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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 find the sum of consecutive integers:
A PERFECT SQUARE
31 -37
11 -13 -17 -19
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.

2. The sum of any two primes will be ____ - unless ______.
The PRODUCT of n consecutive integers is divisible by n!.
Put the coefficient under the radical to get a better approximation
The sum of any two primes will be even - unless one of the two primes is 2.
A PERFECT SQUARE

3. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
Either a multiple of N or a non-multiple of N
The average of an ODD number of consecutive integers will ALWAYS be an integer.
1.4
A non-multiple of N.

4. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
16
ONLY the nonnegative root of the numberUNLIKE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The middle number

5. 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.
2 -3 -5 -7
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The average of an EVEN number of consecutive integers will NEVER be an integer.

6. 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.
If 2 cannot be one of the primes in the sum - the sum must be even.
Put the coefficient under the radical to get a better approximation
ODD

7. Prime Numbers:1x
FACTOR
A PERFECT SQUARE
11 -13 -17 -19
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.

8. In an evenly spaced set - the ____ and the ____ are equal.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
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.
1.4

9. For ODD ROOTS - the root has ______.
Prime factorization
11 -13 -17 -19
The same sign as the base
ODD

10. Positive integers with only two factors must be ___.
14
N is a divisor of x+y
Prime
2 -3 -5 -7

11. 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
The average of the set times the number of elements in the set
16
Put the coefficient under the radical to get a better approximation

12. ³v216 =
25
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 average and the median are equal.
3·3n = 3^{n+1}

13. Prime Numbers:0x
The average of an EVEN number of consecutive integers will NEVER be an integer.
2 -3 -5 -7
NEVER CONTRADICT ONE ANOTHER
83 -89

14. All perfect squares have a(n) _________ number of total factors.
2.5
Prime factorization
2 -3 -5 -7
ODD

15. 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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16. In an evenly spaced set - the mean and median are equal to the _____ of _________.
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.
13
1.4

17. Any integer with an EVEN number of total factors cannot be ______.
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 PERFECT SQUARE
1.4
[(last - first) / increment] + 1

18. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
The sum of any two primes will be even - unless one of the two primes is 2.
13
23 -29

19. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
Never prime
The middle number
FACTOR
Put the coefficient under the radical to get a better approximation

20. Prime factors of _____ must come in pairs of three.
In an evenly spaced set - the average and the median are equal.
PERFECT CUBES
[(last - first) / increment] + 1
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.

21. Positive integers with more than two factors are ____.
Never prime
A MULTIPLE
16
A PERFECT SQUARE

22. If the problem states/assumes that a number is an integer - check to see if you can use _______.
The PRODUCT of n consecutive integers is divisible by n!.
Prime factorization
NEVER CONTRADICT ONE ANOTHER
Never prime

23. In an evenly spaced set - the average can be found by finding ________.
The middle number
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The average of an EVEN number of consecutive integers will NEVER be an integer.
The same sign as the base

24. Prime Numbers:9x
97
31 -37
25
71 -73 -79

25. 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?
13
EVEN
The middle number
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.

26. v625=
The average of the set times the number of elements in the set
Prime factorization
25
A MULTIPLE

27. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
The average of an ODD number of consecutive integers will ALWAYS 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.
The same sign as the base

28. Prime Numbers:8x
23 -29
14
3·3n = 3^{n+1}
83 -89

29. The PRODUCT of n consecutive integers is divisible by ____.
25
The PRODUCT of n consecutive integers is divisible by n!.
In an evenly spaced set - the average and the median are equal.
Put the coefficient under the radical to get a better approximation

30. v196=
NEVER CONTRADICT ONE ANOTHER
14
ODD
[(last - first) / increment] + 1

31. 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
A PERFECT SQUARE
Either a multiple of N or a non-multiple of N
PERFECT CUBES

32. The formula for finding the number of consecutive multiples in a set is _______.
The middle number
13
A PERFECT SQUARE
[(last - first) / increment] + 1

33. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
A PERFECT SQUARE
53 -59
1. The smallest or largest element 2. The increment 3. The number of items in the set
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

34. The two statements in a data sufficiency problem will _______________.
3·3n = 3^{n+1}
Either a multiple of N or a non-multiple of N
The same sign as the base
NEVER CONTRADICT ONE ANOTHER

35. Prime Numbers:6x
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A PERFECT SQUARE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
61 -67

36. v5˜
2.5
Never prime
25
A MULTIPLE

37. v2˜
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
3·3n = 3^{n+1}
ONLY the nonnegative root of the numberUNLIKE
1.4

38. If N is a divisor of x and y - then _______.
31 -37
25
41 -43 -47
N is a divisor of x+y

39. If estimating a root with a coefficient - _____ .
61 -67
15
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
Put the coefficient under the radical to get a better approximation

40. Prime Numbers:7x
1. The smallest or largest element 2. The increment 3. The number of items in the set
A MULTIPLE
71 -73 -79
A PERFECT SQUARE

41. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
23 -29
If 2 cannot be one of the primes in the sum - the sum must be even.
14
ONLY the nonnegative root of the numberUNLIKE

42. The average of an ODD number of consecutive integers will ________ be an integer.
The sum of any two primes will be even - unless one of the two primes is 2.
A MULTIPLE
PERFECT CUBES
The average of an ODD number of consecutive integers will ALWAYS be an integer.

43. Prime Numbers:4x
ODD
A PERFECT SQUARE
41 -43 -47
31 -37

44. v3˜
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
1.7
3·3n = 3^{n+1}
Never prime

45. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
2.5
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!.

46. N! is _____ of all integers from 1 to N.
A MULTIPLE
ONLY the nonnegative root of the numberUNLIKE
A non-multiple of N.
13

47. Prime Numbers:5x
In an evenly spaced set - the average and the median are equal.
1.7
Put the coefficient under the radical to get a better approximation
53 -59

48. 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
16
The sum of any two primes will be even - unless one of the two primes is 2.
1. The smallest or largest element 2. The increment 3. The number of items in the set
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

49. v256=
If 2 cannot be one of the primes in the sum - the sum must be even.
EVEN
16
PERFECT CUBES

50. v169=
EVEN
The sum of any two primes will be even - unless one of the two primes is 2.
13
The average of an EVEN number of consecutive integers will NEVER be an integer.