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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
The middle number
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
14
A MULTIPLE

2. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
A PERFECT SQUARE
1.7
Prime

3. Prime Numbers:4x
ODD
14
N is a divisor of x+y
41 -43 -47

4. Positive integers with only two factors must be ___.
25
In an evenly spaced set - the average and the median are equal.
Prime
83 -89

5. If N is a divisor of x and y - then _______.
2 -3 -5 -7
N is a divisor of x+y
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE

6. 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.
Either a multiple of N or a non-multiple of N
2 -3 -5 -7
N is a divisor of x+y

7. All perfect squares have a(n) _________ number of total factors.
A PERFECT SQUARE
71 -73 -79
ODD
A PERFECT SQUARE

8. Prime Numbers:8x
The same sign as the base
83 -89
A PERFECT SQUARE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

9. If estimating a root with a coefficient - _____ .
Never prime
15
EVEN
Put the coefficient under the radical to get a better approximation

10. The prime factorization of __________ contains only EVEN powers of primes.
13
23 -29
A PERFECT SQUARE
The PRODUCT of n consecutive integers is divisible by n!.

11. How to find the sum of consecutive integers:
23 -29
N is a divisor of x+y
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

12. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Put the coefficient under the radical to get a better approximation
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Prime factorization
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.

13. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
3·3n = 3^{n+1}
The same sign as the base
ONLY the nonnegative root of the numberUNLIKE

14. v2˜
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
1.4
FACTOR
1.7

15. Let N be an integer. If you add two non-multiples of N - the result could be _______.
The PRODUCT of n consecutive integers is divisible by 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.
25
Either a multiple of N or a non-multiple of N

16. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
A non-multiple of N.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
ONLY the nonnegative root of the numberUNLIKE
11 -13 -17 -19

17. ³v216 =
25
Never prime
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
EVEN

18. In an evenly spaced set - the mean and median are equal to the _____ of _________.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is 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.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
1.4

19. N! is _____ of all integers from 1 to N.
13
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
A MULTIPLE
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.

20. v225=
15
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.
13
A PERFECT SQUARE

21. Prime Numbers:9x
1.4
97
[(last - first) / increment] + 1
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

22. v3˜
A PERFECT SQUARE
1.7
1.4
2.5

23. 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?
23 -29
If 2 cannot be one of the primes in the sum - the sum must be 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.
[(last - first) / increment] + 1

24. v256=
23 -29
16
The average of the set times the number of elements in the set
[(last - first) / increment] + 1

25. Prime Numbers:1x
71 -73 -79
The PRODUCT of n consecutive integers is divisible by n!.
11 -13 -17 -19
Prime

26. Prime factors of _____ must come in pairs of three.
Put the coefficient under the radical to get a better approximation
Prime
PERFECT CUBES
14

27. Prime Numbers:2x
If 2 cannot be one of the primes in the sum - the sum must be even.
ODD
23 -29
ONLY the nonnegative root of the numberUNLIKE

28. Any integer with an EVEN number of total factors cannot be ______.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
A PERFECT SQUARE
EVEN
1.7

29. For ODD ROOTS - the root has ______.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The same sign as the base
If 2 cannot be one of the primes in the sum - the sum must be even.
11 -13 -17 -19

30. v196=
31 -37
71 -73 -79
14
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

31. Prime Numbers:7x
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
71 -73 -79
EVEN

32. Prime Numbers:0x
14
16
Never prime
2 -3 -5 -7

33. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
13
NEVER CONTRADICT ONE ANOTHER
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.
FACTOR

34. 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

35. 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
97
Never prime
41 -43 -47

36. In an evenly spaced set - the average can be found by finding ________.
A non-multiple of N.
The middle number
N is a divisor of x+y
A MULTIPLE

37. v169=
14
FACTOR
13
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.

38. The formula for finding the number of consecutive multiples in a set is _______.
A PERFECT SQUARE
The average of the set times the number of elements in the set
[(last - first) / increment] + 1
71 -73 -79

39. If 2 cannot be one of the primes in the sum - the sum must 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 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.
53 -59

40. In an evenly spaced set - the sum of the terms is equal to ____.
The average of the set times the number of elements in the set
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
14

41. The two statements in a data sufficiency problem will _______________.
NEVER CONTRADICT ONE ANOTHER
Put the coefficient under the radical to get a better approximation
The average of the set times the number of elements in the set
The average of an ODD number of consecutive integers will ALWAYS be an integer.

42. Any integer with an ODD number of total factors must be _______.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A PERFECT SQUARE
N is a divisor of x+y
11 -13 -17 -19

43. Prime Numbers:6x
23 -29
ONLY the nonnegative root of the numberUNLIKE
61 -67
71 -73 -79

44. Prime Numbers:5x
3·3n = 3^{n+1}
The PRODUCT of n consecutive integers is divisible by n!.
25
53 -59

45. v625=
25
FACTOR
Either a multiple of N or a non-multiple of N
Prime

46. The average of an EVEN number of consecutive integers will ________ be an integer.
[(last - first) / increment] + 1
83 -89
The average of an EVEN number of consecutive integers will NEVER be an integer.
The sum of any two primes will be even - unless one of the two primes is 2.

47. Positive integers with more than two factors are ____.
71 -73 -79
Never prime
1.7
13

48. Prime Numbers:3x
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.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Either a multiple of N or a non-multiple of N
31 -37

49. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
A MULTIPLE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The average of the set times the number of elements in the set
1. The smallest or largest element 2. The increment 3. The number of items in the set

50. The sum of any two primes will be ____ - unless ______.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
ODD
The sum of any two primes will be even - unless one of the two primes is 2.
53 -59