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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 solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
53 -59
1. The smallest or largest element 2. The increment 3. The number of items in the set
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
ODD

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

3. v625=
83 -89
25
Prime
In an evenly spaced set - the average and the median are equal.

4. Prime Numbers:5x
Never prime
53 -59
23 -29
1. The smallest or largest element 2. The increment 3. The number of items in the set

5. For ODD ROOTS - the root has ______.
EVEN
The same sign as the base
14
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.

6. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A non-multiple of N.
PERFECT CUBES

7. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
2 -3 -5 -7
A non-multiple of N.
1.7
The same sign as the base

8. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
83 -89
In an evenly spaced set - the average and the median are equal.
Prime factorization

9. The formula for finding the number of consecutive multiples in a set is _______.
11 -13 -17 -19
2.5
[(last - first) / increment] + 1
ODD

10. 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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11. All perfect squares have a(n) _________ number of total factors.
53 -59
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Either a multiple of N or a non-multiple of N
ODD

12. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE
A non-multiple of N.
Prime factorization

13. Prime Numbers:7x
A PERFECT SQUARE
A non-multiple of N.
71 -73 -79
Put the coefficient under the radical to get a better approximation

14. v256=
97
The sum of any two primes will be even - unless one of the two primes is 2.
A non-multiple of N.
16

15. Positive integers with more than two factors are ____.
1.7
The PRODUCT of n consecutive integers is divisible by n!.
Either a multiple of N or a non-multiple of N
Never prime

16. 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
61 -67
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE
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

17. The prime factorization of a perfect square contains only ______ powers of primes.
[(last - first) / increment] + 1
1.7
EVEN
2.5

18. 3n + 3n + 3n = _____ = ______
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
11 -13 -17 -19
3·3n = 3^{n+1}
Never prime

19. How to find the sum of consecutive integers:
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. 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 SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
15

20. If estimating a root with a coefficient - _____ .
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
The average of the set times the number of elements in the set
13

21. In an evenly spaced set - the sum of the terms is equal to ____.
1.7
[(last - first) / increment] + 1
A non-multiple of N.
The average of the set times the number of elements in the set

22. The average of an ODD number of consecutive integers will ________ be an integer.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
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.
The average of an ODD number of consecutive integers will ALWAYS be an integer.

23. Prime factors of _____ must come in pairs of three.
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.
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.
PERFECT CUBES

24. Prime Numbers:0x
In an evenly spaced set - the average and the median are equal.
2 -3 -5 -7
83 -89
11 -13 -17 -19

25. v3˜
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
ODD
1.7

26. Prime Numbers:4x
41 -43 -47
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.
PERFECT CUBES

27. Prime Numbers:2x
23 -29
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
[(last - first) / increment] + 1
NEVER CONTRADICT ONE ANOTHER

28. In an evenly spaced set - the average can be found by finding ________.
13
In an evenly spaced set - the average and the median are equal.
If 2 cannot be one of the primes in the sum - the sum must be even.
The middle number

29. Prime Numbers:1x
11 -13 -17 -19
A MULTIPLE
PERFECT CUBES
3·3n = 3^{n+1}

30. In an evenly spaced set - the mean and median are equal to the _____ of _________.
2 -3 -5 -7
2.5
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

31. v2˜
A PERFECT SQUARE
1.4
31 -37
ODD

32. 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
FACTOR
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
13
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

33. Let N be an integer. If you add two non-multiples of N - the result could be _______.
31 -37
A non-multiple of N.
Either a multiple of N or a non-multiple of N
The middle number

34. Positive integers with only two factors must be ___.
The average of the set times the number of elements in the set
25
15
Prime

35. v5˜
83 -89
A MULTIPLE
2.5
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.

36. Prime Numbers:6x
53 -59
14
Either a multiple of N or a non-multiple of N
61 -67

37. ³v216 =
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Either a multiple of N or a non-multiple of N
Never prime
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

38. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
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.
1.7
23 -29

39. Any integer with an ODD number of total factors must be _______.
2.5
A PERFECT SQUARE
The PRODUCT of n consecutive integers is divisible by n!.
The average of the set times the number of elements in the set

40. The PRODUCT of n consecutive integers is divisible by ____.
A PERFECT SQUARE
The PRODUCT of n consecutive integers is divisible by n!.
71 -73 -79
83 -89

41. v169=
13
NEVER CONTRADICT ONE ANOTHER
1.7
15

42. If the problem states/assumes that a number is an integer - check to see if you can use _______.
[(last - first) / increment] + 1
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
83 -89
Prime factorization

43. If 2 cannot be one of the primes in the sum - the sum must be _____.
If 2 cannot be one of the primes in the sum - the sum must be even.
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.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

44. Prime Numbers:3x
31 -37
ONLY the nonnegative root of the numberUNLIKE
The average of an ODD number of consecutive integers will ALWAYS be an integer.
53 -59

45. The prime factorization of __________ contains only EVEN powers of primes.
83 -89
71 -73 -79
2 -3 -5 -7
A PERFECT SQUARE

46. Prime Numbers:9x
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
97
11 -13 -17 -19
N is a divisor of x+y

47. v196=
2 -3 -5 -7
14
FACTOR
97

48. Prime Numbers:8x
ODD
The average of an ODD number of consecutive integers will ALWAYS be an integer.
83 -89
The middle number

49. N! is _____ of all integers from 1 to N.
A MULTIPLE
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
A non-multiple of N.

50. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
2.5
1. The smallest or largest element 2. The increment 3. The number of items in the set
97
A PERFECT SQUARE