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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. Positive integers with more than two factors are ____.
61 -67
3·3n = 3^{n+1}
1. The smallest or largest element 2. The increment 3. The number of items in the set
Never prime

2. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
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.

3. The sum of any two primes will be ____ - unless ______.
1.7
16
The average of the set times the number of elements in the set
The sum of any two primes will be even - unless one of the two primes is 2.

4. Prime Numbers:3x
31 -37
53 -59
PERFECT CUBES
Prime factorization

5. v5˜
A PERFECT SQUARE
Never prime
3·3n = 3^{n+1}
2.5

6. If the problem states/assumes that a number is an integer - check to see if you can use _______.
61 -67
Prime factorization
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 EVEN number of consecutive integers will NEVER be an integer.

7. 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.
A PERFECT SQUARE
14
FACTOR

8. In an evenly spaced set - the mean and median are equal to the _____ of _________.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The middle number
The sum of any two primes will be even - unless one of the two primes is 2.

9. The PRODUCT of n consecutive integers is divisible by ____.
23 -29
The PRODUCT of n consecutive integers is divisible by n!.
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.

10. v196=
In an evenly spaced set - the average and the median are equal.
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
14

11. Prime Numbers:1x
The middle number
11 -13 -17 -19
N is a divisor of x+y
1.4

12. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
The PRODUCT of n consecutive integers is divisible by n!.
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.
41 -43 -47

13. Prime Numbers:5x
53 -59
A MULTIPLE
3·3n = 3^{n+1}
ODD

14. If N is a divisor of x and y - then _______.
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set
N is a divisor of x+y
Never prime

15. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
13
A non-multiple of N.
A PERFECT SQUARE
A MULTIPLE

16. 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.
N is a divisor of x+y
In an evenly spaced set - the average and the median are equal.
A PERFECT SQUARE

17. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
The same sign as the base
ONLY the nonnegative root of the numberUNLIKE
Either a multiple of N or a non-multiple of N
FACTOR

18. Prime Numbers:4x
14
41 -43 -47
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.
The average of an EVEN number of consecutive integers will NEVER be an integer.

19. The prime factorization of a perfect square contains only ______ powers of primes.
Put the coefficient under the radical to get a better approximation
EVEN
[(last - first) / increment] + 1
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

20. 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
Either a multiple of N or 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.
A non-multiple of N.

21. 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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
2 -3 -5 -7
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The middle number

22. v3˜
ODD
1.7
The average of an EVEN number of consecutive integers will NEVER be an integer.
53 -59

23. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
In an evenly spaced set - the mean and median are equal to the average of the first and the last 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.
A non-multiple of N.

24. Any integer with an ODD number of total factors must be _______.
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.
N is a divisor of x+y
A PERFECT SQUARE
2.5

25. The two statements in a data sufficiency problem will _______________.
NEVER CONTRADICT ONE ANOTHER
If 2 cannot be one of the primes in the sum - the sum must be even.
41 -43 -47
97

26. In an evenly spaced set - the ____ and the ____ are equal.
A non-multiple of N.
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
ONLY the nonnegative root of the numberUNLIKE

27. Prime Numbers:9x
41 -43 -47
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A PERFECT SQUARE
97

28. v256=
16
A PERFECT SQUARE
1.7
N is a divisor of x+y

29. Prime Numbers:0x
Never prime
N is a divisor of x+y
2 -3 -5 -7
83 -89

30. For ODD ROOTS - the root has ______.
The same sign as the base
31 -37
A non-multiple of N.
If 2 cannot be one of the primes in the sum - the sum must be even.

31. v169=
FACTOR
83 -89
13
71 -73 -79

32. In an evenly spaced set - the average can be found by finding ________.
16
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.
The middle number

33. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
Prime
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
ONLY the nonnegative root of the numberUNLIKE
1.7

34. Positive integers with only two factors must be ___.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Prime
97
53 -59

35. Prime Numbers:6x
Prime factorization
The average of the set times the number of elements in the set
61 -67
71 -73 -79

36. v625=
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.
1. The smallest or largest element 2. The increment 3. The number of items in the set
31 -37
25

37. All perfect squares have a(n) _________ number of total factors.
11 -13 -17 -19
1.7
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
ODD

38. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
83 -89
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
N is a divisor of x+y

39. In an evenly spaced set - the sum of the terms is equal to ____.
A PERFECT SQUARE
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.
A non-multiple of N.

40. v225=
16
15
Prime factorization
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

41. ³v216 =
FACTOR
16
23 -29
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

42. If 2 cannot be one of the primes in the sum - the sum must be _____.
71 -73 -79
13
The average of an EVEN number of consecutive integers will NEVER be an integer.
If 2 cannot be one of the primes in the sum - the sum must be even.

43. 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
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.
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

44. 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?
1.7
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
53 -59
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.

45. N! is _____ of all integers from 1 to N.
A MULTIPLE
16
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Prime factorization

46. 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
NEVER CONTRADICT ONE ANOTHER
The average of the set times the number of elements in the set

47. The average of an EVEN number of consecutive integers will ________ be an integer.
1. The smallest or largest element 2. The increment 3. The number of items in the set
The sum of any two primes will be even - unless one of the two primes is 2.
[(last - first) / increment] + 1
The average of an EVEN number of consecutive integers will NEVER be an integer.

48. Prime Numbers:8x
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A PERFECT SQUARE
83 -89
25

49. 3n + 3n + 3n = _____ = ______
ODD
3·3n = 3^{n+1}
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
31 -37

50. The average of an ODD number of consecutive integers will ________ be an integer.
97
The average of an ODD number of consecutive integers will ALWAYS be an integer.
16
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