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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. The formula for finding the number of consecutive multiples in a set is _______.
2 -3 -5 -7
[(last - first) / increment] + 1
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.

2. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
23 -29
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
FACTOR

3. In an evenly spaced set - the sum of the terms is equal to ____.
Either a multiple of N or a non-multiple of N
A PERFECT SQUARE
The average of the set times the number of elements in the set
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.

4. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
11 -13 -17 -19
In an evenly spaced set - the average and the median are equal.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
53 -59

5. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
The average of an EVEN number of consecutive integers will NEVER be an integer.
ONLY the nonnegative root of the numberUNLIKE
14
25

6. v625=
25
FACTOR
[(last - first) / increment] + 1
NEVER CONTRADICT ONE ANOTHER

7. 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?
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.
83 -89
FACTOR

8. 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
Prime factorization
83 -89
FACTOR

9. 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
Prime factorization
PERFECT CUBES
A PERFECT SQUARE

10. In an evenly spaced set - the ____ and the ____ are equal.
2 -3 -5 -7
In an evenly spaced set - the average and the median are equal.
The same sign as the base
A PERFECT SQUARE

11. v3˜
Never prime
A PERFECT SQUARE
1.7
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

12. N! is _____ of all integers from 1 to N.
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
13
The same sign as the base
A MULTIPLE

13. Prime Numbers:6x
61 -67
A MULTIPLE
The middle number
25

14. v256=
16
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.
61 -67

15. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
The same sign as the base
1. The smallest or largest element 2. The increment 3. The number of items in the set
ONLY the nonnegative root of the numberUNLIKE

16. In an evenly spaced set - the average can be found by finding ________.
11 -13 -17 -19
The middle number
97
The PRODUCT of n consecutive integers is divisible by n!.

17. Positive integers with more than two factors are ____.
Never prime
Prime
25
NEVER CONTRADICT ONE ANOTHER

18. Any integer with an EVEN number of total factors cannot be ______.
The same sign as the base
2.5
1.4
A PERFECT SQUARE

19. If estimating a root with a coefficient - _____ .
3·3n = 3^{n+1}
83 -89
Prime factorization
Put the coefficient under the radical to get a better approximation

20. If N is a divisor of x and y - then _______.
1.4
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.
N is a divisor of x+y

21. Prime Numbers:8x
41 -43 -47
83 -89
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Put the coefficient under the radical to get a better approximation

22. ³v216 =
A MULTIPLE
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The PRODUCT of n consecutive integers is divisible by n!.
PERFECT CUBES

23. Prime Numbers:4x
The sum of any two primes will be even - unless one of the two primes is 2.
Either a multiple of N or a non-multiple of N
2.5
41 -43 -47

24. Prime Numbers:7x
97
71 -73 -79
2.5
1.7

25. Any integer with an ODD number of total factors must be _______.
13
A PERFECT SQUARE
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.

26. Prime Numbers:9x
A PERFECT SQUARE
97
The average of the set times the number of elements in the set
If 2 cannot be one of the primes in the sum - the sum must be even.

27. For ODD ROOTS - the root has ______.
Prime
A PERFECT SQUARE
83 -89
The same sign as the base

28. Prime Numbers:2x
83 -89
Never prime
23 -29
Prime

29. The prime factorization of __________ contains only EVEN powers of primes.
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.
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.

30. If the problem states/assumes that a number is an integer - check to see if you can use _______.
A PERFECT SQUARE
Prime factorization
3·3n = 3^{n+1}
The average of an EVEN number of consecutive integers will NEVER be an integer.

31. v2˜
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
11 -13 -17 -19
1.4
15

32. v196=
Prime
16
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

33. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
If 2 cannot be one of the primes in the sum - the sum must be even.
A non-multiple of N.
In an evenly spaced set - the average and the median are equal.
11 -13 -17 -19

34. 3n + 3n + 3n = _____ = ______
31 -37
1.7
3·3n = 3^{n+1}
[(last - first) / increment] + 1

35. The sum of any two primes will be ____ - unless ______.
If 2 cannot be one of the primes in the sum - the sum must be even.
11 -13 -17 -19
2 -3 -5 -7
The sum of any two primes will be even - unless one of the two primes is 2.

36. 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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37. Positive integers with only two factors must be ___.
83 -89
Prime
A MULTIPLE
97

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

39. 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 factorization
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
15

40. Prime Numbers:5x
A MULTIPLE
25
53 -59
In an evenly spaced set - the average and the median are equal.

41. v5˜
N is a divisor of x+y
25
16
2.5

42. All perfect squares have a(n) _________ number of total factors.
ODD
EVEN
83 -89
A PERFECT SQUARE

43. If 2 cannot be one of the primes in the sum - the sum must be _____.
The average of the set times the number of elements in the set
23 -29
If 2 cannot be one of the primes in the sum - the sum must be even.
14

44. v169=
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Prime factorization
13
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

45. How to find the sum of consecutive integers:
83 -89
The middle number
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.
A non-multiple of N.

46. The two statements in a data sufficiency problem will _______________.
53 -59
If 2 cannot be one of the primes in the sum - the sum must be even.
NEVER CONTRADICT ONE ANOTHER
The middle number

47. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
61 -67
Prime
23 -29

48. Prime Numbers:0x
16
2 -3 -5 -7
The sum of any two primes will be even - unless one of the two primes is 2.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

49. In an evenly spaced set - the mean and median are equal to the _____ of _________.
2 -3 -5 -7
15
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The sum of any two primes will be even - unless one of the two primes is 2.

50. Prime Numbers:3x
The sum of any two primes will be even - unless one of the two primes is 2.
83 -89
31 -37
Either a multiple of N or a non-multiple of N