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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. v5˜
A non-multiple of N.
2.5
1.7
53 -59

2. Prime Numbers:8x
The sum of any two primes will be even - unless one of the two primes is 2.
83 -89
If 2 cannot be one of the primes in the sum - the sum must be even.
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

3. If 2 cannot be one of the primes in the sum - the sum must be _____.
71 -73 -79
A PERFECT SQUARE
If 2 cannot be one of the primes in the sum - the sum must be even.
N is a divisor of x+y

4. Prime Numbers:5x
53 -59
25
3·3n = 3^{n+1}
Either a multiple of N or a non-multiple of N

5. Prime factors of _____ must come in pairs of three.
The average of an EVEN number of consecutive integers will NEVER be an integer.
PERFECT CUBES
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.
Prime

6. Positive integers with only two factors must be ___.
41 -43 -47
23 -29
Prime
1.4

7. 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
53 -59
11 -13 -17 -19
16

8. In an evenly spaced set - the sum of the terms is equal to ____.
N is a divisor of x+y
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 average of the set times the number of elements in the set
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

9. v625=
The PRODUCT of n consecutive integers is divisible by n!.
53 -59
83 -89
25

10. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The middle number

11. 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
14
ODD
A non-multiple of N.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

12. 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.
N is a divisor of x+y
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 average of the set times the number of elements in the set

13. v2˜
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
61 -67

14. Prime Numbers:4x
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
41 -43 -47
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

15. If the problem states/assumes that a number is an integer - check to see if you can use _______.
EVEN
71 -73 -79
25
Prime factorization

16. N! is _____ of all integers from 1 to N.
11 -13 -17 -19
EVEN
A MULTIPLE
The PRODUCT of n consecutive integers is divisible by n!.

17. 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

18. Any integer with an EVEN number of total factors cannot be ______.
83 -89
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
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE

19. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
1. The smallest or largest element 2. The increment 3. The number of items in the set
Prime factorization
The same sign as the base
A non-multiple of N.

20. Prime Numbers:3x
83 -89
31 -37
15
2.5

21. In an evenly spaced set - the mean and median are equal to the _____ of _________.
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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
71 -73 -79
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

22. The PRODUCT of n consecutive integers is divisible by ____.
41 -43 -47
16
Either a multiple of N or a non-multiple of N
The PRODUCT of n consecutive integers is divisible by n!.

23. How to find the sum of consecutive integers:
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 EVEN number of consecutive integers will NEVER be an integer.
25
N is a divisor of x+y

24. ³v216 =
Never prime
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
71 -73 -79
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. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
2 -3 -5 -7
3·3n = 3^{n+1}
1.7

26. The average of an ODD number of consecutive integers will ________ be an integer.
ODD
14
Never prime
The average of an ODD number of consecutive integers will ALWAYS be an integer.

27. Prime Numbers:9x
11 -13 -17 -19
97
25
In an evenly spaced set - the average and the median are equal.

28. v225=
23 -29
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.
53 -59
15

29. For ODD ROOTS - the root has ______.
A non-multiple of N.
The same sign as the base
Put the coefficient under the radical to get a better approximation
25

30. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
Prime
FACTOR
A PERFECT SQUARE
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.

31. v256=
71 -73 -79
16
In an evenly spaced set - the average and the median are equal.
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.

32. Positive integers with more than two factors are ____.
ODD
Never prime
The middle number
15

33. All perfect squares have a(n) _________ number of total factors.
ODD
14
11 -13 -17 -19
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

34. The sum of any two primes will be ____ - unless ______.
A PERFECT SQUARE
11 -13 -17 -19
Either a multiple of N or a non-multiple of N
The sum of any two primes will be even - unless one of the two primes is 2.

35. The formula for finding the number of consecutive multiples in a set is _______.
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.
[(last - first) / increment] + 1
3·3n = 3^{n+1}
The middle number

36. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
In an evenly spaced set - the average and the median are equal.
1. The smallest or largest element 2. The increment 3. The number of items in the set
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

37. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
97
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
3·3n = 3^{n+1}
N is a divisor of x+y

38. Prime Numbers:1x
Prime factorization
83 -89
53 -59
11 -13 -17 -19

39. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
2 -3 -5 -7
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The average of an ODD number of consecutive integers will ALWAYS be an integer.

40. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
61 -67
A PERFECT SQUARE
53 -59

41. If estimating a root with a coefficient - _____ .
23 -29
A PERFECT SQUARE
53 -59
Put the coefficient under the radical to get a better approximation

42. The prime factorization of a perfect square contains only ______ powers of primes.
A PERFECT SQUARE
EVEN
The middle number
A non-multiple of N.

43. In an evenly spaced set - the ____ and the ____ are equal.
1.7
23 -29
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.
In an evenly spaced set - the average and the median are equal.

44. v3˜
1.7
The PRODUCT of n consecutive integers is divisible by n!.
11 -13 -17 -19
The sum of any two primes will be even - unless one of the two primes is 2.

45. Prime Numbers:0x
2 -3 -5 -7
3·3n = 3^{n+1}
2.5
The sum of any two primes will be even - unless one of the two primes is 2.

46. v169=
13
23 -29
The sum of any two primes will be even - unless one of the two primes is 2.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

47. 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
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
EVEN
Either a multiple of N or a non-multiple of N
31 -37

48. Prime Numbers:2x
NEVER CONTRADICT ONE ANOTHER
61 -67
2.5
23 -29

49. Prime Numbers:6x
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.
61 -67
A PERFECT SQUARE
A PERFECT SQUARE

50. In an evenly spaced set - the average can be found by finding ________.
11 -13 -17 -19
97
The middle number
N is a divisor of x+y