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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. In an evenly spaced set - the ____ and the ____ are equal.
13
31 -37
In an evenly spaced set - the average and the median are equal.
The average of the set times the number of elements in the set

2. Prime Numbers:0x
EVEN
2 -3 -5 -7
Never prime
83 -89

3. The prime factorization of a perfect square contains only ______ powers of primes.
Never prime
EVEN
1.4
1. The smallest or largest element 2. The increment 3. The number of items in the set

4. N! is _____ of all integers from 1 to N.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
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
25
A MULTIPLE

5. v625=
16
The average of an EVEN number of consecutive integers will NEVER be an integer.
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
25

6. If 2 cannot be one of the primes in the sum - the sum must be _____.
25
EVEN
Never prime
If 2 cannot be one of the primes in the sum - the sum must be even.

7. The two statements in a data sufficiency problem will _______________.
ODD
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
[(last - first) / increment] + 1
NEVER CONTRADICT ONE ANOTHER

8. v225=
1.7
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
15
1.4

9. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
[(last - first) / increment] + 1
ONLY the nonnegative root of the numberUNLIKE
1.7

10. If N is a divisor of x and y - then _______.
If 2 cannot be one of the primes in the sum - the sum must be even.
31 -37
N is a divisor of x+y
The sum of any two primes will be even - unless one of the two primes is 2.

11. 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.
2 -3 -5 -7
2.5
The same sign as the base

12. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
NEVER CONTRADICT ONE ANOTHER
The average of the set times the number of elements 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.

13. v5˜
53 -59
Never prime
2.5
1. The smallest or largest element 2. The increment 3. The number of items in the set

14. v3˜
[(last - first) / increment] + 1
1.7
N is a divisor of x+y
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

15. v196=
NEVER CONTRADICT ONE ANOTHER
97
2 -3 -5 -7
14

16. The average of an ODD number of consecutive integers will ________ be an integer.
PERFECT CUBES
A PERFECT SQUARE
The average of an ODD number of consecutive integers will ALWAYS be an integer.
ONLY the nonnegative root of the numberUNLIKE

17. The formula for finding the number of consecutive multiples in a set is _______.
15
[(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.
1.4

18. Prime Numbers:6x
61 -67
A MULTIPLE
14
A PERFECT SQUARE

19. ³v216 =
53 -59
2.5
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
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

20. v169=
25
[(last - first) / increment] + 1
13
A MULTIPLE

21. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
13
A PERFECT SQUARE
The sum of any two primes will be even - unless one of the two primes is 2.

22. Prime Numbers:7x
71 -73 -79
A MULTIPLE
The same sign as the base
A PERFECT SQUARE

23. If the problem states/assumes that a number is an integer - check to see if you can use _______.
1.7
A non-multiple of N.
Prime factorization
A PERFECT SQUARE

24. The average of an EVEN number of consecutive integers will ________ be an integer.
A PERFECT SQUARE
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
FACTOR
The average of an EVEN number of consecutive integers will NEVER be an integer.

25. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
1.4
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.

26. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
The average of the set times the number of elements in the set
13
A non-multiple of N.
FACTOR

27. Prime Numbers:4x
41 -43 -47
16
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
31 -37

28. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
41 -43 -47
The average of an EVEN number of consecutive integers will NEVER be an integer.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

29. Prime Numbers:9x
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.
97
16

30. Prime Numbers:3x
53 -59
Prime
ODD
31 -37

31. Prime factors of _____ must come in pairs of three.
11 -13 -17 -19
N is a divisor of x+y
13
PERFECT CUBES

32. For ODD ROOTS - the root has ______.
The same sign as the base
A PERFECT SQUARE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
14

33. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
Prime
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
ONLY the nonnegative root of the numberUNLIKE
ODD

34. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
23 -29
The sum of any two primes will be even - unless one of the two primes is 2.
A non-multiple of N.

35. In an evenly spaced set - the average can be found by finding ________.
1.4
A PERFECT SQUARE
Prime
The middle number

36. How to find the sum of consecutive integers:
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.
NEVER CONTRADICT ONE ANOTHER
53 -59

37. 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?
NEVER CONTRADICT ONE ANOTHER
83 -89
53 -59
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.

38. 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.
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
FACTOR

39. Positive integers with only two factors must be ___.
83 -89
31 -37
Put the coefficient under the radical to get a better approximation
Prime

40. 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
23 -29
41 -43 -47
The same sign as the base
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

41. Prime Numbers:5x
The sum of any two primes will be even - unless one of the two primes is 2.
EVEN
53 -59
A PERFECT SQUARE

42. Positive integers with more than two factors are ____.
31 -37
23 -29
Never prime
1. The smallest or largest element 2. The increment 3. The number of items in the set

43. Prime Numbers:1x
3·3n = 3^{n+1}
1.4
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.
11 -13 -17 -19

44. Prime Numbers:2x
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.
23 -29
61 -67
41 -43 -47

45. 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

46. Let N be an integer. If you add two non-multiples of N - the result could be _______.
ONLY the nonnegative root of the numberUNLIKE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
If 2 cannot be one of the primes in the sum - the sum must be even.
Either a multiple of N or a non-multiple of N

47. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
The average of the set times the number of elements in the set
ONLY the nonnegative root of the numberUNLIKE
A non-multiple of N.
N is a divisor of x+y

48. v256=
The average of an EVEN number of consecutive integers will NEVER be an integer.
41 -43 -47
A non-multiple of N.
16

49. Prime Numbers:8x
83 -89
53 -59
Never prime
1. The smallest or largest element 2. The increment 3. The number of items in the set

50. All perfect squares have a(n) _________ number of total factors.
The PRODUCT of n consecutive integers is divisible by n!.
3·3n = 3^{n+1}
11 -13 -17 -19
ODD