of items in the set
14
31 -37

18. The sum of any two primes will be ____ - unless ______.
83 -89
In an evenly spaced set - the average and the median are equal.
A MULTIPLE
The sum of any two primes will be even - unless one of the two primes is 2.

19. Prime Numbers:8x
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.
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
NEVER CONTRADICT ONE ANOTHER

20. 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 same sign as the base
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.
ONLY the nonnegative root of the numberUNLIKE

21. How to find the sum of consecutive integers:
FACTOR
In an evenly spaced set - the mean and median are equal to the average of the first and the last 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.
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.

22. Prime Numbers:0x
The middle number
1.4
2 -3 -5 -7
ODD

23. 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

24. The formula for finding the number of consecutive multiples in a set is _______.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
[(last - first) / increment] + 1
97
13

25. v225=
1. The smallest or largest element 2. The increment 3. The number of items in the set
A non-multiple of N.
15
2.5

26. Positive integers with more than two factors are ____.
Never prime
The sum of any two primes will be even - unless one of the two primes is 2.
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set

27. Prime Numbers:9x
97
The average of an ODD number of consecutive integers will ALWAYS be an integer.
If 2 cannot be one of the primes in the sum - the sum must be even.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

28. Prime Numbers:5x
The same sign as the base
Never prime
53 -59
N is a divisor of x+y

29. 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.
83 -89
The PRODUCT of n consecutive integers is divisible by n!.
2.5

30. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
97
FACTOR
A MULTIPLE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

31. If 2 cannot be one of the primes in the sum - the sum must be _____.
14
PERFECT CUBES
15
If 2 cannot be one of the primes in the sum - the sum must be even.

32. The average of an ODD number of consecutive integers will ________ be an integer.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
13
A PERFECT SQUARE
If 2 cannot be one of the primes in the sum - the sum must be even.

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

34. If N is a divisor of x and y - then _______.
The PRODUCT of n consecutive integers is divisible by n!.
13
A PERFECT SQUARE
N is a divisor of x+y

35. Prime Numbers:6x
[(last - first) / increment] + 1
1.4
61 -67
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.

36. Prime Numbers:7x
A MULTIPLE
71 -73 -79
2 -3 -5 -7
Never prime

37. Positive integers with only two factors must be ___.
The PRODUCT of n consecutive integers is divisible by n!.
The average of an EVEN number of consecutive integers will NEVER be an integer.
14
Prime

38. Prime Numbers:4x
41 -43 -47
A PERFECT SQUARE
PERFECT CUBES
83 -89

39. The two statements in a data sufficiency problem will _______________.
ODD
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
NEVER CONTRADICT ONE ANOTHER
EVEN

40. In an evenly spaced set - the sum of the terms is equal to ____.
13
The average of the set times the number of elements in the set
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.

41. In an evenly spaced set - the average can be found by finding ________.
A PERFECT SQUARE
The middle number
53 -59
61 -67

42. v2˜
Prime factorization
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
1.4
16

43. v5˜
2 -3 -5 -7
A PERFECT SQUARE
The PRODUCT of n consecutive integers is divisible by n!.
2.5

44. The average of an EVEN number of consecutive integers will ________ be an integer.
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
ODD
The average of an EVEN number of consecutive integers will NEVER be an integer.

45. v196=
Prime factorization
1. The smallest or largest element 2. The increment 3. The number of items in the set
If 2 cannot be one of the primes in the sum - the sum must be even.
14

46. 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.
The average of the set times the number of elements in the set
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Prime factorization

47. In an evenly spaced set - the ____ and the ____ are equal.
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.
[(last - first) / increment] + 1
31 -37

48. v169=
Prime factorization
13
Either a multiple of N or a non-multiple of N
61 -67

49. v625=
25
A MULTIPLE
The average of an EVEN number of consecutive integers will NEVER be an integer.
Put the coefficient under the radical to get a better approximation

50. All perfect squares have a(n) _________ number of total factors.
2.5
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A MULTIPLE
ODD